Carr Model Based On Robust Estimation And Its Applications In Stock Price Volatility

Since the emergence of the stock market,price fluctuation has been the main feature.How to accurately describe the price of the stock market and predict the future situation of the stock is our concern.For a long time,the research content is mainly based on GARCH models,including the multivariate GARCH model,the parametric,non-parametric and semi-parametric GARCH model and so on.Since the conditional autoregressive range model(CARR)was proposed,it is found that range can better describe the volatility of the stock market,so it is widely used in the study of volatility.There are many researches concerned the volatility of the stock market with GARCH model,and the studies on describing stock market volatility by range are not adequate.It is noted that most of the studies on parametric estimation of CARR model is based on maximum likelihood estimation.However,the stock market data often have obvious“fat tail”,as well as abnormal value,which makes the commonly used maximum likelihood estimation is not robust enough to eliminate the effects of outliers.In view of this,this paper studies the parameter CARR model based on the robust estimation.Firstly,the consistency of robust estimation statistics in CARR model is proved theoretically.By stochastic simulation,the random error term follows five different distribution,including light-tailed and heavy-tailed distributions,and in the random error term exists outliers condition,the maximum likelihood estimation of the parametric CARR model and the robust estimation of the parametric CARR model are conducted in the paper,after contrasting the two methods,we find that the MSE and MAE of the robust estimation of the parametric CARR model are smaller,which shows that the robust estimation of the parametric CARR model can better simulate the data of fat tail and outliers and is more suitable for describing stock data.Finally,in view of the excellent performance of robust estimation in the simulated data,when CARR(1,1)is modeled for eight stocks at home and abroad,the mean square error and the average absolute error of the robust estimation are significantly lower than the maximum likelihood estimation.Due to the excellent performance of robust estimation in numerical simulation and empirical analysis,the parameter CARR model based on robust estimation is more suitable for the stock market data.