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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)

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    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.

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    Article provided by John Wiley & Sons, Ltd. in its journal Journal of Forecasting.

    Volume (Year): 28 (2009)
    Issue (Month): 2 ()
    Pages: 89-101

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    Handle: RePEc:jof:jforec:v:28:y:2009:i:2:p:89-101
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