THE IMPLICATIONS OF PERIODICALLY VARYING COEFFICIENTS FOR SEASONAL TIME-SERIES PROCESSES

Periodic ARMA processes have seasonally varying parameters superimposed on a conventional ARMA structure. These varying parameters can arise when seasonality is incorporated into the theory of economic decision-making. Analogously to the aggregate of component ARMA processes having a univariate representation, the periodic process has a corresponding ARMA representation. This univariate representation may, however, imply high orders and substantial dynamic misspecification. In terms of forecast efficiency, the true periodic dynamic process dominates its univariate counterpart.