Full Bayesian analysis of double seasonal autoregressive models with real applications

We present a full Bayesian analysis of multiplicative double seasonal autoregressive (DSAR) models in a unified way, considering identification (best subset selection), estimation, and prediction problems. We assume that the DSAR model errors are normally distributed and introduce latent variables for the model lags, and then we embed the DSAR model in a hierarchical Bayes normal mixture structure. By employing the Bernoulli prior for each latent variable and the mixture normal and inverse gamma priors for the DSAR model coefficients and variance, respectively, we derive the full conditional posterior and predictive distributions in closed form. Using these derived conditional posterior and predictive distributions, we present the full Bayesian analysis of DSAR models by proposing the Gibbs sampling algorithm to approximate the posterior and predictive distributions and provide multi-step-ahead predictions. We evaluate the efficiency of the proposed full Bayesian analysis of DSAR models using an extensive simulation study, and we then apply our work to several real-world hourly electricity load time series datasets in 16 European countries.