Effects of temporal aggregation on estimates and forecasts of fractionally integrated processes: A Monte-Carlo study

Abstract

For a fractionally integrated ARFIMA(p, d, q) model, temporal aggregation changes the order of the process to an ARFIMA(p, d,∞), while leaving the value of d unchanged. This paper analyses the effects of temporal aggregation on the estimated long memory parameter, d, using both semi-parametric and parametric estimation methods. We find that if, for the non-aggregated series, the bias in the fractional parameter is large due to the influence of short run AR and MA parameters, temporal aggregation can reduce this bias. We compare aggregated forecasts from the underlying (non-aggregated) series with forecasts from the aggregated series and find that for d <0, forecasts from the aggregated series are generally superior. For d >0, the forecast comparison results are less clear-cut. © 2003 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.