The Bayesian Analysis Of ARCH Model Family And Its Application In Economy

The classical estimation methods such as the maximum likelihood estimation (MLE)have been always employed to estimate the GARCH models.The classical methods are difficult to use in numerical optimization of the objective function,which is not necessarily convex.And constraints imposed on GARCH coefficients complicate statistical inference on the coefficients as well as the optimization rocedures.However, in the Bayesian approach,we compute integrals of the posterior distribution to estimate them instead of the maximum of the likelihood function.Besides,the constraints on GARCH coefficients are also easily handled by using the truncated posterior distribution of the GARCH coefficients.Meanwhile,with the development of MCMC method,the application of Bayesian analysis in time series theory will be wider and wider.This paper discussed several typical ARCH models,form a Bayesian analysis point. The contents were as follows:Firstly,we reviewed the background of the theory,summerized the documents on these aspects,analyzed the ARCH family of models systemically and their classification. We also showed the classical methods such as the BHHH algorithm and explained its disadvantages in detail.Secondly,from a Bayesian view,we discussed serval models under the Normal distribution and Mixed Normal distribution assumption:GARCH,GARCH-M, AGARCH,SW-GARCH,TGARCH model.We used MCMC method to discuss the estimation of parameters,and then gave the forecasting distribution.Finally,we focused on the application of ARCH family models.This paper discuss two issues:(â…°) discussed the volatility in Shanghai national bond index using AGARCH model,and demonstrated its "leverage effects";(â…±) made a comparation between GARCH and SWGARCH,found that the GARCH model showed a pseudo persistence, and built a SW-GARCH model.