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The estimation of misspecified long memory models

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  • Robinson, Peter M.

Abstract

We consider time series that, possibly after integer differencing or integrating or other detrending, are covariance stationary with spectral density that is regularly varying near zero frequency, and unspecified elsewhere. This semiparametric framework includes series with short, long and negative memory. We consider the consistency of the popular log-periodogram memory estimate that, conventionally but wrongly, assumes the spectral density obeys a pure power law. The local-to zero misspecification leads to increased bias, such that the usual central limit theorem may only hold for bandwidths entailing considerable imprecision. The order of the bias is calculated for several slowly-varying factors, and some discussion of mean squared error and bandwidth choice is included.

Suggested Citation

  • Robinson, Peter M., 2014. "The estimation of misspecified long memory models," LSE Research Online Documents on Economics 53692, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:53692
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    File URL: http://eprints.lse.ac.uk/53692/
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    References listed on IDEAS

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    1. Clifford M. Hurvich & Rohit Deo & Julia Brodsky, 1998. "The mean squared error of Geweke and Porter‐Hudak's estimator of the memory parameter of a long‐memory time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(1), pages 19-46, January.
    2. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
    3. Liudas Giraitis & Peter M. Robinson & Alexander Samarov, 1997. "Rate Optimal Semiparametric Estimation Of The Memory Parameter Of The Gaussian Time Series With Long‐Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(1), pages 49-60, January.
    4. Liudas Giraitis & Peter M Robinson & Alexander Samarov, 1997. "Rate Optimal Semiparametric Estimation of the Memory Parameter of the Gaussian Time Serieswith Long-Range Dependence - (Now published in 'Journal of Time Series Analysis', 18 (1997), pp.49-60.)," STICERD - Econometrics Paper Series 323, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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    Cited by:

    1. Martin, Gael M. & Nadarajah, K. & Poskitt, D.S., 2020. "Issues in the estimation of mis-specified models of fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 215(2), pages 559-573.
    2. Annika Betken, 2016. "Testing for Change-Points in Long-Range Dependent Time Series by Means of a Self-Normalized Wilcoxon Test," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(6), pages 785-809, November.

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    More about this item

    Keywords

    long memory; slowly-varying function; log-periodogram estimate;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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