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


  • K. S. Man

    (Western Illinois University, Illinois, USA)

  • G. C. Tiao

    (University of Chicago, Illinois, USA)


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.

Suggested Citation

  • K. S. Man & G. C. Tiao, 2009. "ARFIMA approximation and forecasting of the limiting aggregate structure of long-memory process," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(2), pages 89-101.
  • Handle: RePEc:jof:jforec:v:28:y:2009:i:2:p:89-101
    DOI: 10.1002/for.1086

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    References listed on IDEAS

    1. Man, K.S. & Tiao, G.C., 2006. "Aggregation effect and forecasting temporal aggregates of long memory processes," International Journal of Forecasting, Elsevier, vol. 22(2), pages 267-281.
    2. Man, K. S., 2003. "Long memory time series and short term forecasts," International Journal of Forecasting, Elsevier, vol. 19(3), pages 477-491.
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