THE EFFECT OF AGGREGATION ON PREDICTION IN AUTOREGRESSIVE INTEGRATED MOVING‐AVERAGE MODELS

Abstract

Abstract. Let x t be a time series generated by an autoregressive integrated moving‐average process ARIMA( p, d, q ). The non‐overlapping aggregate series also follows an ARIMA process. Thus, the prediction of the aggregated observations could be done by either the disaggregate model or the aggregate model. We derive the efficiency of the predictors for two important disaggregate models, ARIMA(0, 1, 1) and ARIMA(0, 2, 2), when the models are assumed known. When the models are not known we estimate the efficiency through simulation with the models being selected using Akaike's information criterion.