Table 5 Goodness-of-fit tests 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 | 0.0758 | 0.0670 | 0.1042 | 0.1207 | 0.0795 | 0.0630 |
(p-value) | (0.8432) | (0.6967) | (0.6776) | (0.3669) | (0.7269) | (0.9627) |
LL | 16689.24 | 18226.48 | 17715.06 | 16857.67 | 16235.18 | 16986.63 |
AIC | − 33372.48 | − 36446.95 | − 35424.13 | − 33709.35 | − 32464.37 | − 32167.25 |
ARMA–GARCH model with non-fractional GH innovations | ||||||
KS | 0.1990 | 0.1789 | 0.2299 | 0.1560 | 0.1967 | 0.1410 |
(p-value) | (0.0007) | (0.0000) | (0.0002) | (0.0646) | (0.0017) | (0.0899) |
LL | 16174.77 | 17708.04 | 17198.05 | 16336.22 | 15715.95 | 15563.07 |
AIC | − 32343.54 | − 35410.08 | − 34390.09 | − 32666.44 | − 31425.91 | − 31120.15 |
ARMA–GARCH model with normal innovations | ||||||
KS | 0.1542 | 0.4748 | 0.3089 | 0.1763 | 0.1391 | 0.2047 |
(p-value) | (0.0168) | (0.0000) | (0.0000) | (0.0383) | (0.0815) | (0.0098) |
LL | 15643.38 | 18121.03 | 17071.17 | 15968.61 | 16156.68 | 15146.00 |
AIC | − 12.1975 | − 13.2808 | − 12.5111 | − 11.7028 | − 11.8407 | − 11.8328 |