| As the barometer of national economy,stock market is the signal system of real economy recognized by all walks of life.The stock market is also a hub connecting enterprises and investors.The research on the volatility risk of stock market can better predict the market volatility,which can provide enterprises with better strategies of maintaining and increasing value,and provide investors with a strong reference to prevent risks.As a representative variable of risk measurement,volatility measures the change degree of the underlying asset price(yield),which is the core factor that institutions and investors pay attention to when they price,hedge and manage financial products.However,volatility itself can not be directly observed from market data,so it needs to be measured by using relevant theories and methods.The volatility of financial asset return is easy to observe and obtain,and it is used as a common measure agent of volatility.Based on the high-frequency data,using the realized variance,which contains rich explanatory variables,as the measurement object of volatility,the regression modeling under the high-frequency data has become one of the mainstream research trends.Based on the HAR model,this paper attempts to add the time-varying coefficients and leverage effect into the HAR model,and proposes the asymmetric HAR(TVC-AHAR)model with time-varying coefficient.The improved method is to replace the daily realized variance of explanatory variables with positive and negative realized semi-variance,emphasizing the leverage effect of negative return on volatility;to replace the fixed coefficient before the two semi-variance with time-varying coefficient,respectively construct state equations,reflect the continuous characteristics of positive and negative semi-variance,and reflect the impact of different market investment emotions on their own volatility.The parameter estimation of the model is feasible easily,and the maximum likelihood method under Kalman filter can be used for parameter estimation.In order to further investigate the role of one-way variance in modeling,this paper constructs a one-way time-varying constraint model with only positive and negative semi-variance,and compares the performance of the model only with positive or negative realized semi-variance.In the empirical part of this paper,we select 5 indexes of Shanghai Composite Index,Shenzhen composite index,Hang Seng Index,foreign Nikkei index and Seoul index from January 1,2010 to September 30,2019 in 3 major Asian countries.The results show that:(1)in samples,the fixed coefficient model is estimated by the maximum likelihood method,the time-varying model parameters are estimated by the Kalman filter maximum likelihood method,the maximum likelihood value,the Akaike information criterion and Bayesian information criterion are used In general,the performance of the five indexes under TVC-AHAR model is better than that of TVC-HAR,AHAR and standard HAR model,and the persistence of variables under the new model is significantly enhanced,and the coefficient of the lag period is significantly increased;except for Seoul index,the performance of the negative constraint model is better than that of the positive constraint model,but the performance of the two constraint models is weaker than that of the two constraint models TVC-AHAR model.(2)Out of sample prediction is divided into 500 and 800 prediction wavelengths.Loss function,MZ regression,combination regression and DM test were used to evaluate the prediction ability of each model.The empirical results show that the performance of the new model is different under the five indexes.Domestic Shanghai Composite Index,Shenzhen Composite Index and Hang Seng index,and foreign Seoul index can get the best performance by using TVC-AHAR model.The performance of the 800 forecasting length of Nikkei index is slightly worse.In general,the new model with leverage effect and time-varying coefficient effect is helpful to improve the prediction of volatility. |
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