Realized GAS Model With Time-varying High-order Moments And Its Empirical Applications

As the most common negotiable securities,stock has the important functions of raising funds,allocating investment risks and promoting capital circulation.In recent years,as the number of listed companies and investors on the stock market continues to increase,the correlation between the stock market and the real economy is gradually enhanced.Therefore,how to estimate the volatility model parameters of the stock market and predict the risk of the stock market has become a hot topic for scholars studying financial practice.At the same time,with the development of information technology,high-frequency data containing intraday price change information is favored by many scholars.However,as intraday high-frequency data is accompanied by a large amount of noise,how to avoid the impact of noise has become a difficulty for scholars.In addition,the existing research on stock market volatility often adopts constant high-order moment volatility model.However,empirical research on stock market volatility shows that high-order moments also have time variability,and ignoring the time variability of high-order moments will lead to lower accuracy of stock market volatility risk prediction.Therefore,time-varying modeling considering high-order moments can provide more accurate risk prediction tools for financial asset managers and investors,which has important practical and theoretical significance for financial asset pricing and risk management.Based on the generalized autoregressive scoring framework,this paper builds the realized GAS(TVP-RGAS)model with time-varying high-order moments by modeling the return on assets and realized measures jointly.To be specific,the implemented measure is introduced into the GAS model with robust forecasting ability,and the intraday price change information is helpful to quickly capture the drastic fluctuations of the stock market.At the same time,it is assumed that asset returns follow student t distribution,and the degree of freedom parameters in time-varying student t distribution are considered.In addition,the model is an observation-driven model,which can be estimated by maximum likelihood method,and has the advantage of being easy to implement.The empirical part of this paper selects five-minute high-frequency data and daily closing price data of Shanghai Composite Index,Shenzhen Component Index and Hang Seng Index from January 1,2010 to December 30,2020.The empirical results of realized GARCH(RGARCH)model,realized EGARCH(REGARCH)model,realized GAS(RGAS)model and TVP-RGAS model are compared.The main conclusions are as follows:(1)according to the results of QQ chart,Jarque-Bera(j-b)test and Ljung-Box(Q(10))test of each index,each index has the characteristic of “peak and thick tail”,among which,hang seng index has the most obvious characteristic of “peak and thick tail”.(2)The maximum likelihood method is adopted to estimate the parameters of each model,and the estimation effects of each model are compared through logarithmic likelihood value and red pool information criterion.In general,the model based on GAS model framework under the three indices has better parameter estimation effect than the model based on GARCH model framework,and TVP-RGAS model considering time-varying high-order moment characteristics always has the best parameter estimation effect.(3)The prediction period of samples is divided into 5 years and 10 years,and loss function,DM test and MCS test are used to evaluate the volatility prediction effect of each model.The results show that the volatility prediction effect of the model based on GAS model framework is still better than that of the model based on GARCH model framework,and TVP-RGAS model has the best volatility prediction effect among the three evaluation methods.(4)Value at risk(Va R)is adopted as a risk management tool,and a posterior analysis is adopted to evaluate the risk prediction accuracy of each model.From the results of a posterior analysis,it can be seen that both the GAS model framework and the MODEL under the GARCH model framework can effectively predict risks,and TVP-RGAS model has the best risk prediction results.