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Automatic Semiparametric Estimation Of The Memory Parameter Of A Long‐Memory Time Series

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  • Clifford M. Hurvich
  • Kaizo I. Beltrao

Abstract

. In Geweke and Porter‐Hudak's estimator ωd(GPH) of the memory parameter of a long‐memory process, a critical choice the user must make is the number of frequencies, M, to be used in the regression of the log periodogram on log frequency. This choice is critical in practice because by simply varying M for a given data set it is often possible to obtain a very wide range of values of the estimator. Although Geweke and Porter‐Hudak have found that choosing M to be the square root of the sample size gave good results in simulation, they gave no theoretical justification for this choice. Here, we propose automatic criteria for selecting M, and another tuning constant used in related estimates of the memory parameter, based on frequency domain cross‐validation. We provide some theoretical and heuristic justification for the proposed criteria. In a simulation study, we compare some of the resulting automatic methods of estimating the memory parameter with existing non‐automatic ones.

Suggested Citation

  • Clifford M. Hurvich & Kaizo I. Beltrao, 1994. "Automatic Semiparametric Estimation Of The Memory Parameter Of A Long‐Memory Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(3), pages 285-302, May.
    • Handle: RePEc:bla:jtsera:v:15:y:1994:i:3:p:285-302
    DOI: 10.1111/j.1467-9892.1994.tb00194.x
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    Cited by:

    1. Erhard Reschenhofer & Manveer Kaur Mangat & Christian Zwatz & Sándor Guzmics, 2020. "Evaluation of current research on stock return predictability," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(2), pages 334-351, March.
    2. Christian Leschinski & Michelle Voges & Philipp Sibbertsen, 2021. "Integration and Disintegration of EMU Government Bond Markets," Econometrics, MDPI, vol. 9(1), pages 1-17, March.
    3. Silverberg, Gerald & Verspagen, Bart, 2000. "A Note on Michelacci and Zaffaroni, Long Memory, and Time Series of Economic Growth," Research Memorandum 031, Maastricht University, Maastricht Economic Research Institute on Innovation and Technology (MERIT).
    4. Feng, Yuanhua & Beran, Jan, 2008. "Filtered Log-periodogram Regression of long memory processes," CoFE Discussion Papers 08/10, University of Konstanz, Center of Finance and Econometrics (CoFE).
    5. Saeed Heravi & Kerry Patterson, 2005. "Optimal And Adaptive Semi‐Parametric Narrowband And Broadband And Maximum Likelihood Estimation Of The Long‐Memory Parameter For Real Exchange Rates," Manchester School, University of Manchester, vol. 73(2), pages 165-213, March.

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