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The Approximation of Long-Memory Processes by an ARMA Model

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  • 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.

Suggested Citation

  • Basak, Gopal K & Chan, Ngai Hang & Palma, Wilfredo, 2001. "The Approximation of Long-Memory Processes by an ARMA Model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(6), pages 367-389, September.
    • Handle: RePEc:jof:jforec:v:20:y:2001:i:6:p:367-89
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    Cited by:

    1. Lux, Thomas & Kaizoji, Taisei, 2007. "Forecasting volatility and volume in the Tokyo Stock Market: Long memory, fractality and regime switching," Journal of Economic Dynamics and Control, Elsevier, vol. 31(6), pages 1808-1843, June.
    2. Lux, Thomas & Morales-Arias, Leonardo, 2010. "Relative forecasting performance of volatility models: Monte Carlo evidence," Kiel Working Papers 1582, Kiel Institute for the World Economy (IfW Kiel).
    3. 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.
    4. 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.
    5. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 701-720, November.
    6. Basistha, Arabinda & Kurov, Alexander & Wolfe, Marketa Halova, 2019. "Volatility Forecasting: The Role of Internet Search Activity and Implied Volatility," MPRA Paper 111037, University Library of Munich, Germany.
    7. Breidt, F. Jay & Hsu, Nan-Jung, 2002. "A class of nearly long-memory time series models," International Journal of Forecasting, Elsevier, vol. 18(2), pages 265-281.
    8. Ferraz, Rosemeire O. & Hotta, Luiz K., 2007. "Quasi-Maximum Likelihood Estimation of Long-Memory Stochastic Volatility Models," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 27(2), November.
    9. Hossam M. Ahmed & Ayman G. Awadallah & Alaa El-Din M. El-Zawahry & Khaled H. Hamed, 2022. "Multivariate analysis for medium- and long-range forecasting of Nile River flow to mitigate drought and flood risks," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 110(1), pages 741-763, January.

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