Aggregation and estimation for low‐order periodic ARMA models

Abstract

The aggregated time series resulting from summing over the seasons of a seasonal time series, which is assumed to follow either an AR(1) or ARMA(1, 1) model having periodic (seasonal) parameters, is shown to follow an ARMA(1, 1) model. Parameter estimation for such models is investigated analytically and via simulation. Significant gain in parameter estimation efficiency at the aggregated level is demonstrated when the seasonal data and their model is utilized rather than the aggregated (annual) data and their model.