A BAYESIAN METHOD TO FIT AN ARMA MODEL

Abstract

The method of time series analysis is widely used in many fields of science, engineering, finance and economics etc, and fitting a time series model accurately is the important basis of time series analysis.  Based on the Bayesian statistical theory, this paper presents a Bayesian method which can identify an ARMA (autoregressive moving-average) model and estimate the model parameters simultaneously.  Firstly, in order to determine the orders of the ARMA model, an identification model with the recognition variables is constructed.  Moreover, the problem of determining the orders of the ARMA model is transformed into two sets of hypothesis tests.  By the principle of Bayesian hypothesis testing, it is suggested to solve the above hypothesis test problems by calculating the posterior probabilities of the hypotheses.  However, due to the large number of the unknown parameters in the identification model, this paper proposes to obtain the samples by Gibbs sampling and then calculate the posterior probabilities of the hypotheses, the AR coefficients, the MA coefficients and the variance of the random errors to fit the ARMA model.  Finally, in order to illustrate the good performance of the method proposed in this article, we design three simulation examples and compare the results of our method with two existing methods: RJMCMC method and EACF method.  It can be found clearly that the method proposed in this paper has more accurate results for fitting an ARMA model.