TEMPORAL AGGREGATION IN THE ARIMA PROCESS

Abstract

Abstract. The effect of temporal aggregation on ARIMA models is investigated. The paper discusses the change of model form resulting from aggregation. For the IMA model it is noted that reduction of model order may occur, due to aggregation, which takes an arbitrarily high order IMA ( d , q) process to an IMA ( d , 0) process for the aggregates. For the AR process, we derive the exact order for the aggregate model and show that aggregation of an AR (p) series does not necessarily produce an ARMA (p, q) aggregate series as has been suggested in the literature. In particular, the AR order of AR (p) and ARIMA (p, d, q) can be reduced upon aggregation. The paper gives the general conditions under which this reduction of order may occur.