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Estimation Of The Long‐Memory Parameter, Based On A Multivariate Central Limit Theorem

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  • Jan Beran
  • Norma Terrin

Abstract

. Long memory is known to occur in many fields of statistical application. Stationary processes whose correlations decay asymptotically like ‖k‖2H‐2, where k is the lag and Hε (0.5, 1), provide useful parsimonious models with long memory. The parameter H characterizes the long‐memory features of the data. For long time series, maximum likelihood estimation of H can be costly in terms of CPU time. In this paper, we show that, for disjoint stretches of the data, estimates of H and other parameters that characterize the dependence structure are asymptotically independent. Averaging these estimates leads to a fast and efficient approximate maximum likelihood method.

Suggested Citation

  • Jan Beran & Norma Terrin, 1994. "Estimation Of The Long‐Memory Parameter, Based On A Multivariate Central Limit Theorem," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(3), pages 269-278, May.
    • Handle: RePEc:bla:jtsera:v:15:y:1994:i:3:p:269-278
    DOI: 10.1111/j.1467-9892.1994.tb00192.x
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    Cited by:

    1. Paramsothy Silvapulle, 2001. "A Score Test For Seasonal Fractional Integration And Cointegration," Econometric Reviews, Taylor & Francis Journals, vol. 20(1), pages 85-104.
    2. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    3. Katsumi Shimotsu, 2006. "Simple (but Effective) Tests Of Long Memory Versus Structural Breaks," Working Paper 1101, Economics Department, Queen's University.
    4. Sibbertsen, Philipp & Leschinski, Christian & Busch, Marie, 2018. "A multivariate test against spurious long memory," Journal of Econometrics, Elsevier, vol. 203(1), pages 33-49.
    5. Beran, Jan, 2007. "On parameter estimation for locally stationary long-memory processes," CoFE Discussion Papers 07/13, University of Konstanz, Center of Finance and Econometrics (CoFE).

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