Application Of Approximate Bayesian Computing In Parameter Estimation Of MA(q)Model

Parameter estimation of time series model is an important part of modeling,and common methods include moment estimation,maximum likelihood estimation,least square estimation and MCMC algorithm.In this paper,approximate bayesian calcu?lation method,which is popular this year,is used to estimate the parameters of MA model.This paper mainly studies parameter estimation of MA(q)model whose white noise is the normal distribution and mixture normal distribution,and gives approxi-mate bayesian estimation algorithm of MA(q)model parameters respectively.For ap-proximate bayesian calculation,improving the sampling efficiency of algorithm is the selection of low dimension statistics that contains parameter information as much as possible.In the study of approximate bayesian estimation of MA(q)model parameters whose white noise is normal distribution,we used q order sample autocorrelation co-efficient as the parameter statistics to estimate parameters by the approximate bayesian calculation,and take the MA(1)model and MA(2)model as an example,the parameters of the model are analyzed by numerical simulation,and from the simulation results,the algorithm we proposed has higher accuracy than maximum likelihood estimation.In the study of approximate bayesian estimation of MA(q)model parameters whose white noise is mixed normal distribution,we combine a EM algorithm estimation and approximate bayesian estimation method to estimate the parameters of the model.Esti?mation methods are divided into two steps,first we use the ABC algorithm to estimate the model coefficient,then use EM algorithm to estimate white noise parameters of mixture normal distribution,and take MA(2)model as an example,the parameters of the model are analyzed by numerical simulation.The simulation results show that the proposed algorithm is accurate.