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Adapting to unknown disturbance autocorrelation in regression with long memory

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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.

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en

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application/pdf

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http://eprints.lse.ac.uk/2078/1/Adapting_to_Unknown_Disturbance_Autocorrelation_in_Regression_with_Long_Memory.pdf

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