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Mathematical Problems in Engineering
Volume 2012, Article ID 565894, 15 pages
http://dx.doi.org/10.1155/2012/565894
Research Article

A Bayesian Analysis of Spectral ARMA Model

1DEST, FCT, Unesp, Presidente Prudente 19060-900, SP, Brazil
2DECOM, FEEC, Unicamp, Campinas 13083-852, SP, Brazil

Received 22 November 2011; Revised 9 April 2012; Accepted 12 April 2012

Academic Editor: Kwok W. Wong

Copyright © 2012 Manoel I. Silvestre Bezerra et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Bezerra et al. (2008) proposed a new method, based on Yule-Walker equations, to estimate the ARMA spectral model. In this paper, a Bayesian approach is developed for this model by using the noninformative prior proposed by Jeffreys (1967). The Bayesian computations, simulation via Markov Monte Carlo (MCMC) is carried out and characteristics of marginal posterior distributions such as Bayes estimator and confidence interval for the parameters of the ARMA model are derived. Both methods are also compared with the traditional least squares and maximum likelihood approaches and a numerical illustration with two examples of the ARMA model is presented to evaluate the performance of the procedures.