Table 5 Estimation results for different...

Table 5

Estimation results for different volatility models with t-skew-student error distributions

Panel A: Latin American emerging markets
Series	Colombia			Chile			Mexico			Peru			MILA
Series	GARCH	EGARCH	GJRGARCH	GARCH	EGARCH	GJRGARCH	GARCH	EGARCH	GJRGARCH	GARCH	EGARCH	GJRGARCH	GARCH	EGARCH	GJRGARCH
$μ$	0.001* (0.031)	−0.009* (0.030)	−0.007* (0.031)	−0.007* (0.026)	−0.007* (0.015)	−0.011* (0.026)	−0.014* (0.030)	−0.039* (0.028)	−0.026* (0.030)	0.015* (0.021)	0.021* (0.016)	0.017* (0.021)	0.0009* (0.024)	0.0003* (0.024)	−0.005* (0.024)
$ω$	0.025* (0.013)	0.007* (0.004)	0.021* (0.012)	0.042* (0.027)	0.0003 (0.002)	0.025* (0.010)	0.084* (0.035)	0.010 (0.003)	0.073* (0.030)	0.020* (0.011)	−0.007 (0.005)	0.018* (0.009)	0.014* (0.009)	−0.002 (0.002)	0.010* (0.004)
$α$	0.090* (0.022)	−0.046 (0.012)	0.047* (0.022)	0.034* (0.016)	−0.050* (0.012)	0.000 (0.010)	0.102* (0.025)	−0.092* (0.016)	0.022 (0.023)	0.049* (0.017)	−0.032 (0.013)	0.027* (0.012)	0.046* (0.016)	−0.055* (0.015)	0.004 (0.006)
$β$	0.900* (0.024)	0.986* (0.002)	0.914* (0.027)	0.926* (0.038)	0.976* (0.0008)	0.949* (0.016)	0.848* (0.038)	0.977* (0.0005)	0.873* (0.034)	0.926* (0.028)	0.980* (0.010)	0.928* (0.024)	0.940* (0.021)	0.987* (0.003)	0.956 * (0.006)
$γ$	–	0.132* (0.027)	0.057 (0.021)	–	0.059* (0.004)	0.055* (0.016)	–	0.101* (0.014)	0.122* (0.035)	–	0.100* (0.027)	0.042 (0.019)	–	0.069* (0.031)	0.060 * (0.013)
skew	0.992* (0.034)	0.998* (0.034)	0.996* (0.034)	1.009* (0.036)	1.014* (0.035)	1.006* (0.0366)	0.947* (0.033)	0.936* (0.033)	0.946* (0.033)	0.939* (0.031)	0.954* (0.030)	0.946* (0.031)	0.999* (0.035)	1.021* (0.037)	1.008* (0.036)
$v$	6.513* (1.239)	6.927* (1.390)	6.698 * (1.301)	6.387 (1.027)	6.698* (1.048)	6.804* (1.125)	6.560 (1.184)	6.288* (0.980)	6.418* (1.118)	4.261* (0.563)	4.454* (0.607)	4.459* (0.575)	7.263* (1.400)	7.953* (1.648)	7.826* (1.583)
ln(L)	−2287.149	−2280.912	−2282.884	−2003.121	−1995.366	−1994.151	−2257.235	−2243.526	−2249.833	−1658.27	−1656.838	−1654.922	−1922.067	−1907.025	−1909.964
AIC	3.221	3.213	3.216	2.822	2.812	2.811	3.179	3.161	3.17	2.338	2.337	2.334	2.708	2.688	2.692
LQ2(5)	0.288 [0.592]	2.751 [0.097]	0.489 [0.484]	2.817 [0.093]	4.906 [0.161]	2.479 [0.115]	0.146 [0.702]	14.30 (1.560e-04)	1.310 [0.252]	3.005 [0.083]	9.216 [0.002]	4.260 [0.039]	1.496 [0.221]	1.031 [0.310]	1.166 [0.280]
ARCH LM(5)	1.474 [0.599]	1.054 [0.717]	1.364 [0.629]	2.039 [0.463]	1.538 [0.582]	0.437 [0.902]	1.865 [0.502]	1.556 [0.578]	1.822 [0.512]	0.170 [0.973]	0.333 [0.931]	0.190 [0.968]	6.680 [0.041]	4.371 [0.143]	3.025 [0.286]

Panel A: Latin American emerging markets
Series	Colombia			Chile			Mexico			Peru			MILA
Series	GARCH	EGARCH	GJRGARCH	GARCH	EGARCH	GJRGARCH	GARCH	EGARCH	GJRGARCH	GARCH	EGARCH	GJRGARCH	GARCH	EGARCH	GJRGARCH
$μ$	0.001* (0.031)	−0.009* (0.030)	−0.007* (0.031)	−0.007* (0.026)	−0.007* (0.015)	−0.011* (0.026)	−0.014* (0.030)	−0.039* (0.028)	−0.026* (0.030)	0.015* (0.021)	0.021* (0.016)	0.017* (0.021)	0.0009* (0.024)	0.0003* (0.024)	−0.005* (0.024)
$ω$	0.025* (0.013)	0.007* (0.004)	0.021* (0.012)	0.042* (0.027)	0.0003 (0.002)	0.025* (0.010)	0.084* (0.035)	0.010 (0.003)	0.073* (0.030)	0.020* (0.011)	−0.007 (0.005)	0.018* (0.009)	0.014* (0.009)	−0.002 (0.002)	0.010* (0.004)
$α$	0.090* (0.022)	−0.046 (0.012)	0.047* (0.022)	0.034* (0.016)	−0.050* (0.012)	0.000 (0.010)	0.102* (0.025)	−0.092* (0.016)	0.022 (0.023)	0.049* (0.017)	−0.032 (0.013)	0.027* (0.012)	0.046* (0.016)	−0.055* (0.015)	0.004 (0.006)
$β$	0.900* (0.024)	0.986* (0.002)	0.914* (0.027)	0.926* (0.038)	0.976* (0.0008)	0.949* (0.016)	0.848* (0.038)	0.977* (0.0005)	0.873* (0.034)	0.926* (0.028)	0.980* (0.010)	0.928* (0.024)	0.940* (0.021)	0.987* (0.003)	0.956 * (0.006)
$γ$	–	0.132* (0.027)	0.057 (0.021)	–	0.059* (0.004)	0.055* (0.016)	–	0.101* (0.014)	0.122* (0.035)	–	0.100* (0.027)	0.042 (0.019)	–	0.069* (0.031)	0.060 * (0.013)
skew	0.992* (0.034)	0.998* (0.034)	0.996* (0.034)	1.009* (0.036)	1.014* (0.035)	1.006* (0.0366)	0.947* (0.033)	0.936* (0.033)	0.946* (0.033)	0.939* (0.031)	0.954* (0.030)	0.946* (0.031)	0.999* (0.035)	1.021* (0.037)	1.008* (0.036)
$v$	6.513* (1.239)	6.927* (1.390)	6.698 * (1.301)	6.387 (1.027)	6.698* (1.048)	6.804* (1.125)	6.560 (1.184)	6.288* (0.980)	6.418* (1.118)	4.261* (0.563)	4.454* (0.607)	4.459* (0.575)	7.263* (1.400)	7.953* (1.648)	7.826* (1.583)
ln(L)	−2287.149	−2280.912	−2282.884	−2003.121	−1995.366	−1994.151	−2257.235	−2243.526	−2249.833	−1658.27	−1656.838	−1654.922	−1922.067	−1907.025	−1909.964
AIC	3.221	3.213	3.216	2.822	2.812	2.811	3.179	3.161	3.17	2.338	2.337	2.334	2.708	2.688	2.692
LQ2(5)	0.288 [0.592]	2.751 [0.097]	0.489 [0.484]	2.817 [0.093]	4.906 [0.161]	2.479 [0.115]	0.146 [0.702]	14.30 (1.560e-04)	1.310 [0.252]	3.005 [0.083]	9.216 [0.002]	4.260 [0.039]	1.496 [0.221]	1.031 [0.310]	1.166 [0.280]
ARCH LM(5)	1.474 [0.599]	1.054 [0.717]	1.364 [0.629]	2.039 [0.463]	1.538 [0.582]	0.437 [0.902]	1.865 [0.502]	1.556 [0.578]	1.822 [0.512]	0.170 [0.973]	0.333 [0.931]	0.190 [0.968]	6.680 [0.041]	4.371 [0.143]	3.025 [0.286]

Panel B: Asian emerging markets
Series	Philippines			Singapore			Indonesia			Thailand			Malaysia
Series	GARCH	EGARCH	GJRGARCH	GARCH	EGARCH	GJRGARCH	GARCH	EGARCH	GJRGARCH	GARCH	EGARCH	GJRGARCH	GARCH	EGARCH	GJRGARCH
$μ$	0.025* (0.024)	0.012* (0.024)	0.015* (0.025)	0.021* (0.019)	0.008* (0.018)	0.012* (0.019)	0.022* (0.024)	0.005* (0.023)	0.008* (0.024)	0.040* (0.019)	0.036* (0.018)	0.033* (0.018)	0.002 (0.016)	−0.0004 (0.016)	−0.001 (0.017)
$ω$	0.015 (0.009)	−0.0009 (0.002)	0.013 (0.005)	0.007 (0.004)	−0.007 (0.003)	0.007 (0.003)	0.009* (0.005)	0.0006* (0.003)	0.008* (0.003)	0.004* (0.003)	−0.012 (0.006)	0.010* (0.004)	0.004 (0.002)	−0.006 (0.003)	0.004 (0.002)
$α$	0.042* (0.013)	−0.053 (0.008)	0.008* (0.009)	0.057* (0.015)	−0.059 (0.014)	0.014* (0.011)	0.047* (0.012)	−0.061* (0.013)	0.000 (0.008)	0.060* (0.015)	−0.075 (0.019)	0.016* (0.012)	0.073* (0.017)	−0.031 (0.012)	0.050* (0.018)
$β$	0.944* (0.019)	0.991* (0.00003)	0.955* (0.007)	0.935* (0.017)	0.988* (0.002)	0.944* (0.013)	0.948* (0.012)	0.990* (0.0005)	0.961* (0.005)	0.939* (0.015)	0.976* (0.010)	0.927* (0.017)	0.925* (0.017)	0.990* (0.002)	0.930* (0.015)
$γ$	–	0.028* (0.010)	0.046 (0.014)	–	0.091* (0.021)	0.066 (0.019)	–	0.082* (0.008)	0.065* (0.014)	–	0.131* (0.031)	0.091 (0.025)	–	0.131* (0.025)	0.030 (0.018)
skew	0.983* (0.035)	0.977* (0.035)	0.979* (0.035)	1.021* (0.035)	1.019* (0.035)	1.020* (0.035)	0.948* (0.033)	0.941* (0.033)	0.945* (0.033)	0.966* (0.032)	0.977* (0.032)	0.967* (0.032)	0.993* (0.035)	0.997* (0.034)	0.994* (0.035)
$v$	7.689* (1.418)	8.989* (1.850)	8.183* (1.588)	5.877 (0.988)	6.256* (1.122)	6.156* (1.074)	4.431 (0.542)	4.609* (0.572)	4.670* (0.585)	4.659* (0.635)	5.228* (0.794)	5.204* (0.788)	6.406* (1.089)	6.343* (1.076)	6.511* (1.124)
ln(L)	−1950.79	−1938.418	−1945.746	−1590.623	−1582.762	−1583.315	−1960.438	−1950.525	−1949.215	−1601.659	−1590.296	−1589.986	−1509.128	−1511.269	−1507.838
AIC	2.748	2.732	2.743	2.242	2.233	2.234	2.762	2.749	2.748	2.258	2.243	2.243	2.128	2.132	2.128
LQ2(5)	1.244 [0.802]	3.254 [0.363]	1.258 [0.799]	4.032 [0.250]	3.355 [0.346]	3.039 [0.400]	2.898 [0.426]	0.738 (0.916)	0.713 [0.920]	6.7292 [0.060]	3.068 [0.395]	2.547 [0.496]	6.369 [0.074]	9.525 [0.012]	6.194 [0.08096]
ARCH LM(5)	0.572 [1.440]	1.627 [0.560]	0.406 [0.911]	1.850 [0.505]	4.850 [0.111]	4.497 [0.134]	0.585 [0.858]	0.774 [0.801]	0.671 [0.832]	8.819 [0.012]	3.022 [0.287]	2.839 [0.314]	1.829 [0.510]	2.317 [0.405]	1.663 [0.551]

Panel B: Asian emerging markets
Series	Philippines			Singapore			Indonesia			Thailand			Malaysia
Series	GARCH	EGARCH	GJRGARCH	GARCH	EGARCH	GJRGARCH	GARCH	EGARCH	GJRGARCH	GARCH	EGARCH	GJRGARCH	GARCH	EGARCH	GJRGARCH
$μ$	0.025* (0.024)	0.012* (0.024)	0.015* (0.025)	0.021* (0.019)	0.008* (0.018)	0.012* (0.019)	0.022* (0.024)	0.005* (0.023)	0.008* (0.024)	0.040* (0.019)	0.036* (0.018)	0.033* (0.018)	0.002 (0.016)	−0.0004 (0.016)	−0.001 (0.017)
$ω$	0.015 (0.009)	−0.0009 (0.002)	0.013 (0.005)	0.007 (0.004)	−0.007 (0.003)	0.007 (0.003)	0.009* (0.005)	0.0006* (0.003)	0.008* (0.003)	0.004* (0.003)	−0.012 (0.006)	0.010* (0.004)	0.004 (0.002)	−0.006 (0.003)	0.004 (0.002)
$α$	0.042* (0.013)	−0.053 (0.008)	0.008* (0.009)	0.057* (0.015)	−0.059 (0.014)	0.014* (0.011)	0.047* (0.012)	−0.061* (0.013)	0.000 (0.008)	0.060* (0.015)	−0.075 (0.019)	0.016* (0.012)	0.073* (0.017)	−0.031 (0.012)	0.050* (0.018)
$β$	0.944* (0.019)	0.991* (0.00003)	0.955* (0.007)	0.935* (0.017)	0.988* (0.002)	0.944* (0.013)	0.948* (0.012)	0.990* (0.0005)	0.961* (0.005)	0.939* (0.015)	0.976* (0.010)	0.927* (0.017)	0.925* (0.017)	0.990* (0.002)	0.930* (0.015)
$γ$	–	0.028* (0.010)	0.046 (0.014)	–	0.091* (0.021)	0.066 (0.019)	–	0.082* (0.008)	0.065* (0.014)	–	0.131* (0.031)	0.091 (0.025)	–	0.131* (0.025)	0.030 (0.018)
skew	0.983* (0.035)	0.977* (0.035)	0.979* (0.035)	1.021* (0.035)	1.019* (0.035)	1.020* (0.035)	0.948* (0.033)	0.941* (0.033)	0.945* (0.033)	0.966* (0.032)	0.977* (0.032)	0.967* (0.032)	0.993* (0.035)	0.997* (0.034)	0.994* (0.035)
$v$	7.689* (1.418)	8.989* (1.850)	8.183* (1.588)	5.877 (0.988)	6.256* (1.122)	6.156* (1.074)	4.431 (0.542)	4.609* (0.572)	4.670* (0.585)	4.659* (0.635)	5.228* (0.794)	5.204* (0.788)	6.406* (1.089)	6.343* (1.076)	6.511* (1.124)
ln(L)	−1950.79	−1938.418	−1945.746	−1590.623	−1582.762	−1583.315	−1960.438	−1950.525	−1949.215	−1601.659	−1590.296	−1589.986	−1509.128	−1511.269	−1507.838
AIC	2.748	2.732	2.743	2.242	2.233	2.234	2.762	2.749	2.748	2.258	2.243	2.243	2.128	2.132	2.128
LQ2(5)	1.244 [0.802]	3.254 [0.363]	1.258 [0.799]	4.032 [0.250]	3.355 [0.346]	3.039 [0.400]	2.898 [0.426]	0.738 (0.916)	0.713 [0.920]	6.7292 [0.060]	3.068 [0.395]	2.547 [0.496]	6.369 [0.074]	9.525 [0.012]	6.194 [0.08096]
ARCH LM(5)	0.572 [1.440]	1.627 [0.560]	0.406 [0.911]	1.850 [0.505]	4.850 [0.111]	4.497 [0.134]	0.585 [0.858]	0.774 [0.801]	0.671 [0.832]	8.819 [0.012]	3.022 [0.287]	2.839 [0.314]	1.829 [0.510]	2.317 [0.405]	1.663 [0.551]

Note(s): ln(L) is the value of the maximized log-likelihood. AIC is the Akaike Information Criterion, LQ2(5) is the Ljung and Box statistics of order five computed on the standardized square residuals, ARCH LM is the ARCH Lagrange Multiplier test of order five. * indicates significance at the 1% significance level, standard errors are in parentheses and the numbers in brackets are p-values

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