Bayesian Subset Selection of Seasonal Autoregressive Models

Seasonal autoregressive (SAR) models have many applications in different fields, such as economics and finance. It is well known in the literature that these models are nonlinear in their coefficients and that their Bayesian analysis is complicated. Accordingly, choosing the best subset of these models is a challenging task. Therefore, in this paper, we tackled this problem by introducing a Bayesian method for selecting the most promising subset of the SAR models. In particular, we introduced latent variables for the SAR model lags, assumed model errors to be normally distributed, and adopted and modified the stochastic search variable selection (SSVS) procedure for the SAR models. Thus, we derived full conditional posterior distributions of the SAR model parameters in the closed form, and we then introduced the Gibbs sampler, along with SSVS, to present an efficient algorithm for the Bayesian subset selection of the SAR models. In this work, we employed mixture-normal, inverse gamma, and Bernoulli priors for the SAR model coefficients, variance, and latent variables, respectively. Moreover, we introduced a simulation study and a real-world application to evaluate the accuracy of the proposed algorithm.