The Bayes Factor Estimation Of The Order For Stationary AR Model

The major use of time series analysis is to apply mathematical models to describe and fit the time-series data approximately. This is known as modeling of time series in the Time Series Analysis. Time series modeling includes parameters estimation and order determination.AR model, the simplest model of time series, is also one of the most commonly used models. The AR model with limited order has been used widely in research and production. In the modeling process, we often research estimating of the parameters supposing the order is known. Although the order real exists and has fixed value, it often is unknown. Therefore, it becomes important to identify appropriate values of the order of the AR model.This paper does the following works:One is based on the Bayesian model selection theory. First, we introduce the Bayes factor to decide the order of the AR model, and discuss some methods of calculation. Then we give the specific expression of AR model Bayesian factor in this paper, and proof that the order of the AR model is a strong consistence estimate. Finally, we use stochastic simulation to compare the estimate with that using AIC, BIC criterion.Another is to study the effect of observations on Bayesian choice of an AR model. First, in both complete data situation and incomplete data situation, we use Gibbs sampling method to estimate the Bayes factor of the AR model. Then, we use Q( z)to measure the effect of the observations on the Bayes factor criterion.