Forecasting Stock Market Volatility Under Extreme Volatility

With the globalization of the economy,the stock market has become an important indicator reflecting the real economy of the country.Stock market is not only a barometer of the economy of shareholders in various countries,but also an important place for enterprises to finance and investors to participate in investment,Therefore,the turbulence of the stock market will affect investors' investment sentiment and enterprises' financing in the capital market,and even cause national economic turbulence.Proper stock market volatility can promote a more rational allocation of resources,however,excessive stock market volatility may affect the interests of investors and enterprises and trigger financial crisis.So it is very important to model and forecast the stock market volatility accurately.There are many volatility models in traditional statistical and econometric theories.At present,the traditional GARCH model and the extended GARCH model are mostly used to forecast the stock market volatility,while the traditional GARCH model and the extended GARCH model are mostly used to predict the stock market volatility,however,the traditional GARCH class model is strictly limited to data with the same frequency.Therefore,GARCH model is not suitable for studying the main driving factors of long-term financial market volatility.In this paper,the GARCH-MIDAS model proposed by foreign scholars in recent years is mainly used,The advantage of this model is that it combines MIDAS regression technology with GARCH model,so that short-term high-frequency data and long-term low-frequency data can be considered simultaneously.The stock return tends to have the characteristics of peak and heavy tail,and the residual has an asymmetric effect on the return,in addition,extreme events such as financial crises and regional wars may also cause extreme volatility in stocks.The standard GARCH-MIDAS model can not capture the asymmetric effect in the stock market and the extreme impact of different capture extreme events.Therefore,in this paper we improves GARCH-MIDAS model on the basis of existing research,so that it can capture the asymmetric effect and extreme fluctuation effect.The specificresearch ideas of this paper are as follows:Firstly,for short-term components replacing GARCH process in standard GARCH-MIDAS model with GJR-GARCH model,long-term components decompose realized volatility into realized positive variance and realized negative variance.Besides,in order to capture the extreme volatility caused by extreme events in the market,this paper further improves the GARCH-MIDAS model by introducing different threshold variables into the short-term components while in the long-term component,the approach is to further decompose realized volatility.Fifteen different GARCH-MIDAS models are obtained through the above improvements.Finally,the improved model is empirically analyzed on S&P 500 index to explore the fitting ability of the improved model to data and whether the improved model can have better prediction accuracy.In order to avoid the one-sidedness of a single evaluation index,five loss functions with different criteria are used to evaluate the prediction performance of 15 extended models when large fluctuations occur.Furthermore,by using the model confidence set test(MCS test),it is found that the predicted results of the models with both asymmetric and threshold effects are closer to the observed samples than those with only asymmetric or threshold effects.Although no model has the best out-of-sample prediction results under different evaluation criteria,models including asymmetric and extreme volatility effects can significantly improve the prediction ability of stock market volatility.