First-order seasonal autoregressive processes with periodically varying parameters

Abstract

A time series model combining a first-order periodic autoregressive structure and the Box–Jenkins multiplicative seasonal autoregressive model is introduced. Stationarity conditions (in the periodic sense) for this so-called SPAR(1,1) process are established and its autocovariances are derived. Least-squares estimates of the model parameters are obtained and their limit distribution is derived. An extension to higher-order SPARMA models is suggested.