Bayesian Prediction of Double Seasonal ARMA Processes
Keywords:
Posterior and predictive analyses, DSARMA models, multiple seasonality, hourly electricity loadAbstract
Recent developments in time series analysis extended autoregressive moving average (ARMA) models to accommodate datasets exhibiting two seasonal cycles, leading to the formulation of double seasonal ARMA (DSARMA) models. While Bayesian estimation methods have been explored for these models, Bayesian prediction has not yet been formally developed. In the current work, we advance the existing literature by establishing a Bayesian predictive framework for DSARMA models. Our approach assumes normally distributed error terms and employs both normal-gamma and Jeffreys priors on the model parameters. Under these assumptions, we derive closed-form predictive distributions for future, unobserved values, showing that they follow a univariate-t distribution. This result enables efficient multistep-ahead forecasting. To assess the forecasting accuracy of the current proposed Bayesian prediction methodology, we conduct a comprehensive simulation study and apply the framework to forecasting hourly electricity load across several European countries.
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