Time Series Heteroscedasticity Modeling And Its Application

Time series analysis can predict the future trend and play an extremely important part in the fields of finance,economy,engineering and so on.So the research on volatility modeling of time series has been becoming a hot orientation in recent decades.Fitting the high-peaked and heavy-tailed characteristics of time series well,the generalized autoregressive conditional heteroscedasticity(GARCH)model is widely applied to forecasting and analyzing volatility,which is evaluated as the benchmark model of volatility forecasting.However,the GARCH model is mainly applied to forecasting volatility of low-frequency time series,rarely used to high-frequency time series fields.To solve this problem,based on the information loss caused by the sampling process of low-frequency time series,the GARCH model is improved to increase volatility forecasting capacity.Then according to the microstructure noise characteristic of high-frequency time series,the GARCH model is further analyzed and improved to be employed in volatility forecasting of high-frequency time series.The main researches of this paper are as follows:(1)The volatility forecasting of GARCH model in low-frequency time series is studied.There is the sampling error in the sampling process of low-frequency time series,resulting in some important information loss.The lower sampling frequency is,the more information lost will be.Therefore,a sampling error model is established and introduced into the GARCH model to obtain a GARCH model with sampling error which is solved using the maximum likelihood estimation method.(2)For the sampling error problem of low-frequency time series,the volatility modeling of high-frequency time series is analyzed.It is found that the high-frequency time series has different characteristics,which is affected by the microstructural noise,and the higher the sampling frequency is,the greater the influence of microstructure noise will be.Then the microstructure noise is analyzed and combined with the sampling error,which are introduced into the GARCH model.Therefore,the GARCH model with sampling error and microstructure noise is established,and the parameters are solved.(3)In this paper,firstly,Monte Carlo simulation experiments are used to verify the validity of the GARCH model with sampling error.By comparing six groups of simulation results,the accuracy of parameter estimation of the model is analyzed.At the same time,combined with the daily data of Nasdaq stock,the empirical analysis shows that the GARCH model with sampling error is more accurate in the parameter estimation and better in the volatility forecasting.Then the characteristics of highfrequency time series are analyzed.The Flexible Fourier Form(FFF)regression is used to eliminate the intraday effect of high-frequency time series,and the R/S method is used to test its long memory.With regard of the established GARCH model with sampling error and microstructure noise,the simulation experiments are used to verify the feasibility of the model,and the empirical analysis is carried out with Nasdaq stock five-minute high-frequency data.The experimental results demonstrate that the GARCH model with sampling error and microstructure noise has better volatility forecasting capacity and more accurate parameter estimation in high-frequency time series.