Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)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 MarkovMonte 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.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)RH-TVDConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Faepex/UnicampFundação para o Desenvolvimento da UNESP (FUNDUNESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)