Table 5 Standardized residual test of ARMA (1, 1) + GARCH (1, 1)
Residual test | Variable | Test statistic | Test value | Probability |
|---|---|---|---|---|
Jarque–Bera | R | \(\chi^{2}\) | 170.0431 | 0 |
Shapiro–Wilk | R | W | 0.8750428 | 1.368657E−10 |
Ljung–Box | R | \(Q(10)\) | 8.937746 | 0.5380217 |
Ljung–Box | R | \(Q(15)\) | 16.65662 | 0.3398028 |
Ljung–Box | R | \(Q(20)\) | 20.21719 | 0.4444191 |
Ljung–Box | R 2 | \(Q(10)\) | 6.394848 | 0.7810711 |
Ljung–Box | R 2 | \(Q(15)\) | 8.093766 | 0.9199685 |
Ljung–Box | R 2 | \(Q(20)\) | 10.61964 | 0.9554965 |
LM ARCH | R | \(TR^{2}\) | 9.613653 | 0.6498134 |