The Family Of GARCH Model Based On Wavelet Analysis And Robust Estimation And Its Application In Volatility

Fluctuation in the yield of stocks has always been the focus of research in the financial field.Although ARCH and GARCH models can also describe volatility,they cannot describe features such as long memory.Therefore,this paper mainly establishes NAGARCH,GJRGARCH and FIGARCH to describe the volatility of the rate of return.In the research,considering that many noises in financial data can interfere with the accuracy of model fitting,and the maximum likelihood estimation(MLE)is vulnerable to abnormal points,this paper uses wavelet analysis combined with composite quantile regression(CQR).The method estimates the model parameters and improves the fitting accuracy.This paper uses a combination of wavelet analysis and CQR,the NAGARCH(1,1),GJRGARCH(1,1),FIGARCH(1,d,1)models are studied and compared with GARCH(1,1).Firstly,numerical simulation is carried out for the above model.Under the error distributions N(0,1),t(3),and Pareto(3,1)respectively,the data is divided into two cases of abnormal values.The result shows the MAE and RMSE of CQR is smaller than MLE.Secondly,the wavelet denoising is performed for the data with outliers.By comparing the estimation results before and after denoising,it is found that the error indexes of CQR and MLE obtained after denoising are significantly reduced,and the error index of CQR is still smaller than MLE.This proves the validity of wavelet analysis,and combined with wavelet analysis and CQR can better improve the estimation accuracy.Finally,in view of the advantages of wavelet analysis and CQR,we selected the recent closing price of active stocks in Shanghai for the past 6 years,the closing price of inactive stocks in Northeast Pharmaceuticals,and the closing price of US stocks NVIDIA(NVDA),in the establishment of GARCH(1,1),NAGARCH(1,1),GJR-GARCH(1,1),FIGARCH(1,d,1)model,prioritize the combination of wavelet analysis and CQR and compare the estimated results with MLE.The error indicators of CQR and MLE obtained by wavelet-based denoising data show a significant decrease,and the error index of CQR is generally smaller than MLE.Observing the fitting results of the four models,it is found that GJR-GARCH is superior.In view of the good performance of wavelet analysis,CQR and GJR-GARCH model in data simulation and empirical application,we believe that the combination of wavelet analysis and CQR,GJR-GARCH can be more effectively used in the study of financial yield.