Parameter Estimation And Its Algorithm Of ARCH Models Based On Bootstrap

Nowadays,the research on the uncertainty of price change of the financial market has become one of the core topics in modern financial studies.And this uncertainty is often described and measured by variance.Traditional econometric models always assume that the variance is unchanged.However,with the further development of practical studies,researchers begin to realize that the variances of many time series data in the financial market,such as stock prices,inflation rate, interest rate and foreign exchange interest rate,etc.,vary with time.This phenomenon shows that traditional econometric models,for example,linear regression model,can not describe those financial activities objectively and exactly.Under this circumstance,Engle brings forward the autoregressive conditional heteroscedasticity model(ARCH) in 1982.Since it can quantificationally reflect the characteristic of mutative variance existing in various economic and financial activities,this model is now welcomed by researchers.In addition,many expanded models,such as GARCH, EGRACH,IGARCH,etc.,come into being based on it.In this paper,we introduce the basic theories of ARCH models in details,and analyze their statistical properties and characterizations,then emphasizes on discussing the estimation of the parameters in those models.At present,the most widely used method for estimation is maximum likelihood estimation.In this paper, we propose the maximum likelihood estimation method based on Bootstrap.Since this method makes use of the resampling property of sample observations,thus greatly improved the accuracy and agility of our parametric estimation.This paper mainly focuses on the following aspects:Firstly,systematically elaborate the formation background,statistical significance,the research situations and development levels of home and abroad.Secondly,introduce the basic theory and forms of ARCH model and GARCH model in detail,and emphasize on introducing the maximum likelihood estimation of the parameters of those two kinds of ARCH family models.And we present the maximum estimation method for the parameters of ARCH and GRACH models based on Bootstrap.Thirdly,with the establishment of the time series data of foreign exchange interest rates between Yuan and Dollars of Bank of China,we investigate the application of GARCH model in practical analysis,and give the concrete maximum likelihood estimation of the parameters of this model based on bootstrap.In addition, we do a fitting for the future tendency of exchange rate,which indirectly validate the practicability of ARCH family models.