Table 6 Small sample: goodness-of-fit test for ARMA–GARCH models
From: ARMA–GARCH model with fractional generalized hyperbolic innovations
IBM | Johnson & Johnson | Oracle | Apple | Amazon | CVS | |
|---|---|---|---|---|---|---|
ARMA–GARCH model with fractional GH innovations | ||||||
KS | 0.0800 | 0.0556 | 0.0769 | 0.1029 | 0.0509 | 0.1179 |
(p-value) | (0.8186) | (0.8631) | (0.9524) | (0.4670) | (0.9421) | (0.1327) |
LL | 8984.54 | 9937.79 | 9736.98 | 9151.06 | 8829.31 | 9005.51 |
AIC | − 17963.08 | − 19869.58 | − 19467.95 | − 18296.11 | − 17838.63 | − 18005.02 |
ARMA–GARCH model with non-fractional GH innovations | ||||||
KS | 0.1960 | 0.2102 | 0.2931 | 0.1676 | 0.2679 | 0.0968 |
(p-value) | (0.0009) | (0.0000) | (0.0000) | (0.0131) | (0.0000) | (0.1959) |
LL | 8613.54 | 9568.62 | 9366.99 | 8784.29 | 8556.95 | 8637.40 |
AIC | − 17221.08 | − 19131.23 | − 18727.97 | − 17562.57 | − 17107.90 | − 17268.80 |
ARMA–GARCH model with normal innovations | ||||||
KS | 0.5811 | 0.3075 | 0.1379 | 0.1341 | 0.1807 | 0.2057 |
(p-value) | (0.0000) | (0.0000) | (0.0730) | (0.0801) | (0.0001) | (0.0001) |
LL | 8269.34 | 9023.02 | 8929.74 | 8011.06 | 7804.60 | 7769.13 |
AIC | − 11.9671 | − 13.2404 | − 12.4082 | − 12.0094 | − 11.8806 | − 12.1003 |