Copula-based Multivariate GARCH Model with ... - Economics
Copula-based Multivariate GARCH Model with ... - Economics Copula-based Multivariate GARCH Model with ... - Economics
Table 2. Bivariate C-MGARCH (DM-IL) Panel A. In-sample Results MGARCH C-MGARCH I G GS C CS F DCC θ 1.1587 1.0502 0.0608 0.0762 1.3689 se(θ) 0.0039 0.0018 0.0013 0.0019 0.0472 σ 0.2183 0.0781 0.0479 0.0595 0.2118 logL -1.4001 -1.3859 -1.3877 -1.3889 -1.3893 -1.3896 AIC 2.8162 2.7897 2.7934 2.7957 2.7964 2.7972 SIC 2.8553 2.8337 2.8374 2.8397 2.8404 2.8412 VC θ 1.1884 1.0474 0.0502 0.0976 1.7717 se(θ) 0.0047 0.0020 0.0013 0.0020 0.0436 σ 0.2510 0.0740 0.0397 0.0755 0.2697 logL -1.4300 -1.3948 -1.3984 -1.3997 -1.3990 -1.3977 AIC 2.8760 2.8076 2.8148 2.8174 2.8159 2.8133 SIC 2.9151 2.8516 2.8588 2.8614 2.8599 2.8573 SBEKK θ 1.1456 1.0457 0.0609 0.0789 1.1843 se(θ) 0.0036 0.0017 0.0012 0.0020 0.0457 σ 0.2031 0.0716 0.0479 0.0616 0.1844 logL -1.4032 -1.3871 -1.3892 -1.3898 -1.3902 -1.3901 AIC 2.8103 2.7802 2.7844 2.7856 2.7863 2.7861 SIC 2.8201 2.7948 2.7991 2.8002 2.8010 2.8008 Notes: Daily changes in log exchange rates for Deutschemark and Italian Lira from January 4, 1993 to December 31, 1996 (R = 1005) are used. Also see notes for Table 1A. Panel B. Out-of-sample Results I G GS C CS F DCC logL -0.9849 -0.9750 -0.9875 -0.9844 -0.9786 -0.9630 RC = 0.036 std(logL) 1.0360 1.1215 1.0992 1.0919 1.0910 1.1233 VC logL -1.0152 -0.9532 -0.9630 -0.9621 -0.9563 -0.9481 RC = 0.000 std(logL) 1.0500 1.1625 1.1369 1.1309 1.1357 1.1563 SBEKK logL -0.9043 -0.8910 -0.8884 -0.8909 -0.8931 -0.8840 RC = 0.022 std(logL) 1.1106 1.1614 1.1469 1.1346 1.1328 1.1454 Notes: See notes for Table 1B.
Table 3. Bivariate C-MGARCH (FF-IL) Panel A. In-sample Results MGARCH C-MGARCH I G GS C CS F DCC θ 1.2033 1.0342 0.0501 0.0771 3.1094 se(θ) 0.0061 0.0019 0.0012 0.0020 0.0500 σ 0.2667 0.0542 0.0396 0.0602 0.4381 logL -1.3011 -1.2799 -1.2826 -1.2826 -1.2826 -1.2752 AIC 2.6182 2.5777 2.5830 2.5832 2.5832 2.5682 SIC 2.6573 2.6217 2.6270 2.6272 2.6272 2.6122 VC θ 1.1984 1.0378 0.0507 0.0660 3.5098 se(θ) 0.0073 0.0019 0.0012 0.0020 0.0827 σ 0.2616 0.0597 0.0401 0.0518 0.4807 logL -1.3223 -1.2858 -1.2877 -1.2879 -1.2882 -1.2801 AIC 2.6604 2.5896 2.5932 2.5937 2.5943 2.5782 SIC 2.6995 2.6336 2.6372 2.6377 2.6383 2.6222 SBEKK θ 1.2144 1.0318 0.0495 0.0809 3.1688 se(θ) 0.0060 0.0019 0.0011 0.0021 0.0400 σ 0.2780 0.0507 0.0392 0.0631 0.4447 logL -1.3059 -1.2824 -1.2855 -1.2853 -1.2853 -1.2767 AIC 2.6159 2.5707 2.5769 2.5766 2.5765 2.5593 SIC 2.6256 2.5854 2.5915 2.5912 2.5912 2.5740 Notes: Daily changes in log exchange rates for French Franc and Italian Lira from January 4, 1993 to December 31, 1996 (R = 1005) are used. Also see notes for Table 1A. Panel B. Out-of-sample Results I G GS C CS F DCC logL -0.9142 -0.8841 -0.9049 -0.8994 -0.8957 -0.8613 RC = 0.001 std(logL) 1.0935 1.1504 1.1536 1.1478 1.1460 1.2047 VC logL -1.0133 -0.9687 -0.9817 -0.9812 -0.9792 -0.9613 RC = 0.000 std(logL) 1.0686 1.1090 1.1355 1.1328 1.1192 1.2082 SBEKK logL -0.8440 -0.8027 -0.8055 -0.8062 -0.8069 -0.7802 RC = 0.000 std(logL) 1.1390 1.2230 1.2169 1.2079 1.2050 1.2475 Notes: See notes for Table 1A.
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Table 2. Bivariate C-M<strong>GARCH</strong> (DM-IL)<br />
Panel A. In-sample Results<br />
M<strong>GARCH</strong><br />
C-M<strong>GARCH</strong><br />
I G GS C CS F<br />
DCC θ 1.1587 1.0502 0.0608 0.0762 1.3689<br />
se(θ) 0.0039 0.0018 0.0013 0.0019 0.0472<br />
σ 0.2183 0.0781 0.0479 0.0595 0.2118<br />
logL -1.4001 -1.3859 -1.3877 -1.3889 -1.3893 -1.3896<br />
AIC 2.8162 2.7897 2.7934 2.7957 2.7964 2.7972<br />
SIC 2.8553 2.8337 2.8374 2.8397 2.8404 2.8412<br />
VC θ 1.1884 1.0474 0.0502 0.0976 1.7717<br />
se(θ) 0.0047 0.0020 0.0013 0.0020 0.0436<br />
σ 0.2510 0.0740 0.0397 0.0755 0.2697<br />
logL -1.4300 -1.3948 -1.3984 -1.3997 -1.3990 -1.3977<br />
AIC 2.8760 2.8076 2.8148 2.8174 2.8159 2.8133<br />
SIC 2.9151 2.8516 2.8588 2.8614 2.8599 2.8573<br />
SBEKK θ 1.1456 1.0457 0.0609 0.0789 1.1843<br />
se(θ) 0.0036 0.0017 0.0012 0.0020 0.0457<br />
σ 0.2031 0.0716 0.0479 0.0616 0.1844<br />
logL -1.4032 -1.3871 -1.3892 -1.3898 -1.3902 -1.3901<br />
AIC 2.8103 2.7802 2.7844 2.7856 2.7863 2.7861<br />
SIC 2.8201 2.7948 2.7991 2.8002 2.8010 2.8008<br />
Notes: Daily changes in log exchange rates for Deutschemark and Italian Lira from January 4, 1993 to December 31,<br />
1996 (R = 1005) are used. Also see notes for Table 1A.<br />
Panel B. Out-of-sample Results<br />
I G GS C CS F<br />
DCC logL -0.9849 -0.9750 -0.9875 -0.9844 -0.9786 -0.9630 RC = 0.036<br />
std(logL) 1.0360 1.1215 1.0992 1.0919 1.0910 1.1233<br />
VC logL -1.0152 -0.9532 -0.9630 -0.9621 -0.9563 -0.9481 RC = 0.000<br />
std(logL) 1.0500 1.1625 1.1369 1.1309 1.1357 1.1563<br />
SBEKK logL -0.9043 -0.8910 -0.8884 -0.8909 -0.8931 -0.8840 RC = 0.022<br />
std(logL) 1.1106 1.1614 1.1469 1.1346 1.1328 1.1454<br />
Notes: See notes for Table 1B.
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