Aggregation effect and forecasting temporal aggregates of long memory processes

This article studies the parsimonious effect of temporal aggregation on long memory time series with ARFIMA structure, and the efficiency of forecasting temporal aggregates of long memory processes using low order ARFIMA models. It is well known that the aggregates of an ARFIMA(0, d, 0) process (where d is a positive real number) have autocorrelations that follow an ARFIMA (0, d, ∞) structure in general. In this paper, we derive a low order ARFIMA(0, d, d¯1) approximation to the aggregate structure as the level of aggregation tends to infinity (where d¯1 is the greatest integer strictly less than d + 1). Numerical evaluation and simulation experiments show that this approximation is close, getting more precise as the value of d increases. For forecasting future aggregates, the efficiency of using the low order approximation for the aggregate series and the efficiency of using the underlying disaggregate model is compared. A simulation study is performed to illustrate the results.