Volatility Forecasting Based On Heteroautoregressive Models

Volatility is a vital property of asset.Investors care not only about asset return,but also its risk,especially in the wake of the stock crash occurring in 2015.Volatility better reflects the intrinsic character of asset risk,usually,the higher the asset return is,the higher the asset risk entails.However,it is not easy to acquire volatility,in the past,scholars modeled on time series on asset return,then utilized conditional variance to measure volatility,and effects of such measurement remained controversial.With the rapid development of computer and deepening of financial mathematics,experts discovered effective ways to measure volatility,that is,acquiring volatility through asset return based on high-frequent data,and also found that realized volatility served as the proxy for real volatility,then modeling on volatility directly to predict its trend.Since then,volatility forecast models have been greatly developed and evolved.CSI 300 index,as the first index to reflect the overall market condition in our country,acts as a barometer in reflecting market condition in Shanghai and Shen Zhen.Though there is prolific research into the volatility of Dow Jones and Stand Poor 500 index,the Chinese stock market is different from those of mature foreign markets,so their research results cannot be applied in Chinese market directly,because risk exposure are vastly different.For the investors to achieve long-term and stable investment return,better control the risk of portfolio,optimize asset allocation,it is necessary to carry out deep research into volatility of CSI 300 stock index.CSI 300 future index is the base of study in this article,and the article selected 5-minute data as the subject of study,then establish realized volatility forecast model.The first section of the article is making a brief depiction of index character,such as stationarity,autoregressiveness,ARCH effect,long-term memory.The second section of the thesis used TVP model to forecast realized volatility.The idea of using TVP model is mainly because through massive reading of references,the author found whatever the methods were used,the parameters of the forecasting model were non-changing within in-sample range,but in fact,with the time passage and the change of the market,the role of factors effecting volatility also kept changing,so introduction of time-varying parameters was necessary.TVP model was mainly based on Bayesian method and Kalman Filter to achieve window-rolling prediction,drawing comparison between in-sample and out-of-sample data.The non-time-varying forecast model and traditional forecast model are benchmarks for comparison,the non-time-varying applies OLS model while traditional model is based on GARCH model.Non-TVP and TVP models are direct forecast models while GARCHs are indirect forecast models.The article aims at finding whether TVP model is superior in forecasting volatility to non-TVP model or traditional model.Meanwhile,loss function was introduced to judge the soundness and rationality of model fitting.The article would explore multiple loss functions,work in accordance with actual significance and engage in comparisons with one another,then carrying out a hypothesis test(SPA test)to verify whether the loss function results are rational.The conclusion is that introducing TVP model improved the precision of volatility forecast while traditional GARCH model doesn’t perform well in forecasting.Finally,to summarize the main points and give personal suggestions for future research.