ARFIMA approximation and forecasting of the limiting aggregate structure of long-memory process
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 <TOGGLE>d</TOGGLE> values. In computing autocorrelations over long lags for larger <TOGGLE>d</TOGGLE> value, using the exact formula one might encounter numerical problems. The use of the ARFIMA(0, <TOGGLE>d</TOGGLE>, <TOGGLE>&dmacr;</TOGGLE><INF>1</INF>) 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, <TOGGLE>d</TOGGLE>, <TOGGLE>&dmacr;</TOGGLE><INF>1</INF>) 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.
Year of publication: |
2009
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Authors: | Man, K. S. ; Tiao, G. C. |
Published in: |
Journal of Forecasting. - John Wiley & Sons, Ltd.. - Vol. 28.2009, 2, p. 89-101
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Publisher: |
John Wiley & Sons, Ltd. |
Saved in:
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