Table 12.

GARCH, GJR and EGARCH(1,1), persistence and half-life—NASDAQ

	Full sample	27/07/1998	02/04/2003	12/09/2008	21/04/2009	20/02/2020	18/12/2020
ARCH-LM	2046.298*	1013.827*	116.000*	108.560*	33.232*	391.490*	40.722*
$\alpha$	0.111*	0.115*	0.096*	0.038*	$-$ 0.090***	0.131*	0.172**
$\beta$	0.889*	0.860*	0.866*	0.956*	$-$ 0.605**	0.846*	0.828*
$\alpha +\beta$	0.999	0.975	0.962	0.994	$-$ 0.695	0.977	1.000
Half-life	830.765	27.378	17.892	115.178	NA	29.802	1571.416
t-df	6.726*	5.588*	34.853*	18.935*	89.826*	5.247*	3.891*
$\gamma$ GJR	0.120*	0.104*	0.178*	0.061*	0.229	0.303*	0.272*
$\gamma$ EGARCH	$-$0.087*	$-$ 0.079*	$-$ 0.125*	$-$ 0.050*	$-$ 0.316***	$-$ 0.226*	$-$ 0.122
BIC GARCH	2.909	2.234	4.527	2.975	5.508	2.763	4.157
BIC GJR	2.900	2.231	4.496	2.964	5.557	2.723	4.156
BIC EGARCH	2.897	2.227	4.502	2.965	5.539	2.715	4.175

ARCH-LM test. *, **, ***Denote statistically significant at the 1%, 5% and 10% significance levels, respectively. $\alpha +\beta =1$ is the measure of volatility persistence. Half-life gives the point estimate of the half-life in days given as $HL=\frac{log(0.5)}{log(\alpha +\beta )}$. t-df represents the Student’s t degrees of freedom. GARCH, GJR and EGARCH are conditional heteroskedastic models defined in (4), (6) and (5), respectively