| Summary: | The focus of this research is to model and forecast the volatility (conditional variance) of the Chinese, British and American stock markets. The related stock indices selected include HSI, SSEC, FTSE100, and DJIA indices. The prediction models studied in this research range from symmetric GARCH model to asymmetric models, such as the EGARCH model as well as the TGARCH model.
In order to complete this study, we considered the historical data of the four indices in five years from the beginning of 2015 to the end of 2019. And the entire sample period will be divided into the in-sample period and the out-of-sample period. Conditional variance that is difficult to observe will be replaced by the squared residual. And the findings for these methods are calculated using the Microsoft Excel and the statistical software EVIEWS. In addition, comparisons among these models have been made by doing the graphical representation, the error test statistics, the analysis of the parameters, the Ljung-Box Q-statistic and the Lagrange Multiplier tests etc. And the performance for each model is measured by the RMSE, MAE loss functions and the coefficient of determination of the Mincer–Zarnowitz regression.
The results imply that for the return series of the four stock indexes studied in this article, the GARCH-type model with the non-normal distribution assumption seems to give better out-of-sample estimates than when the normal distribution assumption is adopted. In addition, the EGARCH model seems to be superior to other models, which is similar to the result of the option pricing forecast results.
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