The Approximation of Long-Memory Processes by an ARMA Model

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The Approximation of Long-Memory Processes by an ARMA Model

Author Info

Basak, Gopal K
Chan, Ngai Hang
Palma, Wilfredo

Abstract

A mean square error criterion is proposed in this paper to provide a systematic approach to approximate a long-memory time series by a short-memory ARMA(1, 1) process. Analytic expressions are derived to assess the effect of such an approximation. These results are established not only for the pure fractional noise case, but also for a general autoregressive fractional moving average long-memory time series. Performances of the ARMA(1,1) approximation as compared to using an ARFIMA model are illustrated by both computations and an application to the Nile river series. Results derived in this paper shed light on the forecasting issue of a long-memory process. Copyright © 2001 by John Wiley & Sons, Ltd.

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

Volume (Year): 20 (2001)
Issue (Month): 6 (September)
Pages: 367-89
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Handle: RePEc:jof:jforec:v:20:y:2001:i:6:p:367-89

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Lux, Thomas & Kaizoji, Taisei, 2004. "Forecasting volatility and volume in the Tokyo stock market : the advantage of long memory models," Economics Working Papers 2004,05, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
Torben G. Andersen & Tim Bollerslev & Francis X. Diebold,, 2003. "Some Like it Smooth, and Some Like it Rough: Untangling Continuous and Jump Components in Measuring, Modeling, and Forecasting Asset Return Volatility," CFS Working Paper Series 2003/35, Center for Financial Studies. [Downloadable!]
Other versions:
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2003. "Some Like it Smooth, and Some Like it Rough: Untangling Continuous and Jump Components in Measuring, Modeling, and Forecasting Asset Return Volatility," PIER Working Paper Archive 03-025, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Sep 2003. [Downloadable!]

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