ARFIMA approximation and forecasting of the limiting aggregate structure of long-memory process

K. S. Man and G. C. Tiao
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K. S. Man: Western Illinois University, Illinois, USA, Postal: Western Illinois University, Illinois, USA
G. C. Tiao: University of Chicago, Illinois, USA, Postal: University of Chicago, Illinois, USA

Journal of Forecasting, 2009, vol. 28, issue 2, 89-101

Abstract: This article studies Man and Tiao's (2006) low-order autoregressive fractionally integrated moving-average (ARFIMA) approximation to Tsai and Chan's (2005b) limiting aggregate structure of the long-memory process. In matching the autocorrelations, we demonstrate that the approximation works well, especially for larger d values. In computing autocorrelations over long lags for larger d value, using the exact formula one might encounter numerical problems. The use of the ARFIMA(0, d , &dmacr; 1 ) model provides a useful alternative to compute the autocorrelations as a really close approximation. In forecasting future aggregates, we demonstrate the close performance of using the ARFIMA(0, d , &dmacr; 1 ) model and the exact aggregate structure. In practice, this provides a justification for the use of a low-order ARFIMA model in predicting future aggregates of long-memory process. Copyright © 2008 John Wiley & Sons, Ltd.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:jof:jforec:v:28:y:2009:i:2:p:89-101

DOI: 10.1002/for.1086

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