Hierarchical Bayesian of ARMA Models Using Simulated Annealing Algorithm

Abstract

When the Autoregressive Moving Average (ARMA) model is fitted with real data, the actual value of the model order and the model parameter are often unknown. The goal of this paper is to find an estimator for the model order and the model parameter based on the data. In this paper, the model order identification and model parameter estimation is given in a hierarchical Bayesian framework. In this framework, the model order and model parameter are assumed to have prior distribution, which summarizes all the information available about the process. All the information about the characteristics of the model order and the model parameter are expressed in the posterior distribution. Probability determination of the model order and the model parameter requires the integration of the posterior distribution resulting. It is an operation which is very difficult to be solved analytically. Here the Simuated Annealing Reversible Jump Markov Chain Monte Carlo (MCMC) algorithm was developed to compute the required integration over the posterior distribution simulation. Methods developed are evaluated in simulation studies in a number of set of synthetic data and real data.