A Bayesian analysis of spectral ARMA model (Q1954917)

Summary: \textit{M.I.S. Bezerra} et al. [TEMA, Tend. Mat. Apl. Comput. 9, No. 2, 175--184 (2008; Zbl 1208.60034)] 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 \textit{H. Jeffreys} [Theory of probability. 3\,rd ed., Oxford: Clarendon (1961; Zbl 0116.34904)]. The Bayesian computations, simulations via Markov Monte Carlo (MCMC), are carried out and characteristics of marginal posterior distributions such as Bayes estimators and confidence intervals 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.