Table 4.1.2 Best Model Approach Indices ARIMA GARCH/T-GARCH E-GARCH S&P500 ARIMA (10,1,10) GARCH (2,2) E-GARCH (2,1) With ARIMA (10,1,10) With ARIMA (10,1,10) - excluded No No AR(4) AIC -5.781425 -6.237441 -6.277221 ARIMA (10,1,10) GARCH (2,1) E-GARCH (1,2) S&P400 With ARIMA (10,1,10) With ARIMA (10,1,10) - excluded AR(4), MA(1), MA(4) AR(3), MA(3) AR(1), AR(8), MA(8) AIC -5.4498221 -5.991598 -6.007784 ARIMA (10,1,10) GARCH (2,2) E-GARCH (1,1) S&P600 With ARIMA (10,1,10) With ARIMA (10,1,10) - excluded AR(3), AR(5), MA(5) AR(8), MA(8) AR(4), AR(7), AR(8) AIC -5.567518 -5.789050 -5.809214 4.1.3 Residual Diagnostics The residuals for each test: Jarque-Bera: H0: Skewness being equal to 0 and kurtosis being equal to 3 Q-statistics: H0: Residuals have no serial correlation LM Test: H0: Residual have no autocorrelation ARCH Heteroskedasticity Test: Ho:Residuals are homoskedastic BDS Test: H0: Residuals have linearity
Table 4.1.2 Best Model Approach Indices ARIMA GARCH/T-GARCH E-GARCH S&P500 ARIMA (10,1,10) GARCH (2,2) With ARIMA (10,1,10) E-GARCH (2,1) With ARIMA (10,1,10) - excluded No No AR(4) AIC -5.781425 -6.237441 -6.277221 S&P400 ARIMA (10,1,10) GARCH (2,1) With ARIMA (10,1,10) E-GARCH (1,2) With ARIMA (10,1,10) - excluded AR(4), MA(1), MA(4) AR(3), MA(3) AR(1), AR(8), MA(8) AIC -5.4498221 -5.991598 -6.007784 S&P600 ARIMA (10,1,10) GARCH (2,2) With ARIMA (10,1,10) E-GARCH (1,1) With ARIMA (10,1,10) - excluded AR(3), AR(5), MA(5) AR(8), MA(8) AR(4), AR(7), AR(8) AIC -5.567518 -5.789050 -5.809214 4.1.3 Residual Diagnostics The residuals for each test: Jarque-Bera: H0: Skewness being equal to 0 and kurtosis being equal to 3 Q-statistics: H0: Residuals have no serial correlation LM Test: H0: Residual have no autocorrelation ARCH Heteroskedasticity Test: Ho:Residuals are homoskedastic BDS Test: H0: Residuals have linearity