Modeling S&P 500 STOCK INDEX using ARMA-ASYMMETRIC POWER ARCH models

In this paper, the S&P 500 stock index is studied for its time varying volatility and stylized facts. The ARMA mean equation with asymmetric power ARCH errors is used to model the series correlations and the conditional heteroscadesticity in the asset returns. The conditional distributions of the standardized residuals are assumed to be the normal distribution, the t distribution or the skew-t distribution. Furthermore, to capture the asymmetry and fat tail of the returns, an ARMA (0, 2)-APARCH (1, 1) model with the skew-t distribution is found to fit the data better than other models discussed in this paper. Finally, we use ARMA (0, 2)-APARCH (1, 1) model with the skew-t distribution to do the 10-step-ahead forecasting compared with the ARMA (0, 2)-GARCH (1, 1) model with the normal distribution and get the empirical conclusion that the ARMA (0, 2)-APARCH (1, 1) with the skew-t distribution also gives a better result in the forecasting.