Bayesian Subset Selection of Double Seasonal Autoregressive Models Under Scale-Mixtures of Normal Errors

Identifying the most appropriate lag structure for double seasonal autoregressive models is a fundamental demanding task in time series analysis. Classical model selection tools such as the Akaike information criteria are well known to be inconsistent for identifying the true lag structure. At the same time, standard Bayesian formulations almost invariably assume normality that is often violated in the presence of heavy tails, isolated outliers, or contaminated observations. This paper addresses both limitations simultaneously by proposing a unified Bayesian framework for the best-subset selection of multiplicative double seasonal autoregressive models under the scale-mixtures of normal family of error distributions. Adopting an extended stochastic search variable selection, we assign mixture-normal priors to all primitive autoregressive coefficient vectors and derive tractable closed-form conditional posterior distributions for all model parameters. Building on these results, we design an efficient Markov chain Monte Carlo algorithm integrating Gibbs sampling and Metropolis–Hastings updates for simultaneous subset identification and parameter estimation under heavy-tailed errors. A comprehensive simulation study and real-data applications to hourly electricity demand in the Czech Republic and Germany demonstrate that the proposed algorithm consistently outperforms classical information criteria, particularly when innovations are heavy-tailed.