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Adapting to unknown disturbance autocorrelation in regression with long memory

Author

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  • Hidalgo, Javier
  • Robinson, Peter

Abstract

We show that it is possible to adapt to nonparametric disturbance autocorrelation in time series regression in the presence of long memory in both regressors and disturbances by using a smoothed nonparametric spectrum estimate in frequency-domain generalized least squares. When the collective memory in regressors and disturbances is sufficiently strong, ordinary least squares is not only asymptotically inefficient but asymptotically non-normal and has a slow rate of convergence, whereas generalized least squares is asymptotically normal and Gauss-Markov efficient with standard convergence rate. Despite the anomalous behaviour of nonparametric spectrum estimates near a spectral pole, we are able to justify a standard construction of frequency-domain generalized least squares, earlier considered in case of short memory disturbances. A small Monte Carlo study of finite sample performance is included.

Suggested Citation

  • Hidalgo, Javier & Robinson, Peter, 2001. "Adapting to unknown disturbance autocorrelation in regression with long memory," LSE Research Online Documents on Economics 2078, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:2078
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    File URL: http://eprints.lse.ac.uk/2078/
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    Cited by:

    1. Hwai‐Chung Ho & Nan‐Jung Hsu, 2005. "Polynomial Trend Regression With Long‐memory Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(3), pages 323-354, May.

    More about this item

    Keywords

    Time series regression; long memory; adaptive estimation;
    All these keywords.

    JEL classification:

    • 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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