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Adapting to Unknown Disturbance Autocorrelation in Regression with Long Memory

  • Javier Hidalgo
  • Peter M Robinson

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.

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File URL: http://sticerd.lse.ac.uk/dps/em/em427.pdf
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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2001/427.

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Date of creation: Sep 2001
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Handle: RePEc:cep:stiecm:/2001/427
Contact details of provider: Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

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  1. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-48, May.
  2. Hosoya, Yuzo, 1996. "The quasi-likelihood approach to statistical inference on multiple time-series with long-range dependence," Journal of Econometrics, Elsevier, vol. 73(1), pages 217-236, July.
  3. Robinson, P M, 1976. "Instrumental Variables Estimation of Differential Equations," Econometrica, Econometric Society, vol. 44(4), pages 765-76, July.
  4. Xiao, Zhijie & Phillips, Peter C. B., 2002. "Higher order approximations for Wald statistics in time series regressions with integrated processes," Journal of Econometrics, Elsevier, vol. 108(1), pages 157-198, May.
  5. Hannan, E J & Terrell, R D, 1972. "Time Series Regression with Linear Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(2), pages 189-200, June.
  6. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-63, September.
  7. Hannan, E J & Terrell, R D, 1973. "Multiple Equation Systems with Stationary Errors," Econometrica, Econometric Society, vol. 41(2), pages 299-320, March.
  8. D Marinucci & Peter M. Robinson, 1998. "Semiparametric frequency domain analysis of fractional cointegration," LSE Research Online Documents on Economics 2258, London School of Economics and Political Science, LSE Library.
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