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Adapting to Unknown Disturbance Autocorrelation in Regression with Long Memory

Author

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  • Javier Hidalgo
  • Peter M Robinson

Abstract

We show that it is possible to adapt to nonparametric disturbance auto-correlation 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

  • Javier Hidalgo & Peter M Robinson, 2001. "Adapting to Unknown Disturbance Autocorrelation in Regression with Long Memory," STICERD - Econometrics Paper Series 427, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:427
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    File URL: https://sticerd.lse.ac.uk/dps/em/em427.pdf
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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.

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