Table 3 Estimation results for different...

Table 3

Estimation results for different volatility models with skew-normal 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
$μ$	0.002* (0.030)	−0.019* (0.029)	−0.015* (0.031)	−0.007* (0.027)	0.004* (0.026)	−0.013* (0.027)	−0.023* (0.029)	−0.057* (0.0388)	−0.043* (0.030)	0.024* (0.021)	0.024* (0.023)	0.015 * (0.020)	0.008* (0.024)	0.002* (0.024)	−0.005* (0.024)
$ω$	0.020* (0.009)	0.011* (0.004)	0.019* (0.008)	0.097* (0.045)	0.007 (0.004)	0.033* (0.009)	0.072* (0.024)	0.023* (0.008)	0.068* (0.022)	0.019* (0.008)	−0.0008 (0.005)	0.022* (0.008)	0.0004* (0.003)	0.047* (0.016)	0.012* (0.004)
$α$	0.074* (0.014)	−0.040* (0.008)	0.043* (0.015)	0.105* (0.029)	−0.048* (0.014)	0.009* (0.015)	0.130* (0.021)	−0.074* (0.018)	0.073 (0.022)	0.084* (0.017)	−0.049 (0.013)	0.046* (0.013)	−0.058* (0.010)	−0.112* (0.026)	0.011 (0.008)
$β$	0.917* (0.017)	0.985* (0.003)	0.924* (0.018)	0.811* (0.063)	0.970* (0.010)	0.926* (0.017)	0.832* (0.028)	0.966* (0.012)	0.844* (0.026)	0.893* (0.023)	0.973* (0.010)	0.891* (0.023)	0.985* (0.002)	0.930* (0.023)	0.943* (0.011)
$γ$	–	0.125* (0.020)	0.044* (0.015)	–	0.135* (0.027)	0.074* (0.018)	–	0.208* (0.035)	0.095* (0.031)	–	0.165* (0.026)	0.072 (0.021)	0.091* (0.019)	0.126* (0.030)	0.067* (0.014)
skew	0.966* (0.031)	0.974* (0.031)	0.969* (0.031)	1.008* (0.031)	1.010* (0.031)	0.984* (0.031)	0.909* (0.029)	0.890 * (0.029)	0.902* (0.029)	0.944* (0.027)	0.971* (0.028)	0.961* (0.028)	1.016* (0.033)	0.847* (0.029)	0.999* (0.032)
$v$	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–
ln(L)	−2308.354	−2300.427	−2303.496	−2046.730	−2043.417	−2041.573	−2280.093	−2270.692	−2275.115	−1717.698	−1711.279	−1709.514	−1944.812	−1927.105	−1930.403
AIC	3.249	3.239	3.244	2.882	2.878	2.876	3.209	3.198	3.204	2.42	2.412	2.409	2.739	2.715	2.72
LQ2(5)	1.231 [0.267]	3.221 [0.073]	1.148 [0.284]	0.078 [0.780]	1.090 [0.296]	1.470 [0.225]	0.158 [0.691]	1.059 [0.303]	0.006 [0.940]	0.659 [0.417]	4.176 [0.233]	1.320 [0.251]	0.527 [0.468]	0.397 [0.529]	0.512 [0.475]
ARCH LM(5)	1.459 [0.603]	1.265 [0.656]	1.321 [0.641]	0.634 [0.843]	0.541 [0.871]	0.172 [0.972]	2.247 [0.419]	2.235 [0.422]	3.018 [0.287]	0.577 [0.861]	0.472 [0.892]	0.893 [0.765]	3.322 [0.246]	2.707 [0.335]	1.586 [0.570]

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
$μ$	0.002* (0.030)	−0.019* (0.029)	−0.015* (0.031)	−0.007* (0.027)	0.004* (0.026)	−0.013* (0.027)	−0.023* (0.029)	−0.057* (0.0388)	−0.043* (0.030)	0.024* (0.021)	0.024* (0.023)	0.015 * (0.020)	0.008* (0.024)	0.002* (0.024)	−0.005* (0.024)
$ω$	0.020* (0.009)	0.011* (0.004)	0.019* (0.008)	0.097* (0.045)	0.007 (0.004)	0.033* (0.009)	0.072* (0.024)	0.023* (0.008)	0.068* (0.022)	0.019* (0.008)	−0.0008 (0.005)	0.022* (0.008)	0.0004* (0.003)	0.047* (0.016)	0.012* (0.004)
$α$	0.074* (0.014)	−0.040* (0.008)	0.043* (0.015)	0.105* (0.029)	−0.048* (0.014)	0.009* (0.015)	0.130* (0.021)	−0.074* (0.018)	0.073 (0.022)	0.084* (0.017)	−0.049 (0.013)	0.046* (0.013)	−0.058* (0.010)	−0.112* (0.026)	0.011 (0.008)
$β$	0.917* (0.017)	0.985* (0.003)	0.924* (0.018)	0.811* (0.063)	0.970* (0.010)	0.926* (0.017)	0.832* (0.028)	0.966* (0.012)	0.844* (0.026)	0.893* (0.023)	0.973* (0.010)	0.891* (0.023)	0.985* (0.002)	0.930* (0.023)	0.943* (0.011)
$γ$	–	0.125* (0.020)	0.044* (0.015)	–	0.135* (0.027)	0.074* (0.018)	–	0.208* (0.035)	0.095* (0.031)	–	0.165* (0.026)	0.072 (0.021)	0.091* (0.019)	0.126* (0.030)	0.067* (0.014)
skew	0.966* (0.031)	0.974* (0.031)	0.969* (0.031)	1.008* (0.031)	1.010* (0.031)	0.984* (0.031)	0.909* (0.029)	0.890 * (0.029)	0.902* (0.029)	0.944* (0.027)	0.971* (0.028)	0.961* (0.028)	1.016* (0.033)	0.847* (0.029)	0.999* (0.032)
$v$	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–
ln(L)	−2308.354	−2300.427	−2303.496	−2046.730	−2043.417	−2041.573	−2280.093	−2270.692	−2275.115	−1717.698	−1711.279	−1709.514	−1944.812	−1927.105	−1930.403
AIC	3.249	3.239	3.244	2.882	2.878	2.876	3.209	3.198	3.204	2.42	2.412	2.409	2.739	2.715	2.72
LQ2(5)	1.231 [0.267]	3.221 [0.073]	1.148 [0.284]	0.078 [0.780]	1.090 [0.296]	1.470 [0.225]	0.158 [0.691]	1.059 [0.303]	0.006 [0.940]	0.659 [0.417]	4.176 [0.233]	1.320 [0.251]	0.527 [0.468]	0.397 [0.529]	0.512 [0.475]
ARCH LM(5)	1.459 [0.603]	1.265 [0.656]	1.321 [0.641]	0.634 [0.843]	0.541 [0.871]	0.172 [0.972]	2.247 [0.419]	2.235 [0.422]	3.018 [0.287]	0.577 [0.861]	0.472 [0.892]	0.893 [0.765]	3.322 [0.246]	2.707 [0.335]	1.586 [0.570]

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
$μ$	0.029* (0.025)	0.008* (0.037)	0.014* (0.025)	0.013* (0.019)	−0.0003* (0.018)	0.002* (0.019)	0.016* (0.025)	−0.0006* (0.024)	−0.0005* (0.025)	0.053* (0.019)	0.043* (0.016)	0.037* (0.019)	0.001* (0.017)	−0.003* (0.017)	−0.005* (0.017)
$ω$	0.013 (0.005)	−0.00007* (0.002)	0.008 (0.004)	0.008* (0.004)	−0.003 (0.002)	0.006* (0.002)	0.010* (0.004)	0.004* (0.002)	0.008* (0.002)	0.012* (0.005)	−0.013* (0.005)	0.015* (0.004)	0.004* (0.002)	−0.002 (0.003)	0.004* (0.002)
$α$	0.032* (0.006)	−0.057 (0.005)	0.000* (0.007)	0.051* (0.011)	−0.049 (0.008)	0.011* (0.008)	0.037* (0.006)	−0.049* (0.008)	0.000 (0.005)	0.072* (0.015)	−0.086* (0.015)	0.008* (0.009)	0.065* (0.013)	−0.031 (0.010)	0.042 (0.013)
$β$	0.955* (0.007)	0.991* (0.000005)	0.971* (0.016)	0.938 × 0.014	0.989* (0.001)	0.954* (0.007)	0.954* (0.007)	0.992* (0.00008)	0.967* (0.005)	0.912* (0.018)	0.967* (0.008)	0.916* (0.015)	0.930* (0.013)	0.990* (0.002)	0.935* (0.012)
$γ$	–	0.021* (0.007)	0.041 (0.006)	–	0.066* (0.008)	0.049 (0.012)	–	0.058* (0.007)	0.049* (0.009)	–	0.120* (0.022)	0.104* (0.019)	–	0.119* (0.019)	0.031* (0.015)
skew	0.942* (0.030)	0.962* (0.031)	0.950* (0.030)	0.963* (0.030)	0.976* (0.030)	0.971* (0.030)	0.914* (0.026)	0.927* (0.027)	0.920* (0.027)	0.954* (0.028)	0.987* (0.029)	0.974* (0.029)	0.948* (0.030)	0.961* (0.030)	0.953* (0.031)
$v$	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–
ln(L)	−1985.083	−1958.250	−1973.034	−1619.686	−1610.080	−1611.210	−2024.403	−2008.127	−2008.529	−1648.736	−1625.599	−1625.235	−1536.195	−1538.453	−1533.893
AIC	2.795	2.759	2.78	2.282	2.27	2.271	2.850	2.829	2.829	2.323	2.292	2.291	2.165	2.169	2.163
LQ2(5)	0.784 [0.574]	3.672 [0.2988]	1.957 [0.629]	4.684 [0.180]	4.296 [0.219]	3.495 [0.324]	5.892 [0.095]	2.042 [0.609]	1.903 [0.642]	6.045 [0.088]	3.831 [0.276]	2.899 [0.426]	8.278 [0.025]	11.160 [0.005]	7.436 [0.041]
ARCH LM(5)	1.945 [0.632]	1.945 [0.484]	0.652 [0.838]	1.725 [0.535]	4.279 [0.150]	3.665 [0.207]	1.121 [0.697]	1.3666 [0.628]	1.001 [0.733]	9.117 [0.011]	3.745 [0.198]	3.437 [0.232]	2.241 [0.420]	2.738 [0.330]	1.956 [0.481]

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
$μ$	0.029* (0.025)	0.008* (0.037)	0.014* (0.025)	0.013* (0.019)	−0.0003* (0.018)	0.002* (0.019)	0.016* (0.025)	−0.0006* (0.024)	−0.0005* (0.025)	0.053* (0.019)	0.043* (0.016)	0.037* (0.019)	0.001* (0.017)	−0.003* (0.017)	−0.005* (0.017)
$ω$	0.013 (0.005)	−0.00007* (0.002)	0.008 (0.004)	0.008* (0.004)	−0.003 (0.002)	0.006* (0.002)	0.010* (0.004)	0.004* (0.002)	0.008* (0.002)	0.012* (0.005)	−0.013* (0.005)	0.015* (0.004)	0.004* (0.002)	−0.002 (0.003)	0.004* (0.002)
$α$	0.032* (0.006)	−0.057 (0.005)	0.000* (0.007)	0.051* (0.011)	−0.049 (0.008)	0.011* (0.008)	0.037* (0.006)	−0.049* (0.008)	0.000 (0.005)	0.072* (0.015)	−0.086* (0.015)	0.008* (0.009)	0.065* (0.013)	−0.031 (0.010)	0.042 (0.013)
$β$	0.955* (0.007)	0.991* (0.000005)	0.971* (0.016)	0.938 × 0.014	0.989* (0.001)	0.954* (0.007)	0.954* (0.007)	0.992* (0.00008)	0.967* (0.005)	0.912* (0.018)	0.967* (0.008)	0.916* (0.015)	0.930* (0.013)	0.990* (0.002)	0.935* (0.012)
$γ$	–	0.021* (0.007)	0.041 (0.006)	–	0.066* (0.008)	0.049 (0.012)	–	0.058* (0.007)	0.049* (0.009)	–	0.120* (0.022)	0.104* (0.019)	–	0.119* (0.019)	0.031* (0.015)
skew	0.942* (0.030)	0.962* (0.031)	0.950* (0.030)	0.963* (0.030)	0.976* (0.030)	0.971* (0.030)	0.914* (0.026)	0.927* (0.027)	0.920* (0.027)	0.954* (0.028)	0.987* (0.029)	0.974* (0.029)	0.948* (0.030)	0.961* (0.030)	0.953* (0.031)
$v$	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–
ln(L)	−1985.083	−1958.250	−1973.034	−1619.686	−1610.080	−1611.210	−2024.403	−2008.127	−2008.529	−1648.736	−1625.599	−1625.235	−1536.195	−1538.453	−1533.893
AIC	2.795	2.759	2.78	2.282	2.27	2.271	2.850	2.829	2.829	2.323	2.292	2.291	2.165	2.169	2.163
LQ2(5)	0.784 [0.574]	3.672 [0.2988]	1.957 [0.629]	4.684 [0.180]	4.296 [0.219]	3.495 [0.324]	5.892 [0.095]	2.042 [0.609]	1.903 [0.642]	6.045 [0.088]	3.831 [0.276]	2.899 [0.426]	8.278 [0.025]	11.160 [0.005]	7.436 [0.041]
ARCH LM(5)	1.945 [0.632]	1.945 [0.484]	0.652 [0.838]	1.725 [0.535]	4.279 [0.150]	3.665 [0.207]	1.121 [0.697]	1.3666 [0.628]	1.001 [0.733]	9.117 [0.011]	3.745 [0.198]	3.437 [0.232]	2.241 [0.420]	2.738 [0.330]	1.956 [0.481]

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

[ViewLarge]

Sharing Unavailable