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The approximation of long-memory processes by an ARMA model

✍ Scribed by Gopal K. Basak; Ngai Hang Chan; Wilfredo Palma

Publisher
John Wiley and Sons
Year
2001
Tongue
English
Weight
196 KB
Volume
20
Category
Article
ISSN
0277-6693

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✦ Synopsis

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 John Wiley & Sons, Ltd.

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