Antonakakis et al. (2020).rar_溢出指数_tvp溢出_统计分析

<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/626432b34c65f41259c17c26/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/626432b34c65f41259c17c26/bg1.jpg"><div class="c x1 y1 w2 h2"><div class="t m0 x2 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">Journal of</div><div class="t m0 x2 h4 y3 ff2 fs1 fc1 sc0 ls0 ws0">Risk and Financial</div><div class="t m0 x2 h4 y4 ff2 fs1 fc1 sc0 ls0 ws0">Management</div></div><div class="t m0 x1 h5 y5 ff3 fs2 fc2 sc0 ls0 ws0">Article</div><div class="t m0 x1 h6 y6 ff4 fs3 fc2 sc0 ls0 ws0">Reﬁned<span class="_"> </span>Measures<span class="_"> </span>of<span class="_"> </span>Dynamic<span class="_"> </span>Connectedness<span class="_"> </span>Based</div><div class="t m0 x1 h6 y7 ff4 fs3 fc2 sc0 ls0 ws0">on<span class="_"> </span>T<span class="_ _0"></span>ime-V<span class="_ _1"></span>arying<span class="_"> </span>Parameter<span class="_"> </span>V<span class="_ _1"></span>ector<span class="_"> </span>Autoregressions</div><div class="t m0 x1 h7 y8 ff4 fs2 fc2 sc0 ls0 ws0">Nikolaos<span class="_"> </span>Antonakakis</div><div class="t m0 x3 h8 y9 ff4 fs4 fc2 sc0 ls0 ws0">1,2</div><div class="t m0 x4 h7 y8 ff4 fs2 fc2 sc0 ls0 ws0">,<span class="_"> </span>Ioannis<span class="_"> </span>Chatziantoniou</div><div class="t m0 x5 h8 y9 ff4 fs4 fc2 sc0 ls0 ws0">2</div><div class="t m0 x6 h7 y8 ff4 fs2 fc2 sc0 ls0 ws0">and<span class="_"> </span>David<span class="_"> </span>Gabauer</div><div class="t m0 x7 h8 y9 ff4 fs4 fc2 sc0 ls0 ws0">1,3</div><div class="t m0 x8 h9 ya ff5 fs5 fc2 sc0 ls0 ws0">1</div><div class="t m0 x9 ha yb ff5 fs6 fc2 sc0 ls0 ws0">Department<span class="_"> </span>of<span class="_"> </span>Business<span class="_"> </span>and<span class="_"> </span>Management,<span class="_"> </span>W<span class="_ _0"></span>ebster<span class="_"> </span>V<span class="_ _2"></span>ienna<span class="_"> </span>Private<span class="_"> </span>University<span class="_ _0"></span>,<span class="_"> </span>Praterstraße<span class="_"> </span>23,</div><div class="t m0 x9 ha yc ff5 fs6 fc2 sc0 ls0 ws0">1020<span class="_"> </span>V<span class="_ _2"></span>ienna,<span class="_"> </span>Austria;<span class="_"> </span>Nikolaos.Antonakakis@webster<span class="_ _0"></span>.ac.at</div><div class="t m0 x8 h9 yd ff5 fs5 fc2 sc0 ls0 ws0">2</div><div class="t m0 x9 ha ye ff5 fs6 fc2 sc0 ls0 ws0">Economics<span class="_"> </span>and<span class="_"> </span>Finance<span class="_"> </span>Subject<span class="_"> </span>Group,<span class="_"> </span>University<span class="_"> </span>of<span class="_"> </span>Portsmouth,<span class="_"> </span>Portsmouth<span class="_"> </span>Business<span class="_"> </span>School,</div><div class="t m0 x9 ha yf ff5 fs6 fc2 sc0 ls0 ws0">Portland<span class="_"> </span>Street,<span class="_"> </span>Portsmouth<span class="_"> </span>PO1<span class="_"> </span>3DE,<span class="_"> </span>UK;<span class="_"> </span>ioannis.chatziantoniou@port.ac.uk</div><div class="t m0 x8 h9 y10 ff5 fs5 fc2 sc0 ls0 ws0">3</div><div class="t m0 x9 ha y11 ff5 fs6 fc2 sc0 ls0 ws0">Institute<span class="_"> </span>of<span class="_"> </span>Applied<span class="_"> </span>Statistics,<span class="_"> </span>Johannes<span class="_"> </span>Kepler<span class="_"> </span>University<span class="_ _0"></span>,<span class="_"> </span>Altenbergerstraße<span class="_"> </span>69,<span class="_"> </span>4040<span class="_"> </span>Linz,<span class="_"> </span>Austria</div><div class="t m0 xa ha y12 ff4 fs6 fc2 sc0 ls0 ws0">*<span class="_ _3"> </span><span class="ff5">Correspondence:<span class="_ _4"> </span>david.gabauer@hotmail.com</span></div><div class="t m0 x8 ha y13 ff5 fs6 fc2 sc0 ls0 ws0">Received:<span class="_ _4"> </span>5<span class="_"> </span>March<span class="_"> </span>2020;<span class="_"> </span>Accepted:<span class="_ _4"> </span>18<span class="_"> </span>April<span class="_"> </span>2020;<span class="_"> </span>Published:<span class="_ _5"> </span>24<span class="_"> </span>April<span class="_"> </span>2020</div><div class="c xb y14 w3 hb"><div class="t m0 xc hc y15 ff6 fs7 fc3 sc0 ls1 ws0"><span class="_ _2"></span><span class="_ _2"></span><span class="_ _2"></span><span class="_ _2"></span><span class="ff7 fs8 ls0"><span class="fc5 sc0"></span></span></div><div class="t m0 xc hd y16 ff8 fs7 fc3 sc0 ls2 ws0"><span class="_"> </span></div></div><div class="t m0 xa h7 y17 ff4 fs2 fc2 sc0 ls0 ws0">Abstract:</div><div class="t m1 xd he y17 ff5 fs2 fc2 sc0 ls0 ws0">In<span class="_ _6"> </span>this<span class="_ _6"> </span>study<span class="_ _0"></span>,<span class="_ _6"> </span>we<span class="_ _6"> </span>enhance<span class="_ _6"> </span>the<span class="_ _6"> </span>dynamic<span class="_ _6"> </span>connectedness<span class="_ _6"> </span>measures<span class="_ _6"> </span>originally<span class="_ _6"> </span>introduced</div><div class="t m1 x8 he y18 ff5 fs2 fc2 sc0 ls0 ws0">by<span class="_ _5"> </span>Diebold<span class="_ _6"> </span>and<span class="_ _5"> </span>Yılmaz<span class="_ _5"> </span>(2012,<span class="_ _6"> </span>2014)<span class="_ _6"> </span>with<span class="_ _5"> </span>a<span class="_ _5"> </span>time-varying<span class="_ _6"> </span>parameter<span class="_ _5"> </span>vector<span class="_ _5"> </span>autoregressive<span class="_ _5"> </span>model</div><div class="t m1 xa he y19 ff5 fs2 fc2 sc0 ls0 ws0">(TVP-V<span class="_ _0"></span>AR)<span class="_"> </span>which<span class="_"> </span>pr<span class="_ _2"></span>edicates<span class="_"> </span>upon<span class="_"> </span>a<span class="_"> </span>time-varying<span class="_"> </span>variance-covariance<span class="_"> </span>str<span class="_ _2"></span>ucture.<span class="_ _5"> </span>This<span class="_"> </span>framework</div><div class="t m1 x8 he y1a ff5 fs2 fc2 sc0 ls0 ws0">allows<span class="_ _5"> </span>to<span class="_ _5"> </span>capture<span class="_ _4"> </span>possible<span class="_ _5"> </span>changes<span class="_ _5"> </span>in<span class="_ _5"> </span>the<span class="_ _5"> </span>underlying<span class="_ _6"> </span>structur<span class="_ _2"></span>e<span class="_ _5"> </span>of<span class="_ _5"> </span>the<span class="_ _5"> </span>data<span class="_ _5"> </span>in<span class="_ _5"> </span>a<span class="_ _5"> </span>more<span class="_ _4"> </span>ﬂexible<span class="_ _5"> </span>and</div><div class="t m2 x8 he y1b ff5 fs2 fc2 sc0 ls0 ws0">robust<span class="_"> </span>manner<span class="_ _0"></span>.<span class="_ _5"> </span>Speciﬁcally<span class="_ _0"></span>,<span class="_"> </span>there<span class="_"> </span>is<span class="_"> </span>neither<span class="_"> </span>a<span class="_"> </span>need<span class="_"> </span>to<span class="_"> </span>arbitrarily<span class="_ _7"> </span>set<span class="_"> </span>the<span class="_"> </span>rolling-window<span class="_"> </span>size<span class="_ _7"> </span>nor<span class="_"> </span>a<span class="_"> </span>loss</div><div class="t m3 x8 he y1c ff5 fs2 fc2 sc0 ls0 ws0">of<span class="_"> </span>observations<span class="_"> </span>in<span class="_"> </span>the<span class="_"> </span>calculation<span class="_"> </span>of<span class="_"> </span>the<span class="_"> </span>dynamic<span class="_"> </span>measures<span class="_"> </span>of<span class="_"> </span>connectedness,<span class="_"> </span>as<span class="_"> </span>no<span class="_"> </span>r<span class="_ _2"></span>olling-window</div><div class="t m2 x8 he y1d ff5 fs2 fc2 sc0 ls0 ws0">analysis<span class="_"> </span>is<span class="_ _7"> </span>involved.<span class="_ _5"> </span>Given<span class="_"> </span>that<span class="_ _7"> </span>the<span class="_ _7"> </span>pr<span class="_ _2"></span>oposed<span class="_"> </span>framework<span class="_ _7"> </span>r<span class="_ _2"></span>ests<span class="_"> </span>on<span class="_ _7"> </span>multivariate<span class="_ _7"> </span>Kalman<span class="_"> </span>ﬁlters,<span class="_ _7"> </span>it<span class="_ _7"> </span>is<span class="_"> </span>less</div><div class="t m4 x8 he y1e ff5 fs2 fc2 sc0 ls0 ws0">sensitive<span class="_"> </span>to<span class="_"> </span>outliers.<span class="_ _5"> </span>Furthermore,<span class="_"> </span>we<span class="_"> </span>emphasise<span class="_ _7"> </span>the<span class="_"> </span>merits<span class="_"> </span>of<span class="_"> </span>this<span class="_"> </span>appr<span class="_ _2"></span>oach<span class="_"> </span>by<span class="_"> </span>conducting<span class="_"> </span>Monte</div><div class="t m1 x8 he y1f ff5 fs2 fc2 sc0 ls0 ws0">Carlo<span class="_ _5"> </span>simulations.<span class="_ _8"> </span>W<span class="_ _0"></span>e<span class="_ _5"> </span>put<span class="_ _5"> </span>our<span class="_ _5"> </span>framework<span class="_ _4"> </span>into<span class="_ _5"> </span>practice<span class="_ _5"> </span>by<span class="_ _5"> </span>investigating<span class="_ _5"> </span>dynamic<span class="_ _5"> </span>connectedness</div><div class="t m5 x8 he y20 ff5 fs2 fc2 sc0 ls0 ws0">measures<span class="_"> </span>of<span class="_"> </span>the<span class="_ _7"> </span>four<span class="_"> </span>most<span class="_"> </span>traded<span class="_"> </span>for<span class="_ _2"></span>eign<span class="_"> </span>exchange<span class="_"> </span>rates,<span class="_"> </span>comparing<span class="_"> </span>the<span class="_"> </span>TVP-V<span class="_ _0"></span>AR<span class="_ _7"> </span>results<span class="_"> </span>to<span class="_"> </span>those</div><div class="t m6 x8 he y21 ff5 fs2 fc2 sc0 ls0 ws0">obtained<span class="_"> </span>from<span class="_"> </span>thr<span class="_ _2"></span>ee<span class="_"> </span>differ<span class="_ _2"></span>ent<span class="_"> </span>rolling-window<span class="_"> </span>settings.<span class="_ _5"> </span>Finally<span class="_ _0"></span>,<span class="_"> </span>we<span class="_"> </span>propose<span class="_"> </span>uncertainty<span class="_"> </span>measur<span class="_ _2"></span>es<span class="_"> </span>for</div><div class="t m7 x8 he y22 ff5 fs2 fc2 sc0 ls0 ws0">both<span class="_"> </span>TVP-V<span class="_ _0"></span>AR-based<span class="_"> </span>and<span class="_"> </span>r<span class="_ _2"></span>olling-window<span class="_"> </span>V<span class="_ _0"></span>AR-based<span class="_"> </span>dynamic<span class="_"> </span>connectedness<span class="_"> </span>measur<span class="_ _2"></span>es.</div><div class="t m7 x8 he y23 ff4 fs2 fc2 sc0 ls0 ws0">Keywords:<span class="_ _5"> </span><span class="ff5">TVP-V<span class="_ _0"></span>AR;<span class="_"> </span>dynamic<span class="_"> </span>connectedness;<span class="_"> </span>Monte<span class="_"> </span>Carlo<span class="_"> </span>simulation</span></div><div class="t m7 xa he y24 ff4 fs2 fc2 sc0 ls0 ws0">JEL<span class="_"> </span>Classiﬁcation:<span class="_ _5"> </span><span class="ff5">C32;<span class="_"> </span>C50;<span class="_"> </span>F31;<span class="_"> </span>G15</span></div><div class="t m7 x1 h7 y25 ff4 fs2 fc2 sc0 ls0 ws0">1.<span class="_ _5"> </span>Introduction</div><div class="t m1 x9 he y26 ff5 fs2 fc2 sc0 ls0 ws0">Investigating<span class="_"> </span>the<span class="_ _4"> </span>propagation<span class="_"> </span>of<span class="_ _4"> </span>ﬁnancial<span class="_ _5"> </span>crises<span class="_"> </span>into<span class="_ _4"> </span>the<span class="_ _4"> </span>economy<span class="_ _4"> </span>has<span class="_ _4"> </span>been<span class="_ _5"> </span>at<span class="_"> </span>the<span class="_ _4"> </span>epicenter<span class="_ _4"> </span>of</div><div class="t m8 x1 he y27 ff5 fs2 fc2 sc0 ls0 ws0">academic<span class="_"> </span>resear<span class="_ _2"></span>ch<span class="_"> </span>in<span class="_"> </span>recent<span class="_"> </span>years,<span class="_"> </span>especially<span class="_"> </span>in<span class="_"> </span>the<span class="_"> </span>aftermath<span class="_"> </span>of<span class="_"> </span>the<span class="_"> </span>global<span class="_ _4"> </span>ﬁnancial<span class="_"> </span>crisis<span class="_"> </span>of<span class="_ _4"> </span>2007–2009.</div><div class="t m2 x1 he y28 ff5 fs2 fc2 sc0 ls0 ws0">On<span class="_"> </span>general<span class="_ _7"> </span>principles,<span class="_ _7"> </span>crises<span class="_ _7"> </span>ar<span class="_ _2"></span>e<span class="_"> </span>unpr<span class="_ _2"></span>edictable;<span class="_"> </span>however<span class="_ _0"></span>,<span class="_"> </span>transmission<span class="_ _7"> </span>mechanisms<span class="_ _7"> </span>r<span class="_ _2"></span>elating<span class="_"> </span>to<span class="_ _7"> </span>ﬁnancial</div><div class="t m9 x1 he y29 ff5 fs2 fc2 sc0 ls0 ws0">turmoil<span class="_"> </span>do<span class="_"> </span>share<span class="_"> </span>certain<span class="_"> </span>similarities<span class="_"> </span>(<span class="fc4">Reinhart<span class="_"> </span>and<span class="_"> </span>Rogof<span class="_ _2"></span>f<span class="_"> </span>2008<span class="fc2">).<span class="_ _5"> </span>In<span class="_"> </span>turn,<span class="_"> </span>researchers<span class="_"> </span>have<span class="_"> </span>developed</span></span></div><div class="t m7 x1 he y2a ff5 fs2 fc2 sc0 ls0 ws0">elaborate<span class="_"> </span>methods<span class="_"> </span>aiming<span class="_"> </span>to<span class="_"> </span>capture<span class="_"> </span>transmission<span class="_"> </span>mechanisms<span class="_"> </span>that<span class="_"> </span>r<span class="_ _2"></span>elate<span class="_"> </span>to<span class="_"> </span>such<span class="_"> </span>events.</div><div class="t ma x9 he y2b ff5 fs2 fc2 sc0 ls0 ws0">A<span class="_"> </span>notable<span class="_"> </span>empirical<span class="_"> </span>method<span class="_"> </span>is<span class="_"> </span>the<span class="_"> </span>one<span class="_"> </span>by<span class="_"> </span><span class="fc4">Diebold<span class="_ _4"> </span>and<span class="_"> </span>Yılmaz<span class="_"> </span></span>(<span class="fc4">2009</span>,<span class="_ _4"> </span><span class="fc4">2012</span>,<span class="_"> </span><span class="fc4">2014</span>)<span class="_"> </span>who<span class="_"> </span>introduced</div><div class="t mb x1 he y2c ff5 fs2 fc2 sc0 ls0 ws0">a<span class="_"> </span>variety<span class="_"> </span>of<span class="_"> </span>connectedness<span class="_"> </span>measures<span class="_"> </span>based<span class="_"> </span>on<span class="_"> </span>the<span class="_"> </span>notion<span class="_"> </span>of<span class="_"> </span>the<span class="_"> </span>forecast<span class="_"> </span>err<span class="_ _2"></span>or<span class="_"> </span>variance<span class="_"> </span>decomposition</div><div class="t m1 x1 he y2d ff5 fs2 fc2 sc0 ls0 ws0">that<span class="_ _6"> </span>was<span class="_ _6"> </span>derived<span class="_ _6"> </span>from<span class="_ _6"> </span>the<span class="_ _6"> </span>rolling-window<span class="_ _6"> </span>V<span class="_ _0"></span>ARs.<span class="_ _9"> </span>In<span class="_ _6"> </span>the<span class="_ _6"> </span>present<span class="_ _6"> </span>study<span class="_ _0"></span>,<span class="_ _a"> </span>we<span class="_ _6"> </span>provide<span class="_ _6"> </span>an<span class="_ _6"> </span>extension</div><div class="t m1 x1 he y2e ff5 fs2 fc2 sc0 ls0 ws0">to<span class="_ _5"> </span>the<span class="_ _6"> </span><span class="fc4">Diebold<span class="_ _5"> </span>and<span class="_ _6"> </span>Yılmaz<span class="_ _6"> </span></span>(<span class="fc4">2014</span>)<span class="_ _5"> </span>connectedness<span class="_ _6"> </span>approach<span class="_ _5"> </span>by<span class="_ _5"> </span>applying<span class="_ _6"> </span>a<span class="_ _5"> </span>time-varying<span class="_ _6"> </span>parameter</div><div class="t m3 x1 he y2f ff5 fs2 fc2 sc0 ls0 ws0">vector<span class="_"> </span>autoregr<span class="_ _2"></span>essive<span class="_"> </span>model<span class="_"> </span>(TVP-V<span class="_ _0"></span>AR)<span class="_"> </span>with<span class="_"> </span>a<span class="_"> </span>time-varying<span class="_"> </span>covariance<span class="_"> </span>structur<span class="_ _2"></span>e,<span class="_"> </span>as<span class="_"> </span>opposed<span class="_"> </span>to<span class="_"> </span>the</div><div class="t m7 x1 he y30 ff5 fs2 fc2 sc0 ls0 ws0">constant-parameter<span class="_"> </span>rolling-window<span class="_"> </span>V<span class="_ _b"></span>AR<span class="_"> </span>approach.</div><div class="t m7 xe hf y31 ff5 fs4 fc2 sc0 ls0 ws0">1</div><div class="t m7 x1 h10 y32 ff5 fs9 fc2 sc0 ls0 ws0">1</div><div class="t m1 xf h11 y33 ff5 fsa fc2 sc0 ls0 ws0">Although<span class="_ _7"> </span>there<span class="_ _4"> </span>is<span class="_ _7"> </span>in<span class="_ _4"> </span>fact<span class="_ _7"> </span>a<span class="_ _4"> </span>wealth<span class="_ _7"> </span>of<span class="_ _4"> </span>literature<span class="_ _7"> </span>regarding<span class="_"> </span>TVP-V<span class="_ _c"></span>AR<span class="_ _7"> </span>models<span class="_ _4"> </span>(see,<span class="_ _4"> </span>inter<span class="_ _7"> </span>alia,<span class="_ _4"> </span><span class="fc4">Primiceri<span class="_ _4"> </span>2005</span>;<span class="_ _4"> </span><span class="fc4">Cogley<span class="_ _7"> </span>and</span></div><div class="t mc xf h11 y34 ff5 fsa fc4 sc0 ls0 ws0">Sargent<span class="_"> </span>2005<span class="fc2">;<span class="_"> </span></span>Koop<span class="_"> </span>and<span class="_"> </span>Korobilis<span class="_"> </span>2013<span class="fc2">,<span class="_"> </span></span>2014<span class="fc2">;<span class="_"> </span></span>Del<span class="_"> </span>Negro<span class="_"> </span>and<span class="_"> </span>Primiceri<span class="_"> </span>2015<span class="fc2">;<span class="_"> </span></span>Petrova<span class="_"> </span>2019<span class="fc2">)<span class="_"> </span>we<span class="_"> </span>do<span class="_"> </span>not<span class="_"> </span>focus<span class="_"> </span>on<span class="_"> </span>the<span class="_"> </span>TVP-V<span class="_ _0"></span>AR</span></div><div class="t m2 xf h11 y35 ff5 fsa fc2 sc0 ls0 ws0">framework<span class="_"> </span>speciﬁcally<span class="_ _b"></span>,<span class="_"> </span>but<span class="_"> </span>we<span class="_"> </span>ar<span class="_ _2"></span>e<span class="_"> </span>rather<span class="_"> </span>concerned<span class="_ _d"> </span>with<span class="_"> </span>utilising<span class="_ _d"> </span>the<span class="_"> </span>TVP-V<span class="_ _0"></span>AR<span class="_"> </span>framework<span class="_"> </span>in<span class="_ _d"> </span>order<span class="_ _d"> </span>to<span class="_"> </span>impr<span class="_ _2"></span>ove<span class="_"> </span>the<span class="_"> </span>accuracy</div><div class="t m7 xf h11 y36 ff5 fsa fc2 sc0 ls0 ws0">of<span class="_"> </span>the<span class="_"> </span>dynamic<span class="_"> </span>connectedness<span class="_"> </span>measures.</div><div class="t m7 x1 h12 y37 ff3 fsa fc2 sc0 ls0 ws0">J.<span class="_"> </span>Risk<span class="_"> </span>Financial<span class="_"> </span>Manag.<span class="_"> </span><span class="ff4">2020<span class="ff5">,<span class="_"> </span></span></span>13<span class="ff5">,<span class="_"> </span>84;<span class="_"> </span>doi:10.3390/jrfm13040084<span class="_ _e"> </span>www<span class="_ _c"></span>.mdpi.com/journal/jrfm</span></div><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" 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<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/626432b34c65f41259c17c26/bg2.jpg"><div class="t m7 x1 h12 y38 ff3 fsa fc2 sc0 ls0 ws0">J.<span class="_"> </span>Risk<span class="_"> </span>Financial<span class="_"> </span>Manag.<span class="_"> </span><span class="ff4">2020<span class="ff5">,<span class="_"> </span></span></span>13<span class="ff5">,<span class="_"> </span>84<span class="_ _f"> </span>2<span class="_"> </span>of<span class="_"> </span>23</span></div><div class="t m2 x9 he y39 ff5 fs2 fc2 sc0 ls0 ws0">The<span class="_ _d"> </span><span class="fc4">Dieb<span class="_ _2"></span>old<span class="_ _d"> </span>and<span class="_ _d"> </span>Yılma<span class="_ _2"></span>z<span class="_ _7"> </span><span class="fc2">(<span class="_ _2"></span><span class="fc4">200<span class="_ _2"></span>9<span class="fc2">,<span class="_ _7"> </span></span>2<span class="_ _2"></span>012<span class="_ _2"></span><span class="fc2">,<span class="_ _7"> </span><span class="fc4">20<span class="_ _2"></span>14<span class="fc2">)<span class="_ _d"> </span>V<span class="_ _b"></span>AR-b<span class="_ _2"></span>ased<span class="_ _d"> </span>conn<span class="_ _2"></span>ect<span class="_ _2"></span>edn<span class="_ _2"></span>ess<span class="_ _d"> </span>appr<span class="_ _c"></span>oach<span class="_ _d"> </span>has<span class="_ _10"> </span>alr<span class="_ _c"></span>eady<span class="_ _d"> </span>attr<span class="_ _2"></span>acte<span class="_ _2"></span>d</span></span></span></span></span></span></div><div class="t m1 x1 he y3a ff5 fs2 fc2 sc0 ls0 ws0">sig<span class="_ _2"></span>nif<span class="_ _2"></span>ican<span class="_ _2"></span>t<span class="_"> </span>att<span class="_ _2"></span>ent<span class="_ _2"></span>ion<span class="_"> </span>by<span class="_ _7"> </span>the<span class="_"> </span>e<span class="_ _2"></span>xis<span class="_ _2"></span>ting<span class="_"> </span>e<span class="_ _2"></span>con<span class="_ _2"></span>omi<span class="_ _2"></span>c<span class="_"> </span>and<span class="_"> </span>f<span class="_ _2"></span>inan<span class="_ _2"></span>cia<span class="_ _2"></span>l<span class="_"> </span>lit<span class="_ _2"></span>erat<span class="_ _2"></span>ur<span class="_ _c"></span>e,<span class="_"> </span>and<span class="_"> </span>has<span class="_"> </span>b<span class="_ _2"></span>een<span class="_"> </span>a<span class="_ _2"></span>ppl<span class="_ _2"></span>ied<span class="_"> </span>to<span class="_ _7"> </span>iss<span class="_ _2"></span>ues</div><div class="t me x1 he y3b ff5 fs2 fc2 sc0 ls0 ws0">r<span class="_ _2"></span>elat<span class="_ _2"></span>ing<span class="_ _10"> </span>to<span class="_"> </span>the<span class="_ _7"> </span>sto<span class="_ _2"></span>ck<span class="_"> </span>m<span class="_ _2"></span>arke<span class="_ _2"></span>t<span class="_"> </span>in<span class="_ _2"></span>ter<span class="_ _c"></span>depen<span class="_ _2"></span>den<span class="_ _2"></span>cie<span class="_ _2"></span>s,<span class="_"> </span>vo<span class="_ _2"></span>lat<span class="_ _2"></span>ili<span class="_ _2"></span>ty<span class="_"> </span>sp<span class="_ _2"></span>ill<span class="_ _2"></span>ove<span class="_ _2"></span>rs,<span class="_"> </span>b<span class="_ _2"></span>usi<span class="_ _2"></span>nes<span class="_ _2"></span>s<span class="_"> </span>cyc<span class="_ _2"></span>le<span class="_"> </span>s<span class="_ _2"></span>pil<span class="_ _2"></span>love<span class="_ _2"></span>rs,<span class="_ _10"> </span>as<span class="_"> </span>wel<span class="_ _2"></span>l<span class="_"> </span>as</div><div class="t mf x1 he y3c ff5 fs2 fc2 sc0 ls0 ws0">bon<span class="_ _2"></span>d<span class="_"> </span>yi<span class="_ _2"></span>eld<span class="_"> </span>s<span class="_ _2"></span>pil<span class="_ _2"></span>lov<span class="_ _2"></span>ers<span class="_"> </span>(<span class="_ _2"></span>see<span class="_ _2"></span>,<span class="_"> </span>in<span class="_ _2"></span>ter<span class="_"> </span>a<span class="_ _2"></span>lia<span class="_ _2"></span>,<span class="_"> </span><span class="fc4">Alt<span class="_ _2"></span>er<span class="_"> </span>a<span class="_ _2"></span>nd<span class="_"> </span>B<span class="_ _2"></span>eye<span class="_ _2"></span>r<span class="_"> </span>201<span class="_ _2"></span>4<span class="fc2">;<span class="_"> </span></span>A<span class="_ _2"></span>nton<span class="_ _2"></span>aka<span class="_ _2"></span>kis<span class="_ _7"> </span>201<span class="_ _2"></span>2<span class="fc2">;<span class="_"> </span></span>A<span class="_ _0"></span>war<span class="_ _2"></span>tan<span class="_ _2"></span>i<span class="_"> </span>an<span class="_ _2"></span>d<span class="_"> </span>Mag<span class="_ _2"></span>hye<span class="_ _2"></span>re<span class="_ _2"></span>h</span></div><div class="t m2 x1 he y3d ff5 fs2 fc4 sc0 ls0 ws0">201<span class="_ _2"></span>3<span class="fc2">;<span class="_"> </span></span>B<span class="_ _2"></span>ekae<span class="_ _2"></span>rt<span class="_"> </span>e<span class="_ _2"></span>t<span class="_"> </span>al<span class="_ _2"></span>.<span class="_"> </span>201<span class="_ _2"></span>4<span class="fc2">;<span class="_"> </span></span>B<span class="_ _2"></span>ubá<span class="_ _2"></span>k<span class="_"> </span>et<span class="_"> </span>a<span class="_ _2"></span>l.<span class="_"> </span>2<span class="_ _2"></span>011<span class="_ _2"></span><span class="fc2">;<span class="_"> </span><span class="fc4">Di<span class="_ _2"></span>ebol<span class="_ _2"></span>d<span class="_"> </span>an<span class="_ _2"></span>d<span class="_"> </span>Y<span class="_ _c"></span>il<span class="_ _2"></span>maz<span class="_ _7"> </span>201<span class="_ _2"></span>5<span class="fc2">;<span class="_"> </span></span>M<span class="_ _2"></span>cMil<span class="_ _2"></span>lan<span class="_ _10"> </span>and<span class="_"> </span>Sp<span class="_ _2"></span>eigh<span class="_ _2"></span>t<span class="_"> </span>20<span class="_ _2"></span>10<span class="fc2">)<span class="_ _2"></span>.<span class="_ _5"> </span>At<span class="_"> </span>th<span class="_ _2"></span>e</span></span></span></div><div class="t m1 x1 he y3e ff5 fs2 fc2 sc0 ls0 ws0">sam<span class="_ _2"></span>e<span class="_"> </span>time<span class="_ _2"></span>,<span class="_"> </span>alte<span class="_ _2"></span>rnat<span class="_ _2"></span>ive<span class="_"> </span>me<span class="_ _2"></span>asu<span class="_ _2"></span>r<span class="_ _2"></span>es<span class="_"> </span>of<span class="_"> </span>con<span class="_ _2"></span>nec<span class="_ _2"></span>ted<span class="_ _2"></span>ness<span class="_"> </span>h<span class="_ _2"></span>ave<span class="_"> </span>be<span class="_ _2"></span>en<span class="_"> </span>pr<span class="_ _2"></span>ovi<span class="_ _2"></span>ded<span class="_"> </span>by<span class="_"> </span><span class="fc4">B<span class="_ _2"></span>aru<span class="_ _2"></span>ník<span class="_"> </span>e<span class="_ _2"></span>t<span class="_"> </span>al.<span class="_ _6"> </span><span class="fc2">(</span>2016<span class="_ _2"></span><span class="fc2">,<span class="_"> </span><span class="fc4">2017</span>)<span class="_ _2"></span>,</span></span></div><div class="t m7 x1 he y3f ff5 fs2 fc4 sc0 ls0 ws0">Bar<span class="_ _c"></span>uník<span class="_"> </span>a<span class="_ _2"></span>nd<span class="_"> </span>Kˇ<span class="_ _11"></span>reh<span class="_ _2"></span>lík<span class="_ _10"> </span><span class="fc2">(</span>2018<span class="_ _2"></span><span class="fc2">),<span class="_"> </span>an<span class="_ _2"></span>d<span class="_"> </span><span class="fc4">Ge<span class="_ _2"></span>rac<span class="_ _2"></span>i<span class="_"> </span>an<span class="_ _2"></span>d<span class="_"> </span>Gn<span class="_ _2"></span>abo<span class="_ _7"> </span><span class="fc2">(</span>20<span class="_ _2"></span>18<span class="fc2">)<span class="_ _2"></span>.</span></span></span></div><div class="t m1 x9 he y40 ff5 fs2 fc2 sc0 ls0 ws0">It<span class="_ _a"> </span>would<span class="_ _a"> </span>be<span class="_ _12"> </span>instructive<span class="_ _a"> </span>at<span class="_ _a"> </span>this<span class="_ _a"> </span>point<span class="_ _12"> </span>to<span class="_ _a"> </span>note<span class="_ _a"> </span>that<span class="_ _12"> </span>the<span class="_ _a"> </span><span class="fc4">Diebold<span class="_ _a"> </span>and<span class="_ _12"> </span>Yılmaz<span class="_ _a"> </span></span>(<span class="fc4">2009</span>,<span class="_ _12"> </span><span class="fc4">2012</span>,<span class="_ _8"> </span><span class="fc4">2014</span>)</div><div class="t m2 x1 he y41 ff5 fs2 fc2 sc0 ls0 ws0">approach<span class="_ _10"> </span>facilitates<span class="_"> </span>the<span class="_"> </span>measurement<span class="_ _10"> </span>of<span class="_"> </span>interdependence<span class="_ _10"> </span>across<span class="_"> </span>a<span class="_"> </span>network<span class="_ _10"> </span>of<span class="_"> </span>variables,<span class="_"> </span>thus<span class="_"> </span>pr<span class="_ _2"></span>oviding</div><div class="t m1 x1 he y42 ff5 fs2 fc2 sc0 ls0 ws0">a<span class="_ _8"> </span>framework<span class="_ _13"> </span>for<span class="_ _8"> </span>analysing<span class="_ _13"> </span>both<span class="_ _8"> </span>an<span class="_ _13"> </span>idiosyncratic<span class="_ _8"> </span>inﬂuence<span class="_ _13"> </span>(i.e.,<span class="_ _14"> </span>own)<span class="_ _8"> </span>and<span class="_ _13"> </span>inﬂuence<span class="_ _8"> </span>by<span class="_ _13"> </span>others</div><div class="t m1 x1 he y43 ff5 fs2 fc2 sc0 ls0 ws0">(i.e.,<span class="_ _6"> </span>network).<span class="_ _13"> </span>the<span class="_ _6"> </span>ensuing<span class="_ _5"> </span>measures<span class="_ _5"> </span>predicate<span class="_ _5"> </span>upon<span class="_ _5"> </span>the<span class="_ _5"> </span>estimation<span class="_ _6"> </span>of<span class="_ _5"> </span>the<span class="_ _5"> </span>forecast<span class="_ _5"> </span>error<span class="_ _5"> </span>variance</div><div class="t m10 x1 he y44 ff5 fs2 fc2 sc0 ls0 ws0">decompositions<span class="_"> </span>that<span class="_"> </span>derive<span class="_"> </span>fr<span class="_ _2"></span>om<span class="_"> </span>a<span class="_"> </span>V<span class="_ _b"></span>AR<span class="_"> </span>model.<span class="_ _5"> </span>In<span class="_"> </span>addition,<span class="_"> </span>these<span class="_"> </span>measures<span class="_"> </span>allow<span class="_"> </span>to<span class="_ _7"> </span>further<span class="_"> </span>classify</div><div class="t m2 x1 he y45 ff5 fs2 fc2 sc0 ls0 ws0">interdependence<span class="_"> </span>and<span class="_"> </span>pr<span class="_ _2"></span>ovide<span class="_"> </span>granulated<span class="_"> </span>information,<span class="_"> </span>considering<span class="_ _4"> </span>the<span class="_"> </span>fact<span class="_ _4"> </span>that<span class="_"> </span>results<span class="_"> </span>can<span class="_"> </span>be<span class="_"> </span>obtained</div><div class="t m1 x1 he y46 ff5 fs2 fc2 sc0 ls0 ws0">for<span class="_ _8"> </span>(i)<span class="_ _12"> </span>aggregate,<span class="_ _8"> </span>(ii)<span class="_ _8"> </span>dir<span class="_ _2"></span>ectional,<span class="_ _8"> </span>as<span class="_ _8"> </span>well<span class="_ _8"> </span>as<span class="_ _12"> </span>(iii)<span class="_ _8"> </span>net<span class="_ _12"> </span>interdependence.<span class="_ _15"> </span>More<span class="_ _12"> </span>particularly<span class="_ _0"></span>,<span class="_ _8"> </span>as<span class="_ _8"> </span>far</div><div class="t m1 x1 he y47 ff5 fs2 fc2 sc0 ls0 ws0">as<span class="_ _12"> </span>net<span class="_ _12"> </span>interdependence<span class="_ _a"> </span>is<span class="_ _12"> </span>concerned,<span class="_ _8"> </span>this<span class="_ _12"> </span>measure<span class="_ _a"> </span>allows<span class="_ _12"> </span>for<span class="_ _12"> </span>distinguishing<span class="_ _12"> </span>between<span class="_ _12"> </span>net<span class="_ _12"> </span>shock</div><div class="t m1 x1 he y48 ff5 fs2 fc2 sc0 ls0 ws0">transmitters<span class="_ _8"> </span>and<span class="_ _8"> </span>net<span class="_ _8"> </span>shock<span class="_ _12"> </span>receivers,<span class="_ _13"> </span>which<span class="_ _8"> </span>in<span class="_ _8"> </span>turn<span class="_ _8"> </span>helps<span class="_ _8"> </span>attain<span class="_ _8"> </span>a<span class="_ _8"> </span>better<span class="_ _12"> </span>understanding<span class="_ _8"> </span>of<span class="_ _8"> </span>the</div><div class="t m2 x1 he y49 ff5 fs2 fc2 sc0 ls0 ws0">underlying<span class="_ _10"> </span>dynamics<span class="_"> </span>and<span class="_ _10"> </span>facilitates<span class="_"> </span>the<span class="_ _d"> </span>formulation<span class="_"> </span>of<span class="_ _10"> </span>policy<span class="_"> </span>implications.<span class="_ _4"> </span>As<span class="_"> </span>a<span class="_ _10"> </span>ﬁnal<span class="_ _7"> </span>step,<span class="_ _7"> </span>the<span class="_ _10"> </span>dynamic</div><div class="t m11 x1 he y4a ff5 fs2 fc2 sc0 ls0 ws0">nature<span class="_"> </span>of<span class="_ _7"> </span>interconnectedness<span class="_"> </span>is<span class="_ _7"> </span>typically<span class="_"> </span>being<span class="_"> </span>investigated<span class="_"> </span>thr<span class="_ _2"></span>ough<span class="_"> </span>the<span class="_"> </span>use<span class="_"> </span>of<span class="_"> </span>the<span class="_"> </span>r<span class="_ _c"></span>olling-windows</div><div class="t m12 x1 he y4b ff5 fs2 fc2 sc0 ls0 ws0">approach,<span class="_"> </span>wher<span class="_ _2"></span>eby<span class="_"> </span>the<span class="_"> </span>resear<span class="_ _2"></span>cher<span class="_"> </span>begins<span class="_"> </span>by<span class="_"> </span>deciding<span class="_"> </span>upon<span class="_"> </span>the<span class="_"> </span>relevant<span class="_"> </span>window<span class="_"> </span>length<span class="_"> </span>and<span class="_"> </span>for<span class="_ _2"></span>ecast</div><div class="t m13 x1 he y4c ff5 fs2 fc2 sc0 ls0 ws0">horizon.<span class="_ _5"> </span>What<span class="_"> </span>is<span class="_"> </span>more,<span class="_"> </span>it<span class="_"> </span>should<span class="_ _7"> </span>be<span class="_"> </span>noted<span class="_"> </span>that<span class="_"> </span>in<span class="_"> </span>their<span class="_"> </span>2009<span class="_"> </span>study<span class="_ _b"></span>,<span class="_"> </span>Diebold<span class="_"> </span>and<span class="_"> </span>Y<span class="_ _c"></span>ilmaz<span class="_"> </span>investigated</div><div class="t mb x1 he y4d ff5 fs2 fc2 sc0 ls0 ws0">the<span class="_"> </span>interdependence<span class="_"> </span>acr<span class="_ _2"></span>oss<span class="_"> </span>the<span class="_"> </span>variables<span class="_"> </span>of<span class="_"> </span>interest<span class="_"> </span>by<span class="_"> </span>utilising<span class="_"> </span>a<span class="_"> </span>Cholesky-type<span class="_"> </span>V<span class="_ _0"></span>AR<span class="_"> </span>framework<span class="_"> </span>(i.e.,</div><div class="t m1 x1 he y4e ff5 fs2 fc2 sc0 ls0 ws0">where<span class="_ _5"> </span>the<span class="_ _5"> </span>ordering<span class="_ _5"> </span>of<span class="_ _5"> </span>the<span class="_ _5"> </span>variables<span class="_ _6"> </span>af<span class="_ _2"></span>fects<span class="_ _5"> </span>outcomes),<span class="_ _6"> </span>whereas<span class="_ _5"> </span>in<span class="_ _5"> </span>their<span class="_ _5"> </span>2012<span class="_ _6"> </span>study<span class="_ _b"></span>,<span class="_ _6"> </span>they<span class="_ _5"> </span>utilised<span class="_ _5"> </span>a</div><div class="t m14 x1 he y4f ff5 fs2 fc2 sc0 ls0 ws0">generalised<span class="_"> </span>V<span class="_ _b"></span>AR<span class="_"> </span>approach<span class="_"> </span>(i.e.,<span class="_"> </span>where<span class="_"> </span>the<span class="_"> </span>ordering<span class="_"> </span>of<span class="_"> </span>the<span class="_"> </span>variables<span class="_"> </span>is<span class="_"> </span>irr<span class="_ _2"></span>elevant).<span class="_ _6"> </span>Finally<span class="_ _b"></span>,<span class="_"> </span>in<span class="_"> </span>their<span class="_"> </span>2014</div><div class="t m1 x1 he y50 ff5 fs2 fc2 sc0 ls0 ws0">study<span class="_ _b"></span>,<span class="_ _4"> </span>Diebold<span class="_"> </span>and<span class="_ _4"> </span>Y<span class="_ _c"></span>ilmaz<span class="_ _4"> </span>emphasized<span class="_"> </span>the<span class="_ _4"> </span>concept<span class="_"> </span>of<span class="_ _4"> </span>connectedness<span class="_"> </span>and<span class="_ _4"> </span>offered<span class="_"> </span>ways<span class="_"> </span>to<span class="_"> </span>measure</div><div class="t m7 x1 he y51 ff5 fs2 fc2 sc0 ls0 ws0">connectedness<span class="_"> </span>based<span class="_"> </span>on<span class="_"> </span>their<span class="_"> </span>previous<span class="_"> </span>r<span class="_ _2"></span>elevant<span class="_"> </span>resear<span class="_ _c"></span>ch.</div><div class="t m9 x9 he y52 ff5 fs2 fc2 sc0 ls0 ws0">This<span class="_"> </span>extension<span class="_"> </span>improves<span class="_"> </span>the<span class="_"> </span>existing<span class="_"> </span>method<span class="_"> </span>in<span class="_"> </span>four<span class="_"> </span>ways:<span class="_ _5"> </span>(i)<span class="_"> </span>potential<span class="_"> </span>changes<span class="_"> </span>in<span class="_"> </span>the<span class="_"> </span>values<span class="_"> </span>of</div><div class="t m15 x1 he y53 ff5 fs2 fc2 sc0 ls0 ws0">the<span class="_"> </span>parameters<span class="_"> </span>can<span class="_"> </span>be<span class="_"> </span>more<span class="_"> </span>accurately<span class="_"> </span>determined,<span class="_"> </span>(ii)<span class="_"> </span>outliers<span class="_"> </span>do<span class="_"> </span>not<span class="_"> </span>affect<span class="_"> </span>outcomes,<span class="_"> </span>(iii)<span class="_"> </span>there<span class="_"> </span>is<span class="_"> </span>no</div><div class="t mc x1 he y54 ff5 fs2 fc2 sc0 ls0 ws0">need<span class="_"> </span>to<span class="_"> </span>set<span class="_"> </span>an<span class="_"> </span>arbitrary<span class="_"> </span>rolling-window<span class="_"> </span>size,<span class="_"> </span>and<span class="_"> </span>(iv)<span class="_ _4"> </span>there<span class="_"> </span>is<span class="_"> </span>no<span class="_"> </span>loss<span class="_"> </span>of<span class="_"> </span>observations<span class="_ _4"> </span>in<span class="_"> </span>the<span class="_"> </span>calculation</div><div class="t m16 x1 he y55 ff5 fs2 fc2 sc0 ls0 ws0">of<span class="_"> </span>the<span class="_"> </span>dynamic<span class="_"> </span>measures.<span class="_ _5"> </span>T<span class="_ _0"></span>o<span class="_"> </span>be<span class="_"> </span>more<span class="_"> </span>explicit,<span class="_"> </span>while<span class="_"> </span>the<span class="_"> </span>last<span class="_"> </span>two<span class="_"> </span>impr<span class="_ _c"></span>ovements<span class="_"> </span>are<span class="_"> </span>rather<span class="_"> </span>created<span class="_"> </span>by</div><div class="t m17 x1 he y56 ff5 fs2 fc2 sc0 ls0 ws0">construction,<span class="_"> </span>the<span class="_"> </span>ﬁrst<span class="_"> </span>two<span class="_"> </span>can<span class="_"> </span>be<span class="_"> </span>evidenced<span class="_"> </span>by<span class="_"> </span>the<span class="_"> </span>application<span class="_"> </span>of<span class="_"> </span>Monte<span class="_"> </span>Carlo<span class="_"> </span>simulations.<span class="_ _6"> </span>In<span class="_"> </span>point<span class="_"> </span>of</div><div class="t mf x1 he y57 ff5 fs2 fc2 sc0 ls0 ws0">fact,<span class="_"> </span>when<span class="_"> </span>we<span class="_"> </span>test<span class="_"> </span>the<span class="_"> </span>robustness<span class="_"> </span>of<span class="_"> </span>our<span class="_"> </span>estimations,<span class="_"> </span>both<span class="_"> </span>in<span class="_"> </span>terms<span class="_"> </span>of<span class="_"> </span>outliers’<span class="_ _4"> </span>sensitivity<span class="_"> </span>and<span class="_"> </span>changes</div><div class="t m2 x1 he y58 ff5 fs2 fc2 sc0 ls0 ws0">in<span class="_"> </span>the<span class="_"> </span>values<span class="_"> </span>of<span class="_"> </span>the<span class="_"> </span>parameters,<span class="_"> </span>the<span class="_"> </span>results<span class="_"> </span>indicate<span class="_"> </span>that<span class="_"> </span>the<span class="_"> </span>TVP-V<span class="_ _b"></span>AR<span class="_"> </span>estimations<span class="_"> </span>are<span class="_"> </span>superior<span class="_"> </span>to<span class="_"> </span>those</div><div class="t m7 x1 he y59 ff5 fs2 fc2 sc0 ls0 ws0">generated<span class="_"> </span>by<span class="_"> </span>rolling-windows.</div><div class="t m3 x9 he y5a ff5 fs2 fc2 sc0 ls0 ws0">In<span class="_"> </span>turn,<span class="_"> </span>we<span class="_"> </span>illustrate<span class="_"> </span>the<span class="_"> </span>accuracy<span class="_"> </span>of<span class="_"> </span>our<span class="_"> </span>proposed<span class="_"> </span>method<span class="_"> </span>by<span class="_ _7"> </span>considering<span class="_"> </span>connectedness<span class="_"> </span>in<span class="_"> </span>the</div><div class="t m1 x1 he y5b ff5 fs2 fc2 sc0 ls0 ws0">foreign<span class="_"> </span>exchange<span class="_"> </span>market.<span class="_ _6"> </span>More<span class="_"> </span>speciﬁcally<span class="_ _0"></span>,<span class="_"> </span>we<span class="_ _4"> </span>collect<span class="_ _4"> </span>monthly<span class="_ _4"> </span>data<span class="_ _4"> </span>on<span class="_"> </span>the<span class="_ _4"> </span>exchange<span class="_ _4"> </span>rate<span class="_ _4"> </span>between</div><div class="t m1 x1 he y5c ff5 fs2 fc2 sc0 ls0 ws0">the<span class="_ _a"> </span>USD<span class="_ _12"> </span>and<span class="_ _a"> </span>the<span class="_ _12"> </span>following<span class="_ _a"> </span>currencies:<span class="_ _16"> </span>(i)<span class="_ _a"> </span>EUR/EC,<span class="_ _12"> </span>(ii)<span class="_ _a"> </span>GBP<span class="_ _b"></span>,<span class="_ _12"> </span>(iii)<span class="_ _a"> </span>CHF<span class="_ _c"></span>,<span class="_ _a"> </span>and<span class="_ _a"> </span>(iv),<span class="_ _8"> </span>JPY<span class="_ _b"></span>.<span class="_ _12"> </span>the<span class="_ _a"> </span>choice</div><div class="t m1 x1 he y5d ff5 fs2 fc2 sc0 ls0 ws0">of<span class="_ _6"> </span>the<span class="_ _6"> </span>currencies<span class="_ _6"> </span>was<span class="_ _6"> </span>based<span class="_ _6"> </span>on<span class="_ _6"> </span>their<span class="_ _6"> </span>respective<span class="_ _6"> </span>position<span class="_ _6"> </span>on<span class="_ _6"> </span>the<span class="_ _6"> </span>list<span class="_ _6"> </span>of<span class="_ _6"> </span>the<span class="_ _a"> </span>most<span class="_ _6"> </span>traded<span class="_ _6"> </span>currencies</div><div class="t m1 x1 he y5e ff5 fs2 fc2 sc0 ls0 ws0">of<span class="_ _6"> </span>the<span class="_ _6"> </span>world.<span class="_ _9"> </span>the<span class="_ _6"> </span>USD<span class="_ _a"> </span>ranks<span class="_ _6"> </span>ﬁrst,<span class="_ _a"> </span>and<span class="_ _a"> </span>in<span class="_ _6"> </span>this<span class="_ _6"> </span>regard,<span class="_ _6"> </span>it<span class="_ _6"> </span>serves<span class="_ _a"> </span>as<span class="_ _6"> </span>the<span class="_ _6"> </span>base<span class="_ _6"> </span>currency<span class="_ _6"> </span>of<span class="_ _6"> </span>the<span class="_ _a"> </span>study<span class="_ _b"></span>.</div><div class="t m1 x1 he y5f ff5 fs2 fc2 sc0 ls0 ws0">Subsequently<span class="_ _b"></span>,<span class="_ _a"> </span>we<span class="_ _6"> </span>estimate<span class="_ _6"> </span>results<span class="_ _6"> </span>for<span class="_ _6"> </span>differ<span class="_ _2"></span>ent<span class="_ _6"> </span>window-lengths<span class="_ _6"> </span>(i.e.,<span class="_ _a"> </span>25,<span class="_ _a"> </span>26,<span class="_ _a"> </span>.<span class="_ _d"> </span>.<span class="_ _17"></span>.<span class="_ _17"> </span>,<span class="_ _a"> </span>274,<span class="_ _a"> </span>275<span class="_ _6"> </span>months)</div><div class="t m1 x1 he y60 ff5 fs2 fc2 sc0 ls0 ws0">in<span class="_ _a"> </span>order<span class="_ _a"> </span>to<span class="_ _a"> </span>(i)<span class="_ _12"> </span>deduct<span class="_ _a"> </span>how<span class="_ _12"> </span>dynamic<span class="_ _a"> </span>total<span class="_ _12"> </span>connectedness<span class="_ _a"> </span>changes<span class="_ _12"> </span>with<span class="_ _a"> </span>the<span class="_ _12"> </span>window<span class="_ _a"> </span>size,<span class="_ _8"> </span>and<span class="_ _a"> </span>(ii)</div><div class="t m18 x1 he y61 ff5 fs2 fc2 sc0 ls0 ws0">contrast<span class="_"> </span>these<span class="_"> </span>r<span class="_ _2"></span>esults<span class="_"> </span>with<span class="_"> </span>those<span class="_"> </span>obtained<span class="_"> </span>fr<span class="_ _2"></span>om<span class="_"> </span>our<span class="_"> </span>TVP-V<span class="_ _b"></span>AR<span class="_"> </span>approach.<span class="_ _5"> </span>W<span class="_ _0"></span>e<span class="_"> </span>ﬁnd<span class="_"> </span>that<span class="_"> </span>our<span class="_"> </span>proposed</div><div class="t m2 x1 he y62 ff5 fs2 fc2 sc0 ls0 ws0">TVP-V<span class="_ _b"></span>AR-based<span class="_"> </span>measure<span class="_ _10"> </span>of<span class="_"> </span>connectedness<span class="_ _10"> </span>is<span class="_"> </span>similar<span class="_ _10"> </span>to<span class="_"> </span>the<span class="_"> </span>averaged<span class="_ _10"> </span>dynamic<span class="_"> </span>connectedness<span class="_ _10"> </span>measures</div><div class="t m4 x1 he y63 ff5 fs2 fc2 sc0 ls0 ws0">of<span class="_"> </span>the<span class="_"> </span>rolling-window<span class="_"> </span>V<span class="_ _b"></span>AR<span class="_"> </span>model;<span class="_"> </span>nonetheless,<span class="_"> </span>TVP-V<span class="_ _b"></span>AR<span class="_"> </span>values<span class="_"> </span>immediately<span class="_"> </span>adjust<span class="_"> </span>to<span class="_"> </span>underlying</div><div class="t m19 x1 he y64 ff5 fs2 fc2 sc0 ls0 ws0">events,<span class="_"> </span>while<span class="_"> </span>rolling-window-based<span class="_"> </span>estimates<span class="_"> </span>either<span class="_"> </span>overr<span class="_ _2"></span>eact<span class="_"> </span>(given<span class="_"> </span>an<span class="_"> </span>inadequate<span class="_"> </span>window<span class="_"> </span>size)<span class="_"> </span>or</div><div class="t m7 x1 he y65 ff5 fs2 fc2 sc0 ls0 ws0">smooth<span class="_"> </span>out<span class="_"> </span>the<span class="_"> </span>effect<span class="_"> </span>(given<span class="_"> </span>a<span class="_"> </span>lar<span class="_ _2"></span>ge<span class="_"> </span>window<span class="_"> </span>size).</div><div class="t m1a x9 he y66 ff5 fs2 fc2 sc0 ls0 ws0">In<span class="_"> </span>line<span class="_"> </span>with<span class="_"> </span>the<span class="_"> </span>afor<span class="_ _2"></span>ementioned<span class="_"> </span>analysis,<span class="_"> </span>we<span class="_"> </span>then<span class="_"> </span>select<span class="_"> </span>three<span class="_"> </span>window<span class="_ _7"> </span>sizes<span class="_"> </span>that<span class="_"> </span>are<span class="_"> </span>neither<span class="_ _7"> </span>too</div><div class="t m1b x1 he y67 ff5 fs2 fc2 sc0 ls0 ws0">large<span class="_"> </span>nor<span class="_"> </span>too<span class="_"> </span>small.<span class="_ _4"> </span>In<span class="_"> </span>particular<span class="_ _c"></span>,<span class="_"> </span>we<span class="_"> </span>choose<span class="_"> </span>50,<span class="_"> </span>100,<span class="_"> </span>and<span class="_"> </span>200<span class="_"> </span>observations-wide<span class="_"> </span>windows.<span class="_ _5"> </span>W<span class="_ _c"></span>indows</div><div class="t m1 x1 he y68 ff5 fs2 fc2 sc0 ls0 ws0">were<span class="_ _5"> </span>chosen<span class="_ _5"> </span>on<span class="_ _6"> </span>the<span class="_ _5"> </span>basis<span class="_ _5"> </span>of<span class="_ _6"> </span>their<span class="_ _5"> </span>mean<span class="_ _6"> </span>absolute<span class="_ _5"> </span>prediction<span class="_ _5"> </span>error<span class="_ _5"> </span>(MAPE)<span class="_ _5"> </span>value<span class="_ _6"> </span>stemming<span class="_ _5"> </span>from<span class="_ _5"> </span>a</div><div class="t m1c x1 he y69 ff5 fs2 fc2 sc0 ls0 ws0">12-step-ahead<span class="_"> </span>forecast.<span class="_ _4"> </span>Prominent<span class="_"> </span>among<span class="_"> </span>our<span class="_"> </span>results<span class="_ _7"> </span>is<span class="_"> </span>the<span class="_"> </span>fact<span class="_"> </span>that<span class="_"> </span>(i)<span class="_"> </span>the<span class="_"> </span>TVP-V<span class="_ _b"></span>AR<span class="_"> </span>model<span class="_"> </span>exhibits</div><div class="t m1 x1 he y6a ff5 fs2 fc2 sc0 ls0 ws0">similar<span class="_ _a"> </span>trend-movements<span class="_ _6"> </span>to<span class="_ _a"> </span>the<span class="_ _a"> </span>50-month<span class="_ _a"> </span>rolling-windows<span class="_ _6"> </span>V<span class="_ _0"></span>AR;<span class="_ _a"> </span>nonetheless,<span class="_ _12"> </span>the<span class="_ _a"> </span>latter<span class="_ _a"> </span>is<span class="_ _a"> </span>much</div><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' 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md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>

<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/626432b34c65f41259c17c26/bg3.jpg"><div class="t m7 x1 h12 y38 ff3 fsa fc2 sc0 ls0 ws0">J.<span class="_"> </span>Risk<span class="_"> </span>Financial<span class="_"> </span>Manag.<span class="_"> </span><span class="ff4">2020<span class="ff5">,<span class="_"> </span></span></span>13<span class="ff5">,<span class="_"> </span>84<span class="_ _f"> </span>3<span class="_"> </span>of<span class="_"> </span>23</span></div><div class="t m1 x1 he y39 ff5 fs2 fc2 sc0 ls0 ws0">less<span class="_ _5"> </span>volatile,<span class="_ _a"> </span>and<span class="_ _5"> </span>(ii)<span class="_ _6"> </span>despite<span class="_ _6"> </span>how<span class="_ _5"> </span>the<span class="_ _6"> </span>100-month<span class="_ _5"> </span>rolling-windows<span class="_ _6"> </span>V<span class="_ _b"></span>AR<span class="_ _6"> </span>is<span class="_ _5"> </span>as<span class="_ _6"> </span>persistent<span class="_ _5"> </span>as<span class="_ _6"> </span>its<span class="_ _6"> </span>TVP</div><div class="t m7 x1 he y3a ff5 fs2 fc2 sc0 ls0 ws0">counterpart,<span class="_"> </span>it<span class="_"> </span>does<span class="_"> </span>not<span class="_"> </span>appear<span class="_"> </span>to<span class="_"> </span>adjust<span class="_"> </span>to<span class="_"> </span>changes<span class="_"> </span>as<span class="_"> </span>quickly<span class="_"> </span>as<span class="_"> </span>the<span class="_"> </span>TVP-V<span class="_ _b"></span>AR<span class="_"> </span>model.</div><div class="t m1 x9 he y3b ff5 fs2 fc2 sc0 ls0 ws0">Fin<span class="_ _2"></span>all<span class="_ _2"></span>y<span class="_ _b"></span>,<span class="_ _5"> </span>we<span class="_"> </span>utili<span class="_ _2"></span>se<span class="_"> </span>the<span class="_ _4"> </span>re<span class="_ _2"></span>sult<span class="_ _2"></span>s<span class="_ _4"> </span>fro<span class="_ _2"></span>m<span class="_"> </span>our<span class="_ _4"> </span>empir<span class="_ _2"></span>ica<span class="_ _2"></span>l<span class="_ _4"> </span>appli<span class="_ _2"></span>cat<span class="_ _2"></span>ion<span class="_"> </span>in<span class="_"> </span>orde<span class="_ _2"></span>r<span class="_"> </span>to<span class="_ _5"> </span>pr<span class="_ _c"></span>ovide<span class="_"> </span>two<span class="_"> </span>addi<span class="_ _2"></span>tio<span class="_ _2"></span>nal</div><div class="t m15 x1 he y3c ff5 fs2 fc2 sc0 ls0 ws0">inp<span class="_ _2"></span>uts<span class="_ _7"> </span>to<span class="_"> </span>t<span class="_ _2"></span>he<span class="_"> </span>ex<span class="_ _2"></span>ist<span class="_ _2"></span>ing<span class="_"> </span>l<span class="_ _2"></span>ite<span class="_ _2"></span>rat<span class="_ _2"></span>ur<span class="_ _2"></span>e.<span class="_ _5"> </span>Fir<span class="_ _2"></span>st,<span class="_ _7"> </span>we<span class="_"> </span>p<span class="_ _2"></span>ro<span class="_ _2"></span>pos<span class="_ _2"></span>e<span class="_"> </span>a<span class="_"> </span>me<span class="_ _2"></span>tho<span class="_ _2"></span>d<span class="_"> </span>to<span class="_"> </span>g<span class="_ _2"></span>ene<span class="_ _2"></span>rat<span class="_ _2"></span>e<span class="_"> </span>con<span class="_ _2"></span>fid<span class="_ _2"></span>enc<span class="_ _2"></span>e<span class="_"> </span>int<span class="_ _2"></span>erv<span class="_ _2"></span>als<span class="_"> </span>o<span class="_ _2"></span>f<span class="_"> </span>dy<span class="_ _2"></span>nam<span class="_ _2"></span>ic</div><div class="t m1 x1 he y3d ff5 fs2 fc2 sc0 ls0 ws0">con<span class="_ _2"></span>nec<span class="_ _2"></span>tedn<span class="_ _2"></span>ess<span class="_ _4"> </span>by<span class="_ _5"> </span>combi<span class="_ _2"></span>nin<span class="_ _2"></span>g<span class="_ _5"> </span>boot<span class="_ _2"></span>stra<span class="_ _2"></span>ppe<span class="_ _2"></span>d<span class="_ _5"> </span>gene<span class="_ _2"></span>rali<span class="_ _2"></span>sed<span class="_ _4"> </span>impul<span class="_ _2"></span>se<span class="_ _5"> </span>r<span class="_ _2"></span>espo<span class="_ _2"></span>nse<span class="_ _4"> </span>funct<span class="_ _2"></span>ion<span class="_ _2"></span>s<span class="_ _5"> </span>(see,<span class="_ _4"> </span><span class="fc4">Koop<span class="_ _5"> </span>et<span class="_ _5"> </span>al<span class="_ _2"></span>.</span></div><div class="t m1d x1 he y3e ff5 fs2 fc4 sc0 ls0 ws0">199<span class="_ _2"></span>6<span class="fc2">;<span class="_"> </span></span>P<span class="_ _2"></span>esar<span class="_ _2"></span>an<span class="_"> </span>a<span class="_ _2"></span>nd<span class="_"> </span>S<span class="_ _2"></span>hin<span class="_ _7"> </span>199<span class="_ _2"></span>8<span class="fc2">)<span class="_"> </span>w<span class="_ _2"></span>ith<span class="_ _7"> </span>the<span class="_ _10"> </span>joint<span class="_ _10"> </span>confi<span class="_ _2"></span>denc<span class="_ _2"></span>e<span class="_"> </span>ba<span class="_ _2"></span>nds<span class="_ _10"> </span>for<span class="_"> </span>im<span class="_ _2"></span>puls<span class="_ _2"></span>e<span class="_"> </span>r<span class="_ _c"></span>espon<span class="_ _2"></span>se<span class="_"> </span>f<span class="_ _2"></span>unct<span class="_ _2"></span>ion<span class="_ _2"></span>s<span class="_"> </span>su<span class="_ _2"></span>gges<span class="_ _2"></span>ted</span></div><div class="t m1 x1 he y3f ff5 fs2 fc2 sc0 ls0 ws0">by<span class="_ _6"> </span><span class="fc4">Lütke<span class="_ _2"></span>poh<span class="_ _2"></span>l<span class="_ _a"> </span>et<span class="_ _6"> </span>al.<span class="_ _6"> </span><span class="fc2">(</span>2015<span class="_ _2"></span><span class="fc2">).<span class="_ _18"> </span>Thi<span class="_ _2"></span>s<span class="_ _a"> </span>com<span class="_ _2"></span>bine<span class="_ _2"></span>d<span class="_ _a"> </span>app<span class="_ _2"></span>r<span class="_ _2"></span>oach<span class="_ _6"> </span>re<span class="_ _2"></span>fin<span class="_ _2"></span>es<span class="_ _6"> </span>the<span class="_ _a"> </span>int<span class="_ _2"></span>erv<span class="_ _2"></span>als<span class="_ _6"> </span>appr<span class="_ _c"></span>oach<span class="_ _6"> </span>intr<span class="_ _c"></span>oduce<span class="_ _2"></span>d<span class="_ _a"> </span>by</span></span></div><div class="t m7 x1 he y40 ff5 fs2 fc4 sc0 ls0 ws0">Kil<span class="_ _2"></span>ian<span class="_ _10"> </span><span class="fc2">(</span>1998<span class="fc2">,<span class="_ _10"> </span></span>1999<span class="fc2">)</span></div><div class="t m1 x10 he y40 ff5 fs2 fc2 sc0 ls0 ws0">.<span class="_ _19"> </span>Sec<span class="_ _2"></span>ond<span class="_ _2"></span>,<span class="_ _8"> </span>we<span class="_ _a"> </span>offe<span class="_ _2"></span>r<span class="_ _12"> </span>an<span class="_ _12"> </span>unc<span class="_ _2"></span>ert<span class="_ _2"></span>ain<span class="_ _2"></span>ty<span class="_ _a"> </span>estim<span class="_ _2"></span>atio<span class="_ _2"></span>n<span class="_ _12"> </span>of<span class="_ _a"> </span>TVP-V<span class="_ _b"></span>AR<span class="_ _2"></span>-ba<span class="_ _2"></span>sed<span class="_ _a"> </span>conn<span class="_ _2"></span>ecte<span class="_ _2"></span>dne<span class="_ _2"></span>ss</div><div class="t m7 x1 he y41 ff5 fs2 fc2 sc0 ls0 ws0">mea<span class="_ _2"></span>sur<span class="_ _c"></span>es<span class="_"> </span>by<span class="_ _7"> </span>let<span class="_ _2"></span>tin<span class="_ _2"></span>g<span class="_"> </span>fo<span class="_ _2"></span>rg<span class="_ _2"></span>ett<span class="_ _2"></span>ing<span class="_ _7"> </span>fac<span class="_ _2"></span>tor<span class="_ _2"></span>s<span class="_"> </span>an<span class="_ _2"></span>d<span class="_"> </span>Mi<span class="_ _2"></span>nnes<span class="_ _2"></span>ota<span class="_ _10"> </span>prior<span class="_ _2"></span>s<span class="_"> </span>va<span class="_ _2"></span>ry<span class="_"> </span>r<span class="_ _2"></span>ando<span class="_ _2"></span>mly<span class="_ _b"></span>.</div><div class="t m1 x9 he y42 ff5 fs2 fc2 sc0 ls0 ws0">It<span class="_"> </span>w<span class="_ _2"></span>oul<span class="_ _c"></span>d<span class="_ _4"> </span>als<span class="_ _2"></span>o<span class="_"> </span>be<span class="_"> </span>in<span class="_ _2"></span>st<span class="_ _2"></span>ru<span class="_ _2"></span>ct<span class="_ _2"></span>iv<span class="_ _2"></span>e<span class="_"> </span>at<span class="_"> </span>th<span class="_ _2"></span>is<span class="_"> </span>p<span class="_ _2"></span>oin<span class="_ _c"></span>t<span class="_ _4"> </span>to<span class="_"> </span>no<span class="_ _2"></span>te<span class="_"> </span>th<span class="_ _2"></span>at<span class="_ _2"></span>,<span class="_"> </span>so<span class="_"> </span>fa<span class="_ _2"></span>r<span class="_ _0"></span>,<span class="_ _4"> </span>the<span class="_ _2"></span>r<span class="_ _2"></span>e<span class="_"> </span>hav<span class="_ _c"></span>e<span class="_ _4"> </span>bee<span class="_ _2"></span>n<span class="_"> </span>two<span class="_"> </span>s<span class="_ _2"></span>em<span class="_ _2"></span>in<span class="_ _2"></span>al<span class="_"> </span>st<span class="_ _2"></span>ud<span class="_ _2"></span>ie<span class="_ _2"></span>s</div><div class="t m1 x1 he y43 ff5 fs2 fc2 sc0 ls0 ws0">in<span class="_"> </span>the<span class="_"> </span>fiel<span class="_ _c"></span>d<span class="_ _5"> </span>of<span class="_ _4"> </span>dyn<span class="_ _2"></span>am<span class="_ _2"></span>ic<span class="_"> </span>conn<span class="_ _2"></span>ec<span class="_ _2"></span>te<span class="_ _2"></span>dn<span class="_ _2"></span>ess<span class="_"> </span>thr<span class="_ _c"></span>oug<span class="_ _2"></span>h<span class="_ _4"> </span>TVP<span class="_ _2"></span>-V<span class="_ _b"></span>AR<span class="_ _2"></span>s;<span class="_ _5"> </span>na<span class="_ _2"></span>me<span class="_ _2"></span>ly<span class="_ _b"></span>,<span class="_ _5"> </span><span class="fc4">An<span class="_ _2"></span>to<span class="_ _2"></span>na<span class="_ _2"></span>kak<span class="_ _c"></span>is<span class="_ _5"> </span>an<span class="_ _2"></span>d<span class="_ _4"> </span>Gab<span class="_ _2"></span>aue<span class="_ _2"></span>r<span class="_ _4"> </span><span class="fc2">(</span>20<span class="_ _2"></span>17<span class="fc2">)</span></span></div><div class="t m1 x1 he y44 ff5 fs2 fc2 sc0 ls0 ws0">an<span class="_ _2"></span>d<span class="_ _4"> </span><span class="fc4">Kor<span class="_ _c"></span>obil<span class="_ _c"></span>is<span class="_ _5"> </span>an<span class="_ _2"></span>d<span class="_ _4"> </span>Y<span class="_ _c"></span>ilm<span class="_ _2"></span>az<span class="_"> </span><span class="fc2">(</span>20<span class="_ _2"></span>18<span class="fc2">)<span class="_ _c"></span>.<span class="_ _13"> </span>Bot<span class="_ _2"></span>h<span class="_ _4"> </span>stu<span class="_ _2"></span>die<span class="_ _c"></span>s<span class="_ _5"> </span>ado<span class="_ _2"></span>pt<span class="_"> </span>a<span class="_ _5"> </span>si<span class="_ _2"></span>mil<span class="_ _2"></span>ar<span class="_"> </span>fra<span class="_ _2"></span>me<span class="_ _2"></span>wor<span class="_ _c"></span>k,<span class="_ _5"> </span>alt<span class="_ _2"></span>ho<span class="_ _2"></span>ug<span class="_ _2"></span>h<span class="_ _4"> </span>they<span class="_"> </span>inv<span class="_ _2"></span>es<span class="_ _2"></span>ti<span class="_ _2"></span>gat<span class="_ _c"></span>e</span></span></div><div class="t m1 x1 he y45 ff5 fs2 fc2 sc0 ls0 ws0">di<span class="_ _2"></span>ff<span class="_ _2"></span>er<span class="_ _c"></span>ent<span class="_ _12"> </span>iss<span class="_ _2"></span>ues<span class="_ _c"></span>.<span class="_ _1a"> </span>T<span class="_ _b"></span>o<span class="_ _8"> </span>be<span class="_ _12"> </span>mor<span class="_ _c"></span>e<span class="_ _8"> </span>e<span class="_ _2"></span>xpl<span class="_ _2"></span>ic<span class="_ _2"></span>it<span class="_ _2"></span>,<span class="_ _13"> </span><span class="fc4">An<span class="_ _2"></span>to<span class="_ _2"></span>nak<span class="_ _c"></span>akis<span class="_ _12"> </span>an<span class="_ _2"></span>d<span class="_ _8"> </span>G<span class="_ _2"></span>ab<span class="_ _2"></span>aue<span class="_ _c"></span>r<span class="_ _8"> </span><span class="fc2">(</span>2<span class="_ _2"></span>017<span class="_ _c"></span><span class="fc2">)<span class="_ _8"> </span>pr<span class="_ _c"></span>ovi<span class="_ _2"></span>de<span class="_ _2"></span>d<span class="_ _8"> </span>e<span class="_ _2"></span>vi<span class="_ _2"></span>den<span class="_ _c"></span>ce<span class="_ _8"> </span>o<span class="_ _2"></span>f<span class="_ _8"> </span>t<span class="_ _2"></span>he</span></span></div><div class="t m1 x1 he y46 ff5 fs2 fc2 sc0 ls0 ws0">su<span class="_ _2"></span>pe<span class="_ _2"></span>rio<span class="_ _c"></span>rity<span class="_ _12"> </span>of<span class="_ _8"> </span>T<span class="_ _c"></span>VP-V<span class="_ _b"></span>A<span class="_ _2"></span>R<span class="_ _8"> </span>c<span class="_ _2"></span>on<span class="_ _2"></span>nec<span class="_ _c"></span>tedn<span class="_ _2"></span>es<span class="_ _2"></span>s<span class="_ _8"> </span>e<span class="_ _2"></span>st<span class="_ _2"></span>im<span class="_ _2"></span>ati<span class="_ _c"></span>ons<span class="_ _12"> </span>usin<span class="_ _2"></span>g<span class="_ _8"> </span>t<span class="_ _2"></span>he<span class="_ _12"> </span>exc<span class="_ _2"></span>ha<span class="_ _2"></span>nge<span class="_ _12"> </span>rat<span class="_ _c"></span>e<span class="_ _8"> </span>mar<span class="_ _c"></span>ket<span class="_ _12"> </span>as<span class="_ _8"> </span>a<span class="_ _12"> </span>poin<span class="_ _c"></span>t<span class="_ _8"> </span>of</div><div class="t m1 x1 he y47 ff5 fs2 fc2 sc0 ls0 ws0">r<span class="_ _2"></span>ef<span class="_ _2"></span>er<span class="_ _c"></span>enc<span class="_ _2"></span>e,<span class="_ _4"> </span>wher<span class="_ _c"></span>eas<span class="_"> </span><span class="fc4">Kor<span class="_ _c"></span>obi<span class="_ _2"></span>li<span class="_ _2"></span>s<span class="_ _4"> </span>and<span class="_"> </span>Y<span class="_ _c"></span>ilm<span class="_ _2"></span>az<span class="_"> </span><span class="fc2">(</span>20<span class="_ _2"></span>18<span class="fc2">)<span class="_"> </span>pr<span class="_ _c"></span>ovid<span class="_ _c"></span>ed<span class="_ _5"> </span>si<span class="_ _2"></span>mi<span class="_ _2"></span>la<span class="_ _2"></span>r<span class="_ _4"> </span>evid<span class="_ _2"></span>en<span class="_ _2"></span>ce<span class="_"> </span>by<span class="_ _4"> </span>usin<span class="_ _c"></span>g<span class="_ _5"> </span>the<span class="_"> </span>sto<span class="_ _2"></span>ck<span class="_"> </span>mar<span class="_ _2"></span>ke<span class="_ _2"></span>t</span></span></div><div class="t m1 x1 he y48 ff5 fs2 fc2 sc0 ls0 ws0">as<span class="_ _12"> </span>a<span class="_ _8"> </span>poi<span class="_ _c"></span>nt<span class="_ _8"> </span>of<span class="_ _12"> </span>re<span class="_ _2"></span>fe<span class="_ _2"></span>r<span class="_ _2"></span>enc<span class="_ _c"></span>e.<span class="_ _1a"> </span>The<span class="_ _12"> </span>pr<span class="_ _2"></span>es<span class="_ _2"></span>ent<span class="_ _12"> </span>stu<span class="_ _2"></span>dy<span class="_ _12"> </span>con<span class="_ _2"></span>sti<span class="_ _c"></span>tute<span class="_ _2"></span>s<span class="_ _8"> </span>a<span class="_ _12"> </span>mor<span class="_ _c"></span>e<span class="_ _8"> </span>de<span class="_ _2"></span>tai<span class="_ _2"></span>le<span class="_ _2"></span>d<span class="_ _8"> </span>a<span class="_ _2"></span>nd<span class="_ _12"> </span>comp<span class="_ _2"></span>le<span class="_ _2"></span>te<span class="_ _12"> </span>illu<span class="_ _c"></span>stra<span class="_ _2"></span>ti<span class="_ _2"></span>on</div><div class="t m1 x1 he y49 ff5 fs2 fc2 sc0 ls0 ws0">of<span class="_ _a"> </span>the<span class="_ _a"> </span>ana<span class="_ _2"></span>ly<span class="_ _2"></span>si<span class="_ _2"></span>s<span class="_ _12"> </span>pr<span class="_ _c"></span>ovi<span class="_ _2"></span>ded<span class="_ _a"> </span>by<span class="_ _a"> </span><span class="fc4">Ant<span class="_ _2"></span>on<span class="_ _2"></span>aka<span class="_ _2"></span>ki<span class="_ _2"></span>s<span class="_ _12"> </span>an<span class="_ _2"></span>d<span class="_ _12"> </span>Ga<span class="_ _2"></span>bau<span class="_ _c"></span>er<span class="_ _12"> </span><span class="fc2">(</span>20<span class="_ _c"></span>17<span class="fc2">),<span class="_ _12"> </span>as<span class="_ _12"> </span>th<span class="_ _2"></span>r<span class="_ _2"></span>ee<span class="_ _a"> </span>ro<span class="_ _2"></span>lli<span class="_ _c"></span>ng-w<span class="_ _c"></span>indo<span class="_ _2"></span>w<span class="_ _12"> </span>si<span class="_ _2"></span>ze<span class="_ _2"></span>s<span class="_ _12"> </span>ha<span class="_ _2"></span>ve</span></span></div><div class="t m1 x1 he y4a ff5 fs2 fc2 sc0 ls0 ws0">be<span class="_ _2"></span>en<span class="_ _5"> </span>cho<span class="_ _2"></span>sen<span class="_ _5"> </span>bas<span class="_ _c"></span>ed<span class="_ _6"> </span>up<span class="_ _2"></span>on<span class="_ _5"> </span>the<span class="_ _5"> </span>mea<span class="_ _2"></span>n<span class="_ _6"> </span>ab<span class="_ _2"></span>so<span class="_ _2"></span>lu<span class="_ _2"></span>te<span class="_ _5"> </span>pr<span class="_ _2"></span>edi<span class="_ _c"></span>ctio<span class="_ _2"></span>n<span class="_ _6"> </span>e<span class="_ _2"></span>rr<span class="_ _c"></span>or<span class="_ _0"></span>,<span class="_ _a"> </span>whi<span class="_ _c"></span>ch<span class="_ _6"> </span>is<span class="_ _5"> </span>bet<span class="_ _2"></span>te<span class="_ _2"></span>r<span class="_ _6"> </span>th<span class="_ _2"></span>an<span class="_ _5"> </span>jus<span class="_ _2"></span>t<span class="_ _6"> </span>an<span class="_ _5"> </span>arb<span class="_ _2"></span>it<span class="_ _2"></span>ra<span class="_ _2"></span>ril<span class="_ _c"></span>y</div><div class="t m1 x1 he y4b ff5 fs2 fc2 sc0 ls0 ws0">ch<span class="_ _2"></span>os<span class="_ _2"></span>en<span class="_ _a"> </span>win<span class="_ _2"></span>do<span class="_ _2"></span>w<span class="_ _12"> </span>si<span class="_ _2"></span>ze<span class="_ _2"></span>,<span class="_ _8"> </span>a<span class="_ _2"></span>s<span class="_ _12"> </span>in<span class="_ _a"> </span>th<span class="_ _2"></span>e<span class="_ _12"> </span>or<span class="_ _2"></span>ig<span class="_ _2"></span>ina<span class="_ _c"></span>l<span class="_ _12"> </span>pap<span class="_ _2"></span>er<span class="_ _0"></span>.<span class="_ _19"> </span>Fu<span class="_ _2"></span>rt<span class="_ _2"></span>he<span class="_ _2"></span>rm<span class="_ _2"></span>or<span class="_ _c"></span>e,<span class="_ _8"> </span>we<span class="_ _6"> </span>have<span class="_ _a"> </span>pr<span class="_ _c"></span>ovi<span class="_ _2"></span>de<span class="_ _2"></span>d<span class="_ _12"> </span>a<span class="_ _a"> </span>prio<span class="_ _c"></span>r<span class="_ _12"> </span>sen<span class="_ _2"></span>si<span class="_ _2"></span>tiv<span class="_ _c"></span>ity</div><div class="t m15 x1 he y4c ff5 fs2 fc2 sc0 ls0 ws0">an<span class="_ _2"></span>al<span class="_ _2"></span>ysi<span class="_ _c"></span>s,<span class="_"> </span>un<span class="_ _2"></span>ce<span class="_ _2"></span>rt<span class="_ _2"></span>ai<span class="_ _2"></span>nty<span class="_ _10"> </span>int<span class="_ _2"></span>erv<span class="_ _c"></span>als<span class="_"> </span>f<span class="_ _c"></span>or<span class="_"> </span>al<span class="_ _2"></span>l<span class="_"> </span>c<span class="_ _2"></span>on<span class="_ _2"></span>ne<span class="_ _2"></span>cte<span class="_ _c"></span>dnes<span class="_ _2"></span>s<span class="_"> </span>m<span class="_ _2"></span>ea<span class="_ _2"></span>su<span class="_ _2"></span>re<span class="_ _c"></span>s,<span class="_"> </span>an<span class="_ _2"></span>d<span class="_"> </span>f<span class="_ _2"></span>in<span class="_ _2"></span>al<span class="_ _2"></span>ly<span class="_ _b"></span>,<span class="_"> </span>h<span class="_ _2"></span>av<span class="_ _2"></span>e<span class="_"> </span>e<span class="_ _2"></span>va<span class="_ _2"></span>lua<span class="_ _c"></span>ted<span class="_"> </span>t<span class="_ _2"></span>he<span class="_ _10"> </span>for<span class="_ _c"></span>ecas<span class="_ _c"></span>ting</div><div class="t m1 x1 he y4d ff5 fs2 fc2 sc0 ls0 ws0">pe<span class="_ _2"></span>rf<span class="_ _2"></span>orm<span class="_ _c"></span>ance<span class="_"> </span>o<span class="_ _2"></span>f<span class="_"> </span>the<span class="_"> </span>s<span class="_ _2"></span>ug<span class="_ _2"></span>ge<span class="_ _2"></span>st<span class="_ _2"></span>ed<span class="_"> </span>ap<span class="_ _2"></span>pr<span class="_ _c"></span>oac<span class="_ _2"></span>h.<span class="_ _6"> </span>All<span class="_"> </span>of<span class="_"> </span>t<span class="_ _2"></span>he<span class="_"> </span>ab<span class="_ _c"></span>ove<span class="_"> </span>fu<span class="_ _2"></span>rt<span class="_ _2"></span>her<span class="_"> </span>s<span class="_ _2"></span>tr<span class="_ _c"></span>eng<span class="_ _2"></span>th<span class="_ _2"></span>en<span class="_"> </span>th<span class="_ _c"></span>e<span class="_ _4"> </span>ar<span class="_ _2"></span>gu<span class="_ _2"></span>me<span class="_ _2"></span>nt<span class="_"> </span>in<span class="_"> </span>f<span class="_ _2"></span>av<span class="_ _2"></span>or<span class="_"> </span>of</div><div class="t m1 x1 he y4e ff5 fs2 fc2 sc0 ls0 ws0">TV<span class="_ _2"></span>P-<span class="_ _2"></span>V<span class="_ _b"></span>AR-<span class="_ _2"></span>ge<span class="_ _2"></span>ne<span class="_ _2"></span>rat<span class="_ _c"></span>ed<span class="_ _5"> </span>con<span class="_ _2"></span>ne<span class="_ _2"></span>ct<span class="_ _2"></span>ed<span class="_ _2"></span>nes<span class="_ _c"></span>s<span class="_ _5"> </span>meas<span class="_ _2"></span>ur<span class="_ _c"></span>es.<span class="_ _13"> </span>It<span class="_ _4"> </span>shou<span class="_ _2"></span>ld<span class="_ _4"> </span>als<span class="_ _2"></span>o<span class="_ _5"> </span>be<span class="_ _4"> </span>not<span class="_ _2"></span>ed<span class="_ _4"> </span>that<span class="_ _2"></span>,<span class="_ _5"> </span>des<span class="_ _2"></span>pi<span class="_ _2"></span>te<span class="_ _4"> </span>the<span class="_ _4"> </span>rath<span class="_ _2"></span>er<span class="_ _4"> </span>sca<span class="_ _2"></span>r<span class="_ _2"></span>ce</div><div class="t m8 x1 he y4f ff5 fs2 fc2 sc0 ls0 ws0">li<span class="_ _2"></span>te<span class="_ _2"></span>rat<span class="_ _c"></span>ure<span class="_ _10"> </span>on<span class="_"> </span>T<span class="_ _2"></span>VP<span class="_ _2"></span>-V<span class="_ _b"></span>AR<span class="_ _10"> </span>dyn<span class="_ _2"></span>ami<span class="_ _c"></span>c<span class="_"> </span>con<span class="_ _2"></span>ne<span class="_ _2"></span>ct<span class="_ _2"></span>ed<span class="_ _2"></span>nes<span class="_ _c"></span>s,<span class="_"> </span>st<span class="_ _2"></span>ud<span class="_ _2"></span>ie<span class="_ _2"></span>s<span class="_"> </span>in<span class="_ _10"> </span>thi<span class="_ _2"></span>s<span class="_"> </span>a<span class="_ _2"></span>r<span class="_ _2"></span>ea<span class="_"> </span>h<span class="_ _2"></span>av<span class="_ _2"></span>e<span class="_"> </span>g<span class="_ _2"></span>ra<span class="_ _2"></span>dua<span class="_ _c"></span>lly<span class="_"> </span>s<span class="_ _2"></span>ta<span class="_ _2"></span>rt<span class="_ _2"></span>ed<span class="_"> </span>t<span class="_ _c"></span>o<span class="_"> </span>eme<span class="_ _2"></span>r<span class="_ _2"></span>ge<span class="_"> </span>(see,</div><div class="t m1 x1 he y50 ff5 fs2 fc2 sc0 ls0 ws0">inter<span class="_"> </span>alia,</div><div class="t m7 x11 he y50 ff5 fs2 fc4 sc0 ls0 ws0">Gabauer<span class="_"> </span>and<span class="_"> </span>Gupta<span class="_"> </span>2018<span class="fc2">;<span class="_"> </span></span>Antonakakis<span class="_"> </span>et<span class="_"> </span>al.<span class="_"> </span>2018<span class="fc2">,<span class="_"> </span></span>2019<span class="fc2">,<span class="_"> </span></span>2019a<span class="fc2">,<span class="_"> </span></span>2019b<span class="fc2">;</span></div><div class="t m1 x12 he y50 ff5 fs2 fc4 sc0 ls0 ws0">Chatziantoniou<span class="_"> </span>and</div><div class="t m7 x1 he y51 ff5 fs2 fc4 sc0 ls0 ws0">Gabauer<span class="_"> </span>2019<span class="fc2">),<span class="_"> </span>signifying<span class="_"> </span>a<span class="_"> </span>rather<span class="_"> </span>promising<span class="_"> </span>ar<span class="_ _2"></span>ea<span class="_"> </span>for<span class="_"> </span>future<span class="_"> </span>r<span class="_ _c"></span>esearch.</span></div><div class="t m1 x9 he y52 ff5 fs2 fc2 sc0 ls0 ws0">In<span class="_ _a"> </span>retr<span class="_ _2"></span>ospect,<span class="_ _12"> </span>this<span class="_ _a"> </span>study<span class="_ _a"> </span>contributes<span class="_ _a"> </span>to<span class="_ _a"> </span>the<span class="_ _a"> </span>existing<span class="_ _12"> </span>literature<span class="_ _6"> </span>in<span class="_ _a"> </span>a<span class="_ _a"> </span>number<span class="_ _a"> </span>of<span class="_ _a"> </span>ways.<span class="_ _18"> </span>First,<span class="_ _12"> </span>it</div><div class="t m13 x1 he y53 ff5 fs2 fc2 sc0 ls0 ws0">provides<span class="_"> </span>the<span class="_"> </span>framework<span class="_ _7"> </span>for<span class="_"> </span>generating<span class="_"> </span>r<span class="_ _2"></span>eﬁned<span class="_"> </span>measures<span class="_"> </span>of<span class="_"> </span>connectedness<span class="_"> </span>based<span class="_ _7"> </span>on<span class="_"> </span>a<span class="_"> </span>time-varying</div><div class="t m16 x1 he y54 ff5 fs2 fc2 sc0 ls0 ws0">V<span class="_ _b"></span>AR<span class="_"> </span>modeling<span class="_"> </span>approach.<span class="_ _5"> </span>Second,<span class="_"> </span>it<span class="_"> </span>allows<span class="_"> </span>for<span class="_"> </span>presenting<span class="_"> </span>new<span class="_"> </span>evidence<span class="_"> </span>regar<span class="_ _c"></span>ding<span class="_"> </span>the<span class="_"> </span>exchange-rate</div><div class="t m1 x1 he y55 ff5 fs2 fc2 sc0 ls0 ws0">connectedness<span class="_ _5"> </span>of<span class="_ _5"> </span>some<span class="_ _6"> </span>of<span class="_ _5"> </span>the<span class="_ _5"> </span>most<span class="_ _6"> </span>popular<span class="_ _5"> </span>currencies<span class="_ _5"> </span>of<span class="_ _5"> </span>the<span class="_ _5"> </span>world.<span class="_ _14"> </span>Finally<span class="_ _b"></span>,<span class="_ _6"> </span>it<span class="_ _5"> </span>facilitates<span class="_ _6"> </span>both<span class="_ _5"> </span>the</div><div class="t m1 x1 he y56 ff5 fs2 fc2 sc0 ls0 ws0">introduction<span class="_ _6"> </span>of<span class="_ _a"> </span>alternative<span class="_ _12"> </span>speciﬁcations<span class="_ _a"> </span>of<span class="_ _a"> </span>error<span class="_ _a"> </span>bounds<span class="_ _a"> </span>and<span class="_ _a"> </span>the<span class="_ _a"> </span>implementation<span class="_ _a"> </span>of<span class="_ _12"> </span>a<span class="_ _a"> </span>thorough</div><div class="t m7 x1 he y57 ff5 fs2 fc2 sc0 ls0 ws0">sensitivity<span class="_"> </span>analysis.</div><div class="t m1 x9 he y58 ff5 fs2 fc2 sc0 ls0 ws0">The<span class="_ _6"> </span>remainder<span class="_ _5"> </span>of<span class="_ _6"> </span>this<span class="_ _6"> </span>study<span class="_ _6"> </span>is<span class="_ _6"> </span>organized<span class="_ _6"> </span>as<span class="_ _6"> </span>follows.<span class="_ _16"> </span>In<span class="_ _6"> </span>Section<span class="_ _6"> </span><span class="fc4">2<span class="_ _5"> </span></span>we<span class="_ _6"> </span>describe<span class="_ _6"> </span>our<span class="_ _6"> </span>proposed</div><div class="t m1 x1 he y59 ff5 fs2 fc2 sc0 ls0 ws0">method,<span class="_ _a"> </span>whereas<span class="_ _6"> </span>in<span class="_ _a"> </span>Section<span class="_ _a"> </span><span class="fc4">3<span class="_ _a"> </span></span>we<span class="_ _a"> </span>illustrate<span class="_ _6"> </span>its<span class="_ _a"> </span>advantages<span class="_ _a"> </span>by<span class="_ _a"> </span>applying<span class="_ _6"> </span>Monte<span class="_ _a"> </span>Carlo<span class="_ _a"> </span>simulations.</div><div class="t m1 x1 he y5a ff5 fs2 fc2 sc0 ls0 ws0">In<span class="_ _5"> </span>Section<span class="_ _6"> </span><span class="fc4">4<span class="_ _6"> </span></span>we<span class="_ _5"> </span>provide<span class="_ _5"> </span>a<span class="_ _6"> </span>description<span class="_ _6"> </span>of<span class="_ _5"> </span>the<span class="_ _6"> </span>employed<span class="_ _6"> </span>dataset.<span class="_ _14"> </span>In<span class="_ _6"> </span>Section<span class="_ _5"> </span><span class="fc4">5<span class="_ _6"> </span></span>we<span class="_ _6"> </span>proceed<span class="_ _5"> </span>with<span class="_ _5"> </span>the</div><div class="t m1 x1 he y5b ff5 fs2 fc2 sc0 ls0 ws0">empirical<span class="_ _6"> </span>comparison<span class="_ _6"> </span>between<span class="_ _6"> </span>the<span class="_ _5"> </span>various<span class="_ _6"> </span>connectedness<span class="_ _6"> </span>measures.<span class="_ _16"> </span>Finally<span class="_ _b"></span>,<span class="_ _a"> </span>Section<span class="_ _6"> </span><span class="fc4">6<span class="_ _6"> </span></span>concludes</div><div class="t m7 x1 he y5c ff5 fs2 fc2 sc0 ls0 ws0">the<span class="_"> </span>study<span class="_ _b"></span>.</div><div class="t m7 x1 h7 y6b ff4 fs2 fc2 sc0 ls0 ws0">2.<span class="_ _5"> </span>Methodology</div><div class="t m7 x1 h5 y6c ff3 fs2 fc2 sc0 ls0 ws0">TVP-V<span class="_ _1"></span>AR</div><div class="t m1 x9 he y6d ff5 fs2 fc2 sc0 ls0 ws0">Our<span class="_ _8"> </span>pr<span class="_ _2"></span>oposed<span class="_ _8"> </span>TVP-V<span class="_ _b"></span>AR<span class="_ _8"> </span>method<span class="_ _8"> </span>extends<span class="_ _8"> </span>the<span class="_ _8"> </span>originally<span class="_ _8"> </span>pr<span class="_ _c"></span>oposed<span class="_ _8"> </span>connectedness<span class="_ _8"> </span>approach</div><div class="t m1 x1 he y6e ff5 fs2 fc2 sc0 ls0 ws0">of<span class="_ _a"> </span><span class="fc4">Diebold<span class="_ _12"> </span>and<span class="_ _a"> </span>Yılmaz<span class="_ _12"> </span></span>(<span class="fc4">2014</span>)<span class="_ _a"> </span>by<span class="_ _12"> </span>allowing<span class="_ _a"> </span>the<span class="_ _12"> </span>variance-covariance<span class="_ _a"> </span>matrix<span class="_ _12"> </span>to<span class="_ _a"> </span>vary<span class="_ _12"> </span>via<span class="_ _a"> </span>a<span class="_ _12"> </span>Kalman</div><div class="t m1 x1 he y6f ff5 fs2 fc2 sc0 ls0 ws0">ﬁlter<span class="_"> </span>estimation<span class="_ _4"> </span>with<span class="_ _4"> </span>forgetting<span class="_"> </span>factors<span class="_ _4"> </span>in<span class="_ _5"> </span>the<span class="_"> </span>spirit<span class="_ _4"> </span>of<span class="_ _4"> </span><span class="fc4">Koop<span class="_ _4"> </span>and<span class="_ _4"> </span>Korobilis<span class="_"> </span></span>(<span class="fc4">2014</span>).<span class="_ _12"> </span>By<span class="_"> </span>doing<span class="_ _4"> </span>so,<span class="_ _5"> </span>our</div><div class="t m16 x1 h5 y70 ff5 fs2 fc2 sc0 ls0 ws0">method<span class="_"> </span>(i)<span class="_"> </span><span class="ff3">overcomes<span class="_"> </span>the<span class="_"> </span>burden<span class="_"> </span>of<span class="_"> </span>the<span class="_"> </span>often<span class="_"> </span>arbitrarily<span class="_"> </span>chosen<span class="_"> </span>r<span class="_ _2"></span>olling-window<span class="_"> </span>size<span class="ff5">,<span class="_"> </span>that<span class="_"> </span>could<span class="_"> </span>lead<span class="_"> </span>to<span class="_"> </span>very</span></span></div><div class="t m2 x1 h5 y71 ff5 fs2 fc2 sc0 ls0 ws0">erratic<span class="_"> </span>or<span class="_ _10"> </span>ﬂattened<span class="_"> </span>parameters,<span class="_"> </span>and<span class="_"> </span>(ii)<span class="_ _10"> </span><span class="ff3">avoids<span class="_"> </span>the<span class="_"> </span>loss<span class="_"> </span>of<span class="_ _10"> </span>valuable<span class="_"> </span>observations</span>.<span class="_ _5"> </span>In<span class="_"> </span>this<span class="_"> </span>r<span class="_ _2"></span>espect,<span class="_"> </span>this<span class="_"> </span>method</div><div class="t m4 x1 h5 y72 ff5 fs2 fc2 sc0 ls0 ws0">may<span class="_"> </span>also<span class="_"> </span>be<span class="_"> </span>employed<span class="_"> </span>to<span class="_"> </span>examine<span class="_"> </span>dynamic<span class="_"> </span>connectedness<span class="_"> </span>measur<span class="_ _c"></span>es<span class="_"> </span>for<span class="_"> </span>both<span class="_"> </span><span class="ff3">low-frequency<span class="_"> </span>data<span class="_"> </span></span>and</div><div class="t m1 x1 h5 y73 ff3 fs2 fc2 sc0 ls0 ws0">limited<span class="_ _5"> </span>time-series<span class="_ _6"> </span>data<span class="ff5">.<span class="_ _1b"> </span>Furthermore,<span class="_ _5"> </span><span class="fc4">Koop<span class="_ _6"> </span>and<span class="_ _5"> </span>Korobilis<span class="_ _5"> </span></span>(<span class="fc4">2014</span>)<span class="_ _6"> </span>point<span class="_ _5"> </span>out<span class="_ _6"> </span>that<span class="_ _6"> </span>the<span class="_ _5"> </span>heteroscedastic</span></div><div class="t m7 x1 he y74 ff5 fs2 fc2 sc0 ls0 ws0">procedur<span class="_ _2"></span>e<span class="_"> </span>outperforms<span class="_"> </span>its<span class="_"> </span>homoscedastic<span class="_"> </span>counterpart.</div><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a 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<div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/626432b34c65f41259c17c26/bg4.jpg"><div class="t m7 x1 h12 y38 ff3 fsa fc2 sc0 ls0 ws0">J.<span class="_"> </span>Risk<span class="_"> </span>Financial<span class="_"> </span>Manag.<span class="_"> </span><span class="ff4">2020<span class="ff5">,<span class="_"> </span></span></span>13<span class="ff5">,<span class="_"> </span>84<span class="_ _f"> </span>4<span class="_"> </span>of<span class="_"> </span>23</span></div><div class="t m7 x9 he y39 ff5 fs2 fc2 sc0 ls0 ws0">The<span class="_"> </span>TVP-V<span class="_ _b"></span>AR(p)<span class="_"> </span>model<span class="_"> </span>can<span class="_"> </span>be<span class="_"> </span>written<span class="_"> </span>as<span class="_"> </span>follows:</div><div class="t m7 x13 h13 y75 ff9 fs2 fc2 sc0 ls0 ws0">y</div><div class="t m7 x14 h14 y76 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x15 h15 y75 ffa fsb fc2 sc0 ls0 ws0">=<span class="_ _1c"></span><span class="ff9 fs2">A</span></div><div class="t m7 x16 h14 y76 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x4 h13 y75 ff9 fs2 fc2 sc0 ls0 ws0">z</div><div class="t m7 x17 h16 y77 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 x18 h15 y75 ffa fsb fc2 sc0 ls0 ws0">+<span class="_ _10"> </span><span class="ffc fs2">e</span></div><div class="t m7 x19 h14 y76 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x1a h17 y75 ffc fs2 fc2 sc0 ls0 ws0">e</div><div class="t m7 x1b h14 y76 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x1c h15 y75 ffb fsb fc2 sc0 ls0 ws0">|<span class="ffd fs2">Ω</span></div><div class="t m7 x1d h16 y77 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 x1e h15 y75 ffb fsb fc2 sc0 ls0 ws0">∼<span class="_ _6"> </span><span class="ff3 fs2">N<span class="_ _1c"></span></span><span class="ffa">(<span class="ff4 fs2">0<span class="ff5">,<span class="_ _d"> </span><span class="ffd">Σ</span></span></span></span></div><div class="t m7 x1f h14 y76 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x20 h15 y75 ffa fsb fc2 sc0 ls0 ws0">)<span class="_ _1e"> </span><span class="ff5 fs2">(1)</span></div><div class="t m7 x21 h15 y78 ff3 fs2 fc2 sc0 ls0 ws0">ve<span class="_ _1d"></span>c<span class="_ _1d"></span><span class="ffa fsb">(<span class="_ _1c"></span></span><span class="ff9">A</span></div><div class="t m7 x3 h14 y79 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x22 h15 y78 ffa fsb fc2 sc0 ls0 ws0">)<span class="_ _5"> </span>=<span class="_ _1d"></span><span class="ff3 fs2">v<span class="_ _1d"></span>ec<span class="_ _1d"></span></span>(<span class="_ _1c"></span><span class="ff9 fs2">A</span></div><div class="t m7 x23 h16 y7a ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 x24 h15 y78 ffa fsb fc2 sc0 ls0 ws0">)<span class="_ _10"> </span>+<span class="_ _7"> </span><span class="ffc fs2">ξ</span></div><div class="t m7 x25 h14 y79 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x26 h17 y78 ffc fs2 fc2 sc0 ls0 ws0">ξ</div><div class="t m7 x27 h14 y79 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x1d h15 y78 ffb fsb fc2 sc0 ls0 ws0">|<span class="ffd fs2">Ω</span></div><div class="t m7 x28 h16 y7a ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 x29 h15 y78 ffb fsb fc2 sc0 ls0 ws0">∼<span class="_ _6"> </span><span class="ff3 fs2">N<span class="_ _1c"></span></span><span class="ffa">(<span class="ff4 fs2">0<span class="ff5">,<span class="_ _d"> </span><span class="ffd">Ξ</span></span></span></span></div><div class="t m7 x2a h14 y79 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x2b h15 y78 ffa fsb fc2 sc0 ls0 ws0">)<span class="_ _1f"> </span><span class="ff5 fs2">(2)</span></div><div class="t m7 x1 he y7b ff5 fs2 fc2 sc0 ls0 ws0">with</div><div class="t m7 x2c h13 y7c ff9 fs2 fc2 sc0 ls0 ws0">z</div><div class="t m7 x2d h16 y7d ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 x2e h15 y7c ffa fsb fc2 sc0 ls0 ws0">=</div><div class="t m7 x2f h18 y7e ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x2f h18 y7f ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x2f h18 y80 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x2f h18 y81 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x2f h18 y82 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x2f h18 y83 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x30 h13 y84 ff9 fs2 fc2 sc0 ls0 ws0">y</div><div class="t m7 x31 h16 y85 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 x30 h13 y86 ff9 fs2 fc2 sc0 ls0 ws0">y</div><div class="t m7 x31 h16 y87 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">2</span></div><div class="t m7 x32 he y88 ff5 fs2 fc2 sc0 ls0 ws0">.</div><div class="t m7 x32 he y89 ff5 fs2 fc2 sc0 ls0 ws0">.</div><div class="t m7 x32 he y8a ff5 fs2 fc2 sc0 ls0 ws0">.</div><div class="t m7 x30 h13 y8b ff9 fs2 fc2 sc0 ls0 ws0">y</div><div class="t m7 x31 h16 y8c ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1c"></span></span>p</div><div class="t m7 x33 h18 y7e ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x33 h18 y7f ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x33 h18 y80 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x33 h18 y81 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x33 h18 y82 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x33 h18 y83 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x34 h13 y7c ff9 fs2 fc2 sc0 ls0 ws0">A</div><div class="t m7 x6 h16 y8d ffb fsc fc2 sc0 ls0 ws0">0</div><div class="t m7 x6 h14 y8e ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x35 h15 y7c ffa fsb fc2 sc0 ls0 ws0">=</div><div class="t m7 x36 h18 y8f ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x36 h18 y90 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x36 h18 y91 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x36 h18 y92 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x36 h18 y93 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x37 h13 y94 ff9 fs2 fc2 sc0 ls0 ws0">A</div><div class="t m7 x38 h14 y95 ff5 fs4 fc2 sc0 ls0 ws0">1<span class="ff3">t</span></div><div class="t m7 x37 h13 y96 ff9 fs2 fc2 sc0 ls0 ws0">A</div><div class="t m7 x38 h14 y97 ff5 fs4 fc2 sc0 ls0 ws0">2<span class="ff3">t</span></div><div class="t m7 x1c he y98 ff5 fs2 fc2 sc0 ls0 ws0">.<span class="_ _d"> </span>.<span class="_ _10"> </span>.</div><div class="t m7 x37 h13 y99 ff9 fs2 fc2 sc0 ls0 ws0">A</div><div class="t m7 x38 h14 y9a ff3 fs4 fc2 sc0 ls0 ws0">pt</div><div class="t m7 x39 h18 y8f ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x39 h18 y90 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x39 h18 y91 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x39 h18 y92 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x39 h18 y93 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m1 x1 he y9b ff5 fs2 fc2 sc0 ls0 ws0">where</div><div class="t m7 x3a h19 y9b ffd fs2 fc2 sc0 ls0 ws0">Ω</div><div class="t m7 x3b h16 y9c ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m1 x3c he y9b ff5 fs2 fc2 sc0 ls0 ws0">repr<span class="_ _2"></span>esents<span class="_ _4"> </span>all<span class="_ _5"> </span>information<span class="_ _5"> </span>available<span class="_ _5"> </span>until<span class="_ _5"> </span>t-1,</div><div class="t m7 x3d h13 y9b ff9 fs2 fc2 sc0 ls0 ws0">y</div><div class="t m7 x1a h14 y9d ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m1 x37 he y9b ff5 fs2 fc2 sc0 ls0 ws0">and</div><div class="t m7 x3e h13 y9b ff9 fs2 fc2 sc0 ls0 ws0">z</div><div class="t m7 x3f h16 y9c ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m1 x40 he y9b ff5 fs2 fc2 sc0 ls0 ws0">repr<span class="_ _2"></span>esents</div><div class="t m7 x41 h15 y9b ff3 fs2 fc2 sc0 ls0 ws0">m<span class="_"> </span><span class="ffb fsb">×</span></div><div class="t m1 x42 he y9b ff5 fs2 fc2 sc0 ls0 ws0">1<span class="_ _5"> </span>and</div><div class="t m7 x43 h15 y9b ff3 fs2 fc2 sc0 ls0 ws0">m<span class="_ _1c"></span>p<span class="_"> </span><span class="ffb fsb">×</span></div><div class="t m1 x44 he y9b ff5 fs2 fc2 sc0 ls0 ws0">1</div><div class="t m1 x1 he y9e ff5 fs2 fc2 sc0 ls0 ws0">vectors,<span class="_"> </span>respectively<span class="_ _0"></span>,</div><div class="t m7 x45 h13 y9e ff9 fs2 fc2 sc0 ls0 ws0">A</div><div class="t m7 x46 h14 y9f ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m1 x22 he y9e ff5 fs2 fc2 sc0 ls0 ws0">and</div><div class="t m7 x47 h13 y9e ff9 fs2 fc2 sc0 ls0 ws0">A</div><div class="t m7 x48 h14 ya0 ff3 fs4 fc2 sc0 ls0 ws0">it</div><div class="t m1 x49 he y9e ff5 fs2 fc2 sc0 ls0 ws0">are</div><div class="t m7 x4a h15 y9e ff3 fs2 fc2 sc0 ls0 ws0">m<span class="_"> </span><span class="ffb fsb">×<span class="_ _10"> </span></span>m<span class="_ _1c"></span>p</div><div class="t m1 x4b he y9e ff5 fs2 fc2 sc0 ls0 ws0">and</div><div class="t m7 x4c h15 y9e ff3 fs2 fc2 sc0 ls0 ws0">m<span class="_"> </span><span class="ffb fsb">×<span class="_ _10"> </span></span>m</div><div class="t m1 x4d he y9e ff5 fs2 fc2 sc0 ls0 ws0">dimensional<span class="_"> </span>matrices,<span class="_ _5"> </span>respectively<span class="_ _b"></span>,</div><div class="t m7 x4e h17 y9e ffc fs2 fc2 sc0 ls0 ws0">e</div><div class="t m7 x4f h14 y9f ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m1 x50 he y9e ff5 fs2 fc2 sc0 ls0 ws0">is<span class="_"> </span>an</div><div class="t m7 x1 h15 ya1 ff3 fs2 fc2 sc0 ls0 ws0">m<span class="_ _10"> </span><span class="ffb fsb">×</span></div><div class="t m1e x51 he ya1 ff5 fs2 fc2 sc0 ls0 ws0">1<span class="_"> </span>vector<span class="_ _c"></span>,<span class="_"> </span>and</div><div class="t m7 x10 h17 ya1 ffc fs2 fc2 sc0 ls0 ws0">ξ</div><div class="t m7 x52 h14 ya2 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m1e x53 he ya1 ff5 fs2 fc2 sc0 ls0 ws0">is<span class="_"> </span>an</div><div class="t m7 x54 h5 ya1 ff3 fs2 fc2 sc0 ls0 ws0">m</div><div class="t m7 x16 hf ya3 ff5 fs4 fc2 sc0 ls0 ws0">2</div><div class="t m7 x55 h15 ya1 ff3 fs2 fc2 sc0 ls0 ws0">p<span class="_ _10"> </span><span class="ffb fsb">×</span></div><div class="t m1e x56 he ya1 ff5 fs2 fc2 sc0 ls0 ws0">1<span class="_"> </span>dimensional<span class="_"> </span>vector<span class="_ _c"></span>,<span class="_"> </span>wher<span class="_ _2"></span>eas<span class="_"> </span>the<span class="_"> </span>time-varying<span class="_"> </span>variance-covariance</div><div class="t m2 x1 he ya4 ff5 fs2 fc2 sc0 ls0 ws0">matrices</div><div class="t m7 x3b h19 ya4 ffd fs2 fc2 sc0 ls0 ws0">Σ</div><div class="t m7 x57 h14 ya5 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m2 x58 he ya4 ff5 fs2 fc2 sc0 ls0 ws0">and</div><div class="t m7 x59 h19 ya4 ffd fs2 fc2 sc0 ls0 ws0">Ξ</div><div class="t m7 x5a h14 ya5 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m2 x5b he ya4 ff5 fs2 fc2 sc0 ls0 ws0">are</div><div class="t m7 x5c h15 ya4 ff3 fs2 fc2 sc0 ls0 ws0">m<span class="_ _10"> </span><span class="ffb fsb">×<span class="_ _7"> </span></span>m</div><div class="t m2 x47 he ya4 ff5 fs2 fc2 sc0 ls0 ws0">and</div><div class="t m7 x5d h5 ya4 ff3 fs2 fc2 sc0 ls0 ws0">m</div><div class="t m7 x5e hf ya6 ff5 fs4 fc2 sc0 ls0 ws0">2</div><div class="t m7 x4a h15 ya4 ff3 fs2 fc2 sc0 ls0 ws0">p<span class="_ _10"> </span><span class="ffb fsb">×<span class="_ _7"> </span></span>m</div><div class="t m7 x5f hf ya6 ff5 fs4 fc2 sc0 ls0 ws0">2</div><div class="t m7 x60 h5 ya4 ff3 fs2 fc2 sc0 ls0 ws0">p</div><div class="t m2 x4b he ya4 ff5 fs2 fc2 sc0 ls0 ws0">dimensional<span class="_"> </span>matrices,<span class="_"> </span>respectively<span class="_ _b"></span>.<span class="_ _5"> </span>Moreover<span class="_ _0"></span>,</div><div class="t m7 x61 h15 ya4 ff3 fs2 fc2 sc0 ls0 ws0">ve<span class="_ _1d"></span>c<span class="_ _1d"></span><span class="ffa fsb">(<span class="_ _1c"></span></span><span class="ff9">A</span></div><div class="t m7 x62 h14 ya5 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x63 h15 ya4 ffa fsb fc2 sc0 ls0 ws0">)</div><div class="t m2 x64 he ya4 ff5 fs2 fc2 sc0 ls0 ws0">is</div><div class="t m7 x1 he ya7 ff5 fs2 fc2 sc0 ls0 ws0">the<span class="_"> </span>vectorisation<span class="_"> </span>of<span class="_ _5"> </span><span class="ff9">A</span></div><div class="t m7 x65 h14 ya8 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x66 h5 ya7 ff5 fs2 fc2 sc0 ls0 ws0">which<span class="_"> </span>is<span class="_"> </span>an<span class="_"> </span><span class="ff3">m</span></div><div class="t m7 x67 hf ya9 ff5 fs4 fc2 sc0 ls0 ws0">2</div><div class="t m7 x68 h15 ya7 ff3 fs2 fc2 sc0 ls0 ws0">p<span class="_ _10"> </span><span class="ffb fsb">×<span class="_ _7"> </span></span><span class="ff5">1<span class="_"> </span>dimensional<span class="_"> </span>vector<span class="_ _c"></span>.</span></div><div class="t m1 x9 he yaa ff5 fs2 fc2 sc0 ls0 ws0">For<span class="_ _20"> </span>the<span class="_ _20"> </span>initialization<span class="_ _20"> </span>of<span class="_ _20"> </span>the<span class="_ _20"> </span>Kalman<span class="_ _20"> </span>ﬁlter<span class="_ _c"></span>,<span class="_ _21"> </span>we<span class="_ _20"> </span>used<span class="_ _20"> </span>the<span class="_ _20"> </span><span class="fc4">Primiceri<span class="_ _20"> </span></span>(<span class="fc4">2005</span>)<span class="_ _20"> </span>and</div><div class="t m7 x1 he yab ff5 fs2 fc4 sc0 ls0 ws0">Del<span class="_"> </span>Negro<span class="_"> </span>and<span class="_"> </span>Primiceri<span class="_"> </span><span class="fc2">(</span>2015<span class="fc2">)</span></div><div class="t m1 x56 he yab ff5 fs2 fc2 sc0 ls0 ws0">prior<span class="_ _c"></span>.<span class="_ _21"> </span>Hence,<span class="_ _16"> </span>in<span class="_ _1b"> </span>our<span class="_ _1b"> </span>study<span class="_ _0"></span>,<span class="_ _16"> </span>we<span class="_ _1b"> </span>set</div><div class="t m7 x69 h13 yab ff9 fs2 fc2 sc0 ls0 ws0">A</div><div class="t m7 x6a h14 yac ff3 fs4 fc2 sc0 ls0 ws0">O<span class="_ _1d"></span>L<span class="_ _1d"></span>S</div><div class="t m1 x6b he yab ff5 fs2 fc2 sc0 ls0 ws0">,</div><div class="t m7 x12 h19 yab ffd fs2 fc2 sc0 ls0 ws0">Σ</div><div class="t m7 x6c h14 yad ff3 fs4 fc2 sc0 ls0 ws0">A</div><div class="t m7 x2b h14 yae ff3 fs4 fc2 sc0 ls0 ws0">O<span class="_ _1d"></span>L<span class="_ _1d"></span>S</div><div class="t m1 x6d he yab ff5 fs2 fc2 sc0 ls0 ws0">,<span class="_ _9"> </span>and</div><div class="t m7 x6e h19 yab ffd fs2 fc2 sc0 ls0 ws0">Σ</div><div class="t m7 x43 h14 yac ff3 fs4 fc2 sc0 ls0 ws0">O<span class="_ _1d"></span>L<span class="_ _1d"></span>S</div><div class="t m1 x6f he yab ff5 fs2 fc2 sc0 ls0 ws0">as</div><div class="t m7 x1 he yaf ff5 fs2 fc2 sc0 ls0 ws0">equal<span class="_"> </span>to<span class="_"> </span>the<span class="_"> </span>V<span class="_ _b"></span>AR<span class="_"> </span>estimation<span class="_"> </span>results<span class="_"> </span>of<span class="_"> </span>the<span class="_"> </span>ﬁrst<span class="_"> </span>60<span class="_"> </span>months:</div><div class="t m7 x70 h15 yb0 ff3 fs2 fc2 sc0 ls0 ws0">ve<span class="_ _1d"></span>c<span class="_ _1d"></span><span class="ffa fsb">(<span class="_ _1c"></span></span><span class="ff9">A</span></div><div class="t m7 x71 hf yb1 ff5 fs4 fc2 sc0 ls0 ws0">0</div><div class="t m7 x72 h15 yb0 ffa fsb fc2 sc0 ls0 ws0">)<span class="_ _5"> </span><span class="ffb">∼<span class="_ _1c"></span><span class="ff3 fs2">N<span class="_ _1d"></span></span></span>(<span class="_ _1d"></span><span class="ff3 fs2">v<span class="_ _1d"></span>e<span class="_ _1d"></span>c<span class="_ _1d"></span></span>(<span class="_ _1c"></span><span class="ff9 fs2">A</span></div><div class="t m7 x34 h14 yb2 ff3 fs4 fc2 sc0 ls0 ws0">O<span class="_ _1d"></span>L<span class="_ _1d"></span>S</div><div class="t m7 x73 h15 yb0 ffa fsb fc2 sc0 ls0 ws0">)<span class="ff5 fs2">,<span class="_ _d"> </span><span class="ffd">Σ</span></span></div><div class="t m7 x74 h14 yb3 ff3 fs4 fc2 sc0 ls0 ws0">A</div><div class="t m7 x74 h14 yb4 ff3 fs4 fc2 sc0 ls0 ws0">O<span class="_ _1d"></span>L<span class="_ _1d"></span>S</div><div class="t m7 x75 h15 yb0 ffa fsb fc2 sc0 ls0 ws0">)</div><div class="t m7 x76 h19 yb5 ffd fs2 fc2 sc0 ls0 ws0">Σ</div><div class="t m7 x72 hf yb6 ff5 fs4 fc2 sc0 ls0 ws0">0</div><div class="t m7 x77 h15 yb5 ffa fsb fc2 sc0 ls0 ws0">=<span class="ffd fs2">Σ</span></div><div class="t m7 x78 h14 yb7 ff3 fs4 fc2 sc0 ls0 ws0">O<span class="_ _1d"></span>L<span class="_ _1d"></span>S</div><div class="t m7 x79 he yb5 ff5 fs2 fc2 sc0 ls0 ws0">.</div><div class="t m6 x9 he yb8 ff5 fs2 fc2 sc0 ls0 ws0">In<span class="_"> </span>the<span class="_"> </span>interests<span class="_"> </span>of<span class="_"> </span>numerical<span class="_"> </span>stability<span class="_ _b"></span>,<span class="_"> </span>we<span class="_"> </span>implement<span class="_"> </span>decay<span class="_"> </span>factors<span class="_"> </span>in<span class="_"> </span>the<span class="_"> </span>Kalman<span class="_"> </span>ﬁlter<span class="_"> </span>algorithm.</div><div class="t m1 x1 he yb9 ff5 fs2 fc2 sc0 ls0 ws0">the<span class="_ _4"> </span>choice<span class="_ _5"> </span>of<span class="_ _4"> </span>decay<span class="_ _5"> </span>factors<span class="_ _4"> </span>resembles<span class="_ _4"> </span>the<span class="_ _5"> </span>choice<span class="_ _4"> </span>of<span class="_ _5"> </span>priors<span class="_ _4"> </span>in<span class="_ _5"> </span>general,<span class="_ _5"> </span>and<span class="_"> </span>depends<span class="_ _5"> </span>on<span class="_ _4"> </span>the<span class="_ _5"> </span>expected</div><div class="t m1 x1 he yba ff5 fs2 fc2 sc0 ls0 ws0">amount<span class="_"> </span>of<span class="_"> </span>time<span class="_"> </span>variation<span class="_"> </span>in<span class="_"> </span>the<span class="_"> </span>parameters.<span class="_ _5"> </span>In<span class="_"> </span>this<span class="_"> </span>study<span class="_ _0"></span>,<span class="_"> </span>we<span class="_"> </span>consider<span class="_"> </span>the<span class="_"> </span>benchmark<span class="_"> </span>values<span class="_"> </span>for</div><div class="t m7 x6f h1a yba fff fs2 fc2 sc0 ls0 ws0">κ</div><div class="t m7 x7a hf ybb ff5 fs4 fc2 sc0 ls0 ws0">1</div><div class="t m9 x1 he ybc ff5 fs2 fc2 sc0 ls0 ws0">and</div><div class="t m7 x7b h1a ybc fff fs2 fc2 sc0 ls0 ws0">κ</div><div class="t m7 x7c hf ybd ff5 fs4 fc2 sc0 ls0 ws0">2</div><div class="t m9 x3a he ybc ff5 fs2 fc2 sc0 ls0 ws0">provided<span class="_"> </span>by<span class="_"> </span>the<span class="_"> </span><span class="fc4">Koop<span class="_"> </span>and<span class="_"> </span>Kor<span class="_ _2"></span>obilis<span class="_"> </span><span class="fc2">(</span>2014<span class="fc2">)<span class="_"> </span>study<span class="_ _b"></span>,<span class="_"> </span>according<span class="_"> </span>to<span class="_"> </span>which</span></span></div><div class="t m7 x7 h1a ybc fff fs2 fc2 sc0 ls0 ws0">κ</div><div class="t m7 x6b hf ybe ff5 fs4 fc2 sc0 ls0 ws0">1</div><div class="t m7 x7d h15 ybc ffa fsb fc2 sc0 ls0 ws0">=</div><div class="t m9 x7e he ybc ff5 fs2 fc2 sc0 ls0 ws0">0.99<span class="_"> </span>and</div><div class="t m7 x7f h1a ybc fff fs2 fc2 sc0 ls0 ws0">κ</div><div class="t m7 x6e hf ybd ff5 fs4 fc2 sc0 ls0 ws0">2</div><div class="t m7 x80 h15 ybc ffa fsb fc2 sc0 ls0 ws0">=</div><div class="t m9 x81 he ybc ff5 fs2 fc2 sc0 ls0 ws0">0.96.</div><div class="t m15 x1 he ybf ff5 fs2 fc2 sc0 ls0 ws0">It<span class="_"> </span>should<span class="_"> </span>also<span class="_"> </span>be<span class="_"> </span>stressed<span class="_"> </span>that<span class="_"> </span>even<span class="_"> </span>though<span class="_"> </span>estimation<span class="_"> </span>procedur<span class="_ _2"></span>es<span class="_"> </span>are<span class="_"> </span>available<span class="_"> </span>which<span class="_"> </span>allow<span class="_"> </span>the<span class="_"> </span>decay</div><div class="t m1 x1 he yc0 ff5 fs2 fc2 sc0 ls0 ws0">factors<span class="_ _5"> </span>to<span class="_ _5"> </span>vary<span class="_ _6"> </span>over<span class="_ _5"> </span>time,<span class="_ _6"> </span>we<span class="_ _5"> </span>keep<span class="_ _5"> </span>them<span class="_ _5"> </span>constant<span class="_ _6"> </span>at<span class="_ _5"> </span>ﬁxed<span class="_ _5"> </span>values,<span class="_ _6"> </span>since<span class="_ _5"> </span><span class="fc4">Koop<span class="_ _6"> </span>and<span class="_ _5"> </span>Korobilis<span class="_ _5"> </span></span>(<span class="fc4">2013</span>)</div><div class="t m15 x1 he yc1 ff5 fs2 fc2 sc0 ls0 ws0">found<span class="_"> </span>that<span class="_"> </span>the<span class="_"> </span>value<span class="_"> </span>added<span class="_"> </span>by<span class="_"> </span>time-varying<span class="_"> </span>decay<span class="_"> </span>factors<span class="_"> </span>with<span class="_ _4"> </span>respect<span class="_"> </span>to<span class="_"> </span>the<span class="_"> </span>forecasting<span class="_"> </span>performance</div><div class="t m1a x1 he yc2 ff5 fs2 fc2 sc0 ls0 ws0">was<span class="_"> </span>questionable<span class="_"> </span>and<span class="_"> </span>increased<span class="_"> </span>the<span class="_ _7"> </span>computation<span class="_"> </span>burden<span class="_"> </span>of<span class="_"> </span>the<span class="_"> </span>Kalman<span class="_ _7"> </span>ﬁlter<span class="_"> </span>algorithm<span class="_"> </span>signiﬁcantly<span class="_ _b"></span>.</div><div class="t m7 x1 he yc3 ff5 fs2 fc2 sc0 ls0 ws0">In<span class="_"> </span>turn,<span class="_"> </span>the<span class="_"> </span>multivariate<span class="_"> </span>Kalman<span class="_"> </span>ﬁlter<span class="_"> </span>can<span class="_"> </span>be<span class="_"> </span>formulated<span class="_"> </span>as<span class="_"> </span>follows:</div><div class="t m7 x82 h15 yc4 ff3 fs2 fc2 sc0 ls0 ws0">ve<span class="_ _1d"></span>c<span class="_ _1d"></span><span class="ffa fsb">(<span class="_ _1c"></span></span><span class="ff9">A</span></div><div class="t m7 x5e h14 yc5 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x19 h15 yc4 ffa fsb fc2 sc0 ls0 ws0">)<span class="ffb">|<span class="_ _1d"></span><span class="ff9 fs2">z</span></span></div><div class="t m7 x83 h16 yc6 ff5 fs4 fc2 sc0 ls0 ws0">1:<span class="_ _1d"></span><span class="ff3">t<span class="ffb fsc">−<span class="_ _1d"></span></span></span>1</div><div class="t m7 x84 h15 yc4 ffb fsb fc2 sc0 ls0 ws0">∼<span class="_ _1c"></span><span class="ff3 fs2">N<span class="_ _1d"></span></span><span class="ffa">(<span class="_ _1d"></span><span class="ff3 fs2">v<span class="_ _1d"></span>e<span class="_ _1d"></span>c<span class="_ _1d"></span></span>(<span class="_ _1c"></span><span class="ff9 fs2">A</span></span></div><div class="t m7 x85 h16 yc7 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t<span class="_ _1d"></span><span class="ffb fsc">−</span><span class="ff5">1</span></div><div class="t m7 x3d h15 yc4 ffa fsb fc2 sc0 ls0 ws0">)<span class="ff5 fs2">,<span class="_ _d"> </span><span class="ffd">Σ</span></span></div><div class="t m7 x86 h14 yc8 ff3 fs4 fc2 sc0 ls0 ws0">A</div><div class="t m7 x86 h16 yc9 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t<span class="_ _1d"></span><span class="ffb fsc">−</span><span class="ff5">1</span></div><div class="t m7 x87 h15 yc4 ffa fsb fc2 sc0 ls0 ws0">)</div><div class="t m7 x68 h13 yca ff9 fs2 fc2 sc0 ls0 ws0">A</div><div class="t m7 x88 h16 ycb ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t<span class="_ _1d"></span><span class="ffb fsc">−</span><span class="ff5">1</span></div><div class="t m7 x84 h15 yca ffa fsb fc2 sc0 ls0 ws0">=<span class="_ _1c"></span><span class="ff9 fs2">A</span></div><div class="t m7 x89 h16 ycb ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1<span class="ffb fsc">|<span class="_ _1d"></span></span></span>t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 x8a h17 ycc ffc fs2 fc2 sc0 ls0 ws0">e</div><div class="t m7 x30 h14 ycd ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x84 h15 ycc ffa fsb fc2 sc0 ls0 ws0">=<span class="ff9 fs2">y</span></div><div class="t m7 x8b h14 ycd ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x8c h15 ycc ffb fsb fc2 sc0 ls0 ws0">−<span class="_ _4"> </span><span class="ff9 fs2">A</span></div><div class="t m7 x8d h16 yce ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t<span class="_ _1d"></span><span class="ffb fsc">−</span><span class="ff5">1</span></div><div class="t m7 x4d h13 ycc ff9 fs2 fc2 sc0 ls0 ws0">z</div><div class="t m7 x8e h16 ycf ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 x8f h19 yd0 ffd fs2 fc2 sc0 ls0 ws0">Σ</div><div class="t m7 x30 h14 yd1 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x84 h15 yd0 ffa fsb fc2 sc0 ls0 ws0">=<span class="fff fs2">κ</span></div><div class="t m7 x33 hf yd2 ff5 fs4 fc2 sc0 ls0 ws0">2</div><div class="t m7 x90 h19 yd0 ffd fs2 fc2 sc0 ls0 ws0">Σ</div><div class="t m7 x4c h16 yd3 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1<span class="ffb fsc">|<span class="_ _1d"></span></span></span>t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 x4d h15 yd0 ffa fsb fc2 sc0 ls0 ws0">+<span class="_ _10"> </span>(<span class="_ _1d"></span><span class="ff5 fs2">1<span class="_ _10"> </span></span><span class="ffb">−<span class="_ _7"> </span><span class="fff fs2">κ</span></span></div><div class="t m7 x1d hf yd2 ff5 fs4 fc2 sc0 ls0 ws0">2</div><div class="t m7 x91 h15 yd0 ffa fsb fc2 sc0 ls0 ws0">)<span class="ffc fs2">e</span></div><div class="t m7 x92 h16 yd4 ffb fsc fc2 sc0 ls0 ws0">0</div><div class="t m7 x92 h14 yd5 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x93 h17 yd0 ffc fs2 fc2 sc0 ls0 ws0">e</div><div class="t m7 x94 h14 yd1 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x8f h19 yd6 ffd fs2 fc2 sc0 ls0 ws0">Ξ</div><div class="t m7 x30 h14 yd7 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x84 h15 yd6 ffa fsb fc2 sc0 ls0 ws0">=(<span class="_ _1d"></span><span class="ff5 fs2">1<span class="_ _10"> </span></span><span class="ffb">−<span class="_ _7"> </span><span class="fff fs2">κ</span></span></div><div class="t m7 x95 h16 yd8 ffb fsc fc2 sc0 ls0 ws0">−<span class="ff5 fs4">1</span></div><div class="t m7 x95 hf yd9 ff5 fs4 fc2 sc0 ls0 ws0">1</div><div class="t m7 x96 h15 yd6 ffa fsb fc2 sc0 ls0 ws0">)<span class="ffd fs2">Σ</span></div><div class="t m7 x35 h14 yd8 ff3 fs4 fc2 sc0 ls0 ws0">A</div><div class="t m7 x35 h16 yda ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1<span class="ffb fsc">|<span class="_ _1d"></span></span></span>t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 x68 h19 ydb ffd fs2 fc2 sc0 ls0 ws0">Σ</div><div class="t m7 x88 h14 ydc ff3 fs4 fc2 sc0 ls0 ws0">A</div><div class="t m7 x88 h16 ydd ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t<span class="_ _1d"></span><span class="ffb fsc">−</span><span class="ff5">1</span></div><div class="t m7 x84 h15 ydb ffa fsb fc2 sc0 ls0 ws0">=<span class="ffd fs2">Σ</span></div><div class="t m7 x97 h14 ydc ff3 fs4 fc2 sc0 ls0 ws0">A</div><div class="t m7 x97 h16 ydd ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1<span class="ffb fsc">|<span class="_ _1d"></span></span></span>t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 x96 h15 ydb ffa fsb fc2 sc0 ls0 ws0">+<span class="_ _10"> </span><span class="ffd fs2">Ξ</span></div><div class="t m7 x98 h14 yde ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x68 h19 ydf ffd fs2 fc2 sc0 ls0 ws0">Σ</div><div class="t m7 x88 h16 ye0 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t<span class="_ _1d"></span><span class="ffb fsc">−</span><span class="ff5">1</span></div><div class="t m7 x84 h15 ydf ffa fsb fc2 sc0 ls0 ws0">=<span class="ff9 fs2">z</span></div><div class="t m7 x8b h16 ye1 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 x79 h19 ydf ffd fs2 fc2 sc0 ls0 ws0">Σ</div><div class="t m7 x99 h14 ye2 ff3 fs4 fc2 sc0 ls0 ws0">A</div><div class="t m7 x99 h16 ye3 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t<span class="_ _1d"></span><span class="ffb fsc">−</span><span class="ff5">1</span></div><div class="t m7 x6 h13 ydf ff9 fs2 fc2 sc0 ls0 ws0">z</div><div class="t m7 x35 h16 ye2 ffb fsc fc2 sc0 ls0 ws0">0</div><div class="t m7 x35 h16 ye4 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 x9a h15 ydf ffa fsb fc2 sc0 ls0 ws0">+<span class="_ _10"> </span><span class="ffd fs2">Σ</span></div><div class="t m7 x75 h14 ye5 ff3 fs4 fc2 sc0 ls0 ws0">t</div><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>

<div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/626432b34c65f41259c17c26/bg5.jpg"><div class="t m7 x1 h12 y38 ff3 fsa fc2 sc0 ls0 ws0">J.<span class="_"> </span>Risk<span class="_"> </span>Financial<span class="_"> </span>Manag.<span class="_"> </span><span class="ff4">2020<span class="ff5">,<span class="_"> </span></span></span>13<span class="ff5">,<span class="_"> </span>84<span class="_ _f"> </span>5<span class="_"> </span>of<span class="_"> </span>23</span></div><div class="t m7 x9 he y39 ff5 fs2 fc2 sc0 ls0 ws0">W<span class="_ _0"></span>e<span class="_"> </span>updated<span class="_ _5"> </span><span class="ff9">A</span></div><div class="t m7 x9b h14 ye6 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x9c he y39 ff5 fs2 fc2 sc0 ls0 ws0">,<span class="_"> </span><span class="ffd">Σ</span></div><div class="t m7 x66 h14 ye7 ff3 fs4 fc2 sc0 ls0 ws0">A</div><div class="t m7 x66 h14 ye8 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x9d he y39 ff5 fs2 fc2 sc0 ls0 ws0">,<span class="_"> </span>and<span class="_"> </span><span class="ffd">Σ</span></div><div class="t m7 x9e h14 ye6 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x9f h5 y39 ff5 fs2 fc2 sc0 ls0 ws0">,<span class="_"> </span>given<span class="_"> </span>the<span class="_"> </span>information<span class="_"> </span>at<span class="_"> </span>time<span class="_"> </span><span class="ff3">t</span>,<span class="_"> </span>by<span class="_"> </span>the<span class="_"> </span>following<span class="_"> </span>steps:</div><div class="t m7 x17 h15 y75 ff3 fs2 fc2 sc0 ls0 ws0">ve<span class="_ _1d"></span>c<span class="_ _1d"></span><span class="ffa fsb">(<span class="_ _1c"></span></span><span class="ff9">A</span></div><div class="t m7 x70 h14 y76 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 xa0 h15 y75 ffa fsb fc2 sc0 ls0 ws0">)<span class="ffb">|<span class="_ _1d"></span><span class="ff9 fs2">z</span></span></div><div class="t m7 xa1 h14 y77 ff5 fs4 fc2 sc0 ls0 ws0">1:<span class="_ _1d"></span><span class="ff3">t</span></div><div class="t m7 x8f h15 y75 ffb fsb fc2 sc0 ls0 ws0">∼<span class="_ _1c"></span><span class="ff3 fs2">N<span class="_ _1d"></span></span><span class="ffa">(<span class="_ _1d"></span><span class="ff3 fs2">v<span class="_ _1d"></span>e<span class="_ _1d"></span>c<span class="_ _1d"></span></span>(<span class="_ _1c"></span><span class="ff9 fs2">A</span></span></div><div class="t m7 x95 h16 ye9 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t</div><div class="t m7 xa2 h15 y75 ffa fsb fc2 sc0 ls0 ws0">)<span class="ff5 fs2">,<span class="_ _d"> </span><span class="ffd">Σ</span></span></div><div class="t m7 x73 h14 yea ff3 fs4 fc2 sc0 ls0 ws0">A</div><div class="t m7 xa3 h16 yeb ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t</div><div class="t m7 xa4 h15 y75 ffa fsb fc2 sc0 ls0 ws0">)</div><div class="t m7 xa5 h13 yec ff9 fs2 fc2 sc0 ls0 ws0">K</div><div class="t m7 xa6 h14 yed ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x8f h15 yec ffa fsb fc2 sc0 ls0 ws0">=<span class="ffd fs2">Σ</span></div><div class="t m7 xa7 h14 yee ff3 fs4 fc2 sc0 ls0 ws0">A</div><div class="t m7 xa7 h16 yef ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t<span class="_ _1d"></span><span class="ffb fsc">−</span><span class="ff5">1</span></div><div class="t m7 xa8 h13 yec ff9 fs2 fc2 sc0 ls0 ws0">z</div><div class="t m7 xa9 h16 yee ffb fsc fc2 sc0 ls0 ws0">0</div><div class="t m7 xa9 h16 yf0 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 xaa h19 yec ffd fs2 fc2 sc0 ls0 ws0">Σ</div><div class="t m7 x85 h16 yee ffb fsc fc2 sc0 ls0 ws0">−<span class="ff5 fs4">1</span></div><div class="t m7 x85 h16 yf1 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t<span class="_ _1d"></span><span class="ffb fsc">−</span><span class="ff5">1</span></div><div class="t m7 x24 h13 yf2 ff9 fs2 fc2 sc0 ls0 ws0">A</div><div class="t m7 xab h16 yf3 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t</div><div class="t m7 x8f h15 yf2 ffa fsb fc2 sc0 ls0 ws0">=<span class="_ _1c"></span><span class="ff9 fs2">A</span></div><div class="t m7 xac h16 yf3 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t<span class="_ _1d"></span><span class="ffb fsc">−</span><span class="ff5">1</span></div><div class="t m7 x4c h15 yf2 ffa fsb fc2 sc0 ls0 ws0">+<span class="_ _10"> </span><span class="ff9 fs2">K</span></div><div class="t m7 xad h14 yf4 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x5 h15 yf2 ffa fsb fc2 sc0 ls0 ws0">(<span class="ff9 fs2">y</span></div><div class="t m7 xae h14 yf4 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 xaf h15 yf2 ffb fsb fc2 sc0 ls0 ws0">−<span class="_ _4"> </span><span class="ff9 fs2">A</span></div><div class="t m7 x37 h16 yf3 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t<span class="_ _1d"></span><span class="ffb fsc">−</span><span class="ff5">1</span></div><div class="t m7 xb0 h13 yf2 ff9 fs2 fc2 sc0 ls0 ws0">z</div><div class="t m7 xb1 h16 yf5 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 xb2 h15 yf2 ffa fsb fc2 sc0 ls0 ws0">)</div><div class="t m7 xb3 h19 yf6 ffd fs2 fc2 sc0 ls0 ws0">Σ</div><div class="t m7 xab h14 yf7 ff3 fs4 fc2 sc0 ls0 ws0">A</div><div class="t m7 xab h16 yf8 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t</div><div class="t m7 x8f h15 yf6 ffa fsb fc2 sc0 ls0 ws0">=(<span class="_ _1c"></span><span class="ff9 fs2">I<span class="_ _4"> </span></span><span class="ffb">−<span class="_ _7"> </span><span class="ff9 fs2">K</span></span></div><div class="t m7 x4c h14 yf9 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 xb4 h15 yf6 ffa fsb fc2 sc0 ls0 ws0">)<span class="ffd fs2">Σ</span></div><div class="t m7 xaa h14 yf7 ff3 fs4 fc2 sc0 ls0 ws0">A</div><div class="t m7 xaa h16 yf8 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t<span class="_ _1d"></span><span class="ffb fsc">−</span><span class="ff5">1</span></div><div class="t m7 x68 h17 yfa ffc fs2 fc2 sc0 ls0 ws0">e</div><div class="t m7 xab h16 yfb ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t</div><div class="t m7 x8f h15 yfa ffa fsb fc2 sc0 ls0 ws0">=<span class="ff9 fs2">y</span></div><div class="t m7 x32 h14 yfc ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 xb5 h15 yfa ffb fsb fc2 sc0 ls0 ws0">−<span class="_ _4"> </span><span class="ff9 fs2">A</span></div><div class="t m7 x4c h16 yfb ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t</div><div class="t m7 xe h13 yfa ff9 fs2 fc2 sc0 ls0 ws0">z</div><div class="t m7 xb6 h16 yfd ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 xb3 h19 yfe ffd fs2 fc2 sc0 ls0 ws0">Σ</div><div class="t m7 xab h16 yff ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t</div><div class="t m7 x8f h15 yfe ffa fsb fc2 sc0 ls0 ws0">=<span class="fff fs2">κ</span></div><div class="t m7 xb7 hf y100 ff5 fs4 fc2 sc0 ls0 ws0">2</div><div class="t m7 xb8 h19 yfe ffd fs2 fc2 sc0 ls0 ws0">Σ</div><div class="t m7 x78 h16 yff ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1<span class="ffb fsc">|<span class="_ _1d"></span></span></span>t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 xa2 h15 yfe ffa fsb fc2 sc0 ls0 ws0">+<span class="_ _10"> </span>(<span class="_ _1d"></span><span class="ff5 fs2">1<span class="_ _10"> </span></span><span class="ffb">−<span class="_ _7"> </span><span class="fff fs2">κ</span></span></div><div class="t m7 x1c hf y100 ff5 fs4 fc2 sc0 ls0 ws0">2</div><div class="t m7 x26 h15 yfe ffa fsb fc2 sc0 ls0 ws0">)<span class="ffc fs2">e</span></div><div class="t m7 x39 h16 y101 ffb fsc fc2 sc0 ls0 ws0">0</div><div class="t m7 x39 h16 y102 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t</div><div class="t m7 xb1 h17 yfe ffc fs2 fc2 sc0 ls0 ws0">e</div><div class="t m7 xb9 h16 yff ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t</div><div class="t m7 xb2 he yfe ff5 fs2 fc2 sc0 ls0 ws0">,</div><div class="t m1 x1 he y103 ff5 fs2 fc2 sc0 ls0 ws0">where</div><div class="t m7 xba h13 y103 ff9 fs2 fc2 sc0 ls0 ws0">K</div><div class="t m7 xbb h14 y104 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m1 x11 he y103 ff5 fs2 fc2 sc0 ls0 ws0">repr<span class="_ _2"></span>esents<span class="_ _6"> </span>the<span class="_ _a"> </span>Kalman<span class="_ _a"> </span>gain<span class="_ _a"> </span>that<span class="_ _6"> </span>explains<span class="_ _a"> </span>by<span class="_ _a"> </span>how<span class="_ _a"> </span>much<span class="_ _6"> </span>the<span class="_ _a"> </span>parameters,</div><div class="t m7 xbc h13 y103 ff9 fs2 fc2 sc0 ls0 ws0">A</div><div class="t m7 xbd h14 y104 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m1 xb he y103 ff5 fs2 fc2 sc0 ls0 ws0">,<span class="_ _a"> </span>should<span class="_ _a"> </span>be</div><div class="t m1 x1 he y105 ff5 fs2 fc2 sc0 ls0 ws0">changed<span class="_"> </span>in<span class="_ _4"> </span>any<span class="_ _5"> </span>given<span class="_"> </span>state.<span class="_ _12"> </span>On<span class="_"> </span>the<span class="_ _4"> </span>one<span class="_ _5"> </span>hand,<span class="_"> </span>if<span class="_ _5"> </span>the<span class="_"> </span>parameter<span class="_ _4"> </span>uncertainty<span class="_ _0"></span>,</div><div class="t m7 x7 h19 y105 ffd fs2 fc2 sc0 ls0 ws0">Σ</div><div class="t m7 x20 h14 y106 ff3 fs4 fc2 sc0 ls0 ws0">A</div><div class="t m7 x20 h16 y107 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">|<span class="_ _1d"></span></span>t<span class="_ _1d"></span><span class="ffb fsc">−</span><span class="ff5">1</span></div><div class="t m1 xbe h5 y105 ff5 fs2 fc2 sc0 ls0 ws0">is<span class="_"> </span>small<span class="_ _4"> </span>(<span class="ff3">large</span>),<span class="_ _4"> </span>it</div><div class="t m12 x1 he y108 ff5 fs2 fc2 sc0 ls0 ws0">means<span class="_"> </span>that<span class="_"> </span>the<span class="_"> </span>parameters,</div><div class="t m7 xbf h13 y108 ff9 fs2 fc2 sc0 ls0 ws0">A</div><div class="t m7 x47 h14 y109 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m12 xc0 h5 y108 ff5 fs2 fc2 sc0 ls0 ws0">,<span class="_"> </span>should<span class="_"> </span>be<span class="_"> </span>similar<span class="_"> </span>to<span class="_"> </span>(<span class="ff3">adjusted<span class="_"> </span>to</span>)<span class="_"> </span>their<span class="_"> </span>prior<span class="_"> </span>states.<span class="_ _5"> </span>On<span class="_"> </span>the<span class="_"> </span>other<span class="_"> </span>hand,</div><div class="t m1 x1 he y10a ff5 fs2 fc2 sc0 ls0 ws0">if<span class="_"> </span>the<span class="_"> </span>error<span class="_"> </span>variance</div><div class="t m7 xc1 h19 y10a ffd fs2 fc2 sc0 ls0 ws0">Σ</div><div class="t m7 x14 h14 y10b ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m1 x46 h5 y10a ff5 fs2 fc2 sc0 ls0 ws0">is<span class="_"> </span>small<span class="_"> </span>(<span class="ff3">large</span>),<span class="_"> </span>meaning<span class="_"> </span>that<span class="_"> </span>the<span class="_"> </span>estimation<span class="_"> </span>is<span class="_"> </span>very<span class="_"> </span>accurate<span class="_"> </span>(<span class="ff3">inaccurate</span>),<span class="_"> </span>the</div><div class="t m7 x1 he y10c ff5 fs2 fc2 sc0 ls0 ws0">parameters,<span class="_"> </span><span class="ffd">Φ</span></div><div class="t m7 xc2 h14 y10d ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 xc3 h5 y10c ff5 fs2 fc2 sc0 ls0 ws0">,<span class="_"> </span>should<span class="_"> </span>be<span class="_"> </span>similar<span class="_"> </span>to<span class="_"> </span>(<span class="ff3">adjusted<span class="_"> </span>to</span>)<span class="_"> </span>their<span class="_"> </span>prior<span class="_"> </span>values.</div><div class="t m1f x9 he y10e ff5 fs2 fc2 sc0 ls0 ws0">The<span class="_"> </span>time-varying<span class="_"> </span>coefﬁcients<span class="_"> </span>and<span class="_"> </span>time-varying<span class="_"> </span>variance-covariance<span class="_"> </span>matrices<span class="_"> </span>are<span class="_"> </span>used<span class="_"> </span>to<span class="_"> </span>estimate</div><div class="t m1c x1 he y10f ff5 fs2 fc2 sc0 ls0 ws0">the<span class="_"> </span>generalized<span class="_"> </span>connectedness<span class="_"> </span>pr<span class="_ _2"></span>ocedure<span class="_"> </span>of<span class="_"> </span><span class="fc4">Diebold<span class="_"> </span>and<span class="_"> </span>Yılmaz<span class="_"> </span></span>(<span class="fc4">2014</span>)<span class="_ _7"> </span>that<span class="_"> </span>is<span class="_"> </span>based<span class="_"> </span>on<span class="_"> </span>generalized</div><div class="t m9 x1 he y110 ff5 fs2 fc2 sc0 ls0 ws0">impulse<span class="_"> </span>response<span class="_"> </span>functions<span class="_ _7"> </span>(GIRF)<span class="_"> </span>and<span class="_"> </span>generalized<span class="_"> </span>for<span class="_ _2"></span>ecast<span class="_"> </span>error<span class="_"> </span>variance<span class="_"> </span>decompositions<span class="_"> </span>(GFEVD)</div><div class="t m1 x1 he y111 ff5 fs2 fc2 sc0 ls0 ws0">in<span class="_ _5"> </span>accordance<span class="_ _4"> </span>with<span class="_ _5"> </span><span class="fc4">Koop<span class="_ _5"> </span>et<span class="_ _5"> </span>al.<span class="_ _5"> </span></span>(<span class="fc4">1996</span>)<span class="_ _5"> </span>and<span class="_ _5"> </span><span class="fc4">Pesaran<span class="_ _5"> </span>and<span class="_ _6"> </span>Shin<span class="_ _4"> </span></span>(<span class="fc4">1998</span>).<span class="_ _13"> </span>In<span class="_ _5"> </span>order<span class="_ _5"> </span>to<span class="_ _5"> </span>calculate<span class="_ _5"> </span>the<span class="_ _5"> </span>GIRF</div><div class="t m18 x1 he y112 ff5 fs2 fc2 sc0 ls0 ws0">and<span class="_"> </span>GFEVD,<span class="_"> </span>we<span class="_"> </span>transform<span class="_"> </span>the<span class="_"> </span>TVP-V<span class="_ _b"></span>AR<span class="_"> </span>to<span class="_"> </span>its<span class="_"> </span>vector<span class="_"> </span>moving<span class="_"> </span>average<span class="_"> </span>(VMA)<span class="_"> </span>r<span class="_ _c"></span>epresentation<span class="_"> </span>based</div><div class="t m1 x1 he y113 ff5 fs2 fc2 sc0 ls0 ws0">on<span class="_ _12"> </span>the<span class="_ _8"> </span>W<span class="_ _0"></span>old<span class="_ _8"> </span>r<span class="_ _2"></span>epresentation<span class="_ _12"> </span>theorem.<span class="_ _15"> </span>Retrieving<span class="_ _12"> </span>the<span class="_ _8"> </span>VMA<span class="_ _12"> </span>representation<span class="_ _12"> </span>can<span class="_ _8"> </span>be<span class="_ _12"> </span>illustrated<span class="_ _8"> </span>by</div><div class="t m7 x1 he y114 ff5 fs2 fc2 sc0 ls0 ws0">recursive<span class="_"> </span>substitution:</div><div class="t m7 x82 h13 y115 ff9 fs2 fc2 sc0 ls0 ws0">y</div><div class="t m7 xc4 h14 y116 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x56 h15 y115 ffa fsb fc2 sc0 ls0 ws0">=<span class="_ _1c"></span><span class="ff9 fs2">J</span></div><div class="t m7 xc5 h16 y117 ffb fsc fc2 sc0 ls0 ws0">0</div><div class="t m7 xc6 h15 y115 ffa fsb fc2 sc0 ls0 ws0">(<span class="_ _1c"></span><span class="ff9 fs2">M</span></div><div class="t m7 x83 h14 y116 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 xa6 h15 y115 ffa fsb fc2 sc0 ls0 ws0">(<span class="ff9 fs2">z</span></div><div class="t m7 x25 h16 y118 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">2</span></div><div class="t m7 xb5 h15 y115 ffa fsb fc2 sc0 ls0 ws0">+<span class="_ _10"> </span><span class="ffc fs2">η</span></div><div class="t m7 xc7 h16 y119 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 x95 h15 y115 ffa fsb fc2 sc0 ls0 ws0">)<span class="_ _10"> </span>+<span class="_ _7"> </span><span class="ffc fs2">η</span></div><div class="t m7 x35 h14 y116 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 xaf h15 y115 ffa fsb fc2 sc0 ls0 ws0">)<span class="_ _22"> </span><span class="ff5 fs2">(3)</span></div><div class="t m7 x56 h15 y11a ffa fsb fc2 sc0 ls0 ws0">=<span class="_ _1c"></span><span class="ff9 fs2">J</span></div><div class="t m7 xc5 h16 y11b ffb fsc fc2 sc0 ls0 ws0">0</div><div class="t m7 xc6 h15 y11a ffa fsb fc2 sc0 ls0 ws0">(<span class="_ _1c"></span><span class="ff9 fs2">M</span></div><div class="t m7 x83 h14 y11c ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 xa6 h15 y11a ffa fsb fc2 sc0 ls0 ws0">(<span class="_ _1c"></span><span class="ff9 fs2">M</span></div><div class="t m7 xc8 h14 y11c ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x31 h15 y11a ffa fsb fc2 sc0 ls0 ws0">(<span class="ff9 fs2">z</span></div><div class="t m7 xc9 h16 y11d ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">3</span></div><div class="t m7 xca h15 y11a ffa fsb fc2 sc0 ls0 ws0">+<span class="_ _10"> </span><span class="ffc fs2">η</span></div><div class="t m7 xaa h16 y11d ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">2</span></div><div class="t m7 xcb h15 y11a ffa fsb fc2 sc0 ls0 ws0">)<span class="_ _10"> </span>+<span class="_ _7"> </span><span class="ffc fs2">η</span></div><div class="t m7 x74 h16 y11e ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 xcc h15 y11a ffa fsb fc2 sc0 ls0 ws0">)<span class="_ _10"> </span>+<span class="_ _7"> </span><span class="ffc fs2">η</span></div><div class="t m7 xcd h14 y11c ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 xce h15 y11a ffa fsb fc2 sc0 ls0 ws0">)<span class="_ _23"> </span><span class="ff5 fs2">(4)</span></div><div class="t m7 xcf he y11f ff5 fs2 fc2 sc0 ls0 ws0">.</div><div class="t m7 xcf he y120 ff5 fs2 fc2 sc0 ls0 ws0">.</div><div class="t m7 xcf he y121 ff5 fs2 fc2 sc0 ls0 ws0">.<span class="_ _24"> </span>(5)</div><div class="t m7 x56 h15 y122 ffa fsb fc2 sc0 ls0 ws0">=<span class="_ _1c"></span><span class="ff9 fs2">J</span></div><div class="t m7 xc5 h16 y123 ffb fsc fc2 sc0 ls0 ws0">0</div><div class="t m7 xc6 h15 y122 ffa fsb fc2 sc0 ls0 ws0">(<span class="_ _1c"></span><span class="ff9 fs2">M</span></div><div class="t m7 x88 h16 y123 ff3 fs4 fc2 sc0 ls0 ws0">k<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 x83 h14 y124 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x30 h13 y122 ff9 fs2 fc2 sc0 ls0 ws0">z</div><div class="t m7 xd0 h16 y125 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span>k<span class="_ _1d"></span><span class="ffb fsc">−</span><span class="ff5">1</span></div><div class="t m7 xca h15 y122 ffa fsb fc2 sc0 ls0 ws0">+</div><div class="t m7 xb6 h14 y126 ff3 fs4 fc2 sc0 ls0 ws0">k</div><div class="t m7 x99 h1b y127 ff10 fsd fc2 sc0 ls0 ws0">∑</div><div class="t m7 x99 h16 y128 ff3 fs4 fc2 sc0 ls0 ws0">j<span class="ffa fsc">=<span class="_ _1d"></span></span><span class="ff5">0</span></div><div class="t m7 xd1 h13 y122 ff9 fs2 fc2 sc0 ls0 ws0">M</div><div class="t m7 xa3 h14 y129 ff3 fs4 fc2 sc0 ls0 ws0">j</div><div class="t m7 xa3 h14 y12a ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 xd2 h17 y122 ffc fs2 fc2 sc0 ls0 ws0">η</div><div class="t m7 xa4 h16 y12b ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1c"></span></span>j</div><div class="t m7 x1c h15 y122 ffa fsb fc2 sc0 ls0 ws0">)<span class="_ _25"> </span><span class="ff5 fs2">(6)</span></div><div class="t m7 x1 he y12c ff5 fs2 fc2 sc0 ls0 ws0">with</div><div class="t m7 xd3 h13 y12d ff9 fs2 fc2 sc0 ls0 ws0">M</div><div class="t m7 x9b h14 y12e ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 xd4 h15 y12d ffa fsb fc2 sc0 ls0 ws0">=</div><div class="t m7 xd5 h18 y12f ffe fs2 fc2 sc0 ls0 ws0"> </div><div class="t m7 xd6 h13 y130 ff9 fs2 fc2 sc0 ls0 ws0">A</div><div class="t m7 x17 h14 y131 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 xd7 h13 y132 ff9 fs2 fc2 sc0 ls0 ws0">I</div><div class="t m7 xd8 h16 y133 ff3 fs4 fc2 sc0 ls0 ws0">m<span class="ffa fsc">(<span class="_ _1c"></span></span>p<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1<span class="ffa fsc">)</span></span></div><div class="t m7 xd9 h7 y132 ff4 fs2 fc2 sc0 ls0 ws0">0</div><div class="t m7 xa0 h16 y133 ff3 fs4 fc2 sc0 ls0 ws0">m<span class="ffa fsc">(<span class="_ _1c"></span></span>p<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1<span class="ffa fsc">)<span class="_ _1d"></span><span class="ffb">×</span></span></span>m</div><div class="t m7 xa7 h18 y12f ffe fs2 fc2 sc0 ls0 ws0">!</div><div class="t m7 xe h17 y12d ffc fs2 fc2 sc0 ls0 ws0">η</div><div class="t m7 xb6 h14 y12e ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x5 h15 y12d ffa fsb fc2 sc0 ls0 ws0">=</div><div class="t m7 x4d h18 y134 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x4d h18 y135 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x4d h18 y136 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x4d h18 y137 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x4d h18 y138 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x4d h18 y139 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 xda h17 y13a ffc fs2 fc2 sc0 ls0 ws0">e</div><div class="t m7 xdb h14 y13b ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x3d h7 y13c ff4 fs2 fc2 sc0 ls0 ws0">0</div><div class="t m7 xdc he y13d ff5 fs2 fc2 sc0 ls0 ws0">.</div><div class="t m7 xdc he y13e ff5 fs2 fc2 sc0 ls0 ws0">.</div><div class="t m7 xdc he y13f ff5 fs2 fc2 sc0 ls0 ws0">.</div><div class="t m7 x3d h7 y140 ff4 fs2 fc2 sc0 ls0 ws0">0</div><div class="t m7 x9a h18 y134 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x9a h18 y135 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x9a h18 y136 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x9a h18 y137 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x9a h18 y138 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x9a h18 y139 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x38 h15 y12d ffa fsb fc2 sc0 ls0 ws0">=<span class="_ _a"> </span><span class="ff9 fs2">J<span class="_ _1c"></span><span class="ffc">e</span></span></div><div class="t m7 xb9 h1c y12e ff9 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 xdd h15 y12d ff9 fs2 fc2 sc0 ls0 ws0">J<span class="_ _6"> </span><span class="ffa fsb">=</span></div><div class="t m7 x6b h18 y134 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x6b h18 y135 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x6b h18 y136 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x6b h18 y137 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x6b h18 y138 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x6b h18 y139 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 x12 h13 y13a ff9 fs2 fc2 sc0 ls0 ws0">I</div><div class="t m7 x12 h7 y13c ff4 fs2 fc2 sc0 ls0 ws0">0</div><div class="t m7 xde he y13d ff5 fs2 fc2 sc0 ls0 ws0">.</div><div class="t m7 xde he y141 ff5 fs2 fc2 sc0 ls0 ws0">.</div><div class="t m7 xde he y13f ff5 fs2 fc2 sc0 ls0 ws0">.</div><div class="t m7 x12 h7 y140 ff4 fs2 fc2 sc0 ls0 ws0">0</div><div class="t m7 xdf h18 y134 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 xdf h18 y135 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 xdf h18 y136 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 xdf h18 y137 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 xdf h18 y138 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 xdf h18 y139 ffe fs2 fc2 sc0 ls0 ws0"></div><div class="t m7 xe0 he y12d ff5 fs2 fc2 sc0 ls0 ws0">(7)</div><div class="t m12 x1 he y142 ff5 fs2 fc2 sc0 ls0 ws0">where</div><div class="t m7 x3a h13 y142 ff9 fs2 fc2 sc0 ls0 ws0">M</div><div class="t m7 x3b h14 y143 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m12 x11 he y142 ff5 fs2 fc2 sc0 ls0 ws0">is<span class="_"> </span>an</div><div class="t m7 xe1 h15 y142 ff3 fs2 fc2 sc0 ls0 ws0">m<span class="_ _1c"></span>p<span class="_"> </span><span class="ffb fsb">×<span class="_ _10"> </span></span>m<span class="_ _1c"></span>p</div><div class="t m12 xe2 he y142 ff5 fs2 fc2 sc0 ls0 ws0">dimensional<span class="_"> </span>matrix,</div><div class="t m7 xe3 h17 y142 ffc fs2 fc2 sc0 ls0 ws0">η</div><div class="t m7 x33 h14 y143 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m12 x8c he y142 ff5 fs2 fc2 sc0 ls0 ws0">is<span class="_"> </span>an</div><div class="t m7 xad h15 y142 ff3 fs2 fc2 sc0 ls0 ws0">m<span class="_ _1c"></span>p<span class="_"> </span><span class="ffb fsb">×</span></div><div class="t m12 xdc he y142 ff5 fs2 fc2 sc0 ls0 ws0">1<span class="_"> </span>dimensional<span class="_"> </span>vector<span class="_ _0"></span>,<span class="_"> </span>and</div><div class="t m7 xe4 h13 y142 ff9 fs2 fc2 sc0 ls0 ws0">J</div><div class="t m12 xe5 he y142 ff5 fs2 fc2 sc0 ls0 ws0">is<span class="_"> </span>an</div><div class="t m7 xe6 h15 y142 ff3 fs2 fc2 sc0 ls0 ws0">m<span class="_ _1c"></span>p<span class="_"> </span><span class="ffb fsb">×<span class="_ _10"> </span></span>m</div><div class="t m7 x1 he y144 ff5 fs2 fc2 sc0 ls0 ws0">dimensional<span class="_"> </span>matrix.</div><div class="t m7 x9 h1d y145 ff5 fs2 fc2 sc0 ls0 ws0">T<span class="_ _0"></span>aking<span class="_"> </span>the<span class="_"> </span>limit<span class="_"> </span>as<span class="_"> </span><span class="ff3">k<span class="_ _4"> </span></span>approaches<span class="_"> </span><span class="ff10">∞<span class="_ _4"> </span></span>yields<span class="_"> </span>to</div><div class="t m7 x45 h13 y146 ff9 fs2 fc2 sc0 ls0 ws0">y</div><div class="t m7 xe7 h14 y147 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 xe8 h15 y146 ffa fsb fc2 sc0 ls0 ws0">=<span class="ff3 fs2">l<span class="_ _1c"></span>i<span class="_ _1d"></span>m</span></div><div class="t m7 x47 h16 y148 ff3 fs4 fc2 sc0 ls0 ws0">k<span class="ffb fsc">→<span class="_ _1d"></span></span><span class="ff10">∞</span></div><div class="t m7 x23 h13 y146 ff9 fs2 fc2 sc0 ls0 ws0">J</div><div class="t m7 x70 h16 y149 ffb fsc fc2 sc0 ls0 ws0">0</div><div class="t m7 x5e h15 y146 ffa fsb fc2 sc0 ls0 ws0">(<span class="_ _1c"></span><span class="ff9 fs2">M</span></div><div class="t m7 x83 h16 y149 ff3 fs4 fc2 sc0 ls0 ws0">k<span class="ffb fsc">−<span class="_ _1d"></span></span><span class="ff5">1</span></div><div class="t m7 xab h14 y14a ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 xe9 h13 y146 ff9 fs2 fc2 sc0 ls0 ws0">z</div><div class="t m7 x77 h16 y148 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1d"></span></span>k<span class="_ _1d"></span><span class="ffb fsc">−</span><span class="ff5">1</span></div><div class="t m7 xc7 h15 y146 ffa fsb fc2 sc0 ls0 ws0">+</div><div class="t m7 x8d h14 y14b ff3 fs4 fc2 sc0 ls0 ws0">k</div><div class="t m7 xe h1b y14c ff10 fsd fc2 sc0 ls0 ws0">∑</div><div class="t m7 xe h16 y14d ff3 fs4 fc2 sc0 ls0 ws0">j<span class="ffa fsc">=<span class="_ _1d"></span></span><span class="ff5">0</span></div><div class="t m7 x85 h13 y146 ff9 fs2 fc2 sc0 ls0 ws0">M</div><div class="t m7 x35 h14 y14e ff3 fs4 fc2 sc0 ls0 ws0">j</div><div class="t m7 x35 h14 y14f ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 xaf h17 y146 ffc fs2 fc2 sc0 ls0 ws0">η</div><div class="t m7 x3d h16 y150 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1c"></span></span>j</div><div class="t m7 x37 h15 y146 ffa fsb fc2 sc0 ls0 ws0">)<span class="_ _5"> </span>=</div><div class="t m7 x87 h1e y14b ff10 fs4 fc2 sc0 ls0 ws0">∞</div><div class="t m7 xb0 h1b y151 ff10 fsd fc2 sc0 ls0 ws0">∑</div><div class="t m7 x91 h16 y14d ff3 fs4 fc2 sc0 ls0 ws0">j<span class="ffa fsc">=<span class="_ _1d"></span></span><span class="ff5">0</span></div><div class="t m7 xea h13 y146 ff9 fs2 fc2 sc0 ls0 ws0">J</div><div class="t m7 xb2 h16 y149 ffb fsc fc2 sc0 ls0 ws0">0</div><div class="t m7 x40 h13 y146 ff9 fs2 fc2 sc0 ls0 ws0">M</div><div class="t m7 xeb h14 y14e ff3 fs4 fc2 sc0 ls0 ws0">j</div><div class="t m7 xec h14 y14f ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 xed h17 y146 ffc fs2 fc2 sc0 ls0 ws0">η</div><div class="t m7 xee h16 y150 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1c"></span></span>j</div><div class="t m7 x6b he y146 ff5 fs2 fc2 sc0 ls0 ws0">,<span class="_ _26"> </span>(8)</div><div class="t m7 x1 he y152 ff5 fs2 fc2 sc0 ls0 ws0">where<span class="_"> </span>it<span class="_"> </span>dir<span class="_ _2"></span>ectly<span class="_"> </span>follows</div><div class="t m7 xef h13 y153 ff9 fs2 fc2 sc0 ls0 ws0">y</div><div class="t m7 xf0 h14 y154 ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x55 h15 y153 ffa fsb fc2 sc0 ls0 ws0">=</div><div class="t m7 x9e h1e y155 ff10 fs4 fc2 sc0 ls0 ws0">∞</div><div class="t m7 xc4 h1b y156 ff10 fsd fc2 sc0 ls0 ws0">∑</div><div class="t m7 xc4 h16 y157 ff3 fs4 fc2 sc0 ls0 ws0">j<span class="ffa fsc">=<span class="_ _1d"></span></span><span class="ff5">0</span></div><div class="t m7 x23 h13 y153 ff9 fs2 fc2 sc0 ls0 ws0">J</div><div class="t m7 xf1 h16 y158 ffb fsc fc2 sc0 ls0 ws0">0</div><div class="t m7 xc6 h13 y153 ff9 fs2 fc2 sc0 ls0 ws0">M</div><div class="t m7 xa5 h14 y159 ff3 fs4 fc2 sc0 ls0 ws0">j</div><div class="t m7 x2e h14 y15a ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x83 h17 y153 ff9 fs2 fc2 sc0 ls0 ws0">J<span class="_ _1c"></span><span class="ffc">e</span></div><div class="t m7 x8f h16 y15b ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1c"></span></span>j</div><div class="t m7 xf2 h13 y153 ff9 fs2 fc2 sc0 ls0 ws0">B</div><div class="t m7 xa9 h14 y15b ff3 fs4 fc2 sc0 ls0 ws0">jt</div><div class="t m7 x95 h15 y153 ffa fsb fc2 sc0 ls0 ws0">=<span class="_ _a"> </span><span class="ff9 fs2">J</span></div><div class="t m7 x6 h16 y158 ffb fsc fc2 sc0 ls0 ws0">0</div><div class="t m7 xae h13 y153 ff9 fs2 fc2 sc0 ls0 ws0">M</div><div class="t m7 xda h14 y159 ff3 fs4 fc2 sc0 ls0 ws0">j</div><div class="t m7 xf3 h14 y15a ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x36 h15 y153 ff9 fs2 fc2 sc0 ls0 ws0">J<span class="_ _1d"></span><span class="ff5">,<span class="_ _27"> </span><span class="ff3">j<span class="_ _5"> </span><span class="ffa fsb">=<span class="_ _5"> </span></span></span>0,<span class="_ _d"> </span>1,<span class="_ _d"> </span>.<span class="_ _10"> </span>.<span class="_ _10"> </span>.<span class="_ _28"> </span>(9)</span></div><div class="t m7 xef h13 y15c ff9 fs2 fc2 sc0 ls0 ws0">y</div><div class="t m7 xf0 h14 y15d ff3 fs4 fc2 sc0 ls0 ws0">t</div><div class="t m7 x55 h15 y15c ffa fsb fc2 sc0 ls0 ws0">=</div><div class="t m7 x9e h1e y15e ff10 fs4 fc2 sc0 ls0 ws0">∞</div><div class="t m7 xc4 h1b y15f ff10 fsd fc2 sc0 ls0 ws0">∑</div><div class="t m7 xc4 h16 y160 ff3 fs4 fc2 sc0 ls0 ws0">j<span class="ffa fsc">=<span class="_ _1d"></span></span><span class="ff5">0</span></div><div class="t m7 x23 h13 y15c ff9 fs2 fc2 sc0 ls0 ws0">B</div><div class="t m7 x5e h14 y161 ff3 fs4 fc2 sc0 ls0 ws0">jt</div><div class="t m7 x4a h17 y15c ffc fs2 fc2 sc0 ls0 ws0">e</div><div class="t m7 x2e h16 y161 ff3 fs4 fc2 sc0 ls0 ws0">t<span class="ffb fsc">−<span class="_ _1c"></span></span>j</div><div class="t m7 x62 he y15c ff5 fs2 fc2 sc0 ls0 ws0">(10)</div><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d md"></div></a></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>