An Empirical Analysis Of Autoregressive Model With ARCH Error

Since Engel put forward in 1982,the family of ARCH model has been widely used by scholars and financial practitioners and has been growing in the field of econometrics.Since the creation,there have been two important breakthroughs in this field.One of it is the generalized ARCH model,short for GARCH model,which is proposed by Bollerslev T.The second breakthrough is the result of a more effective portrayal for long memory economic phenomena by using this model in the field of economics.In the analysis of real financial time series data,the random perturbation term often has the characteristic of heteroscedasticity,which is mainly embodied in the analysis of cross section data.Meanwhile It is reflected in the stock market,which means that if the returning rate of the previous stage is more volatile,then the volatility of the returning rate is often larger at this moment.Therefore,the ARCH model has the ability to describe the characteristics of the volatility cluster.In recent years,researchers have found that it is necessary to add some related covariates in the model in order to predict the data better.In fact,adding some potential covariates in arch model could fit the model better.This has also become the focus of our research.In this paper,the author focuses on the AR(1)model with ARCH error by using statistical method to explore the stability of the model.The parameter estimation of the model is given.In the stage of empirical analysis,the stock monthly return sequence is combined with interest rate and CPI as covariates to fit the model.At the same time,an ARCH error autoregressive model which does not have any covariate is compared,then the effect of covariance on the actual results is discussed.After empirical analysis,we find that the autoregressive model with covariates has a better result by promoting the accuracy of its estimation and it has a practical usage in this field.