Publication:
Non-stationary log-periodogram regression

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1999-08
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Elsevier
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Abstract
We study asymptotic properties of the log-periodogram semiparametric estimate of the memory parameter d for non-stationary (d>=1/2) time series with Gaussian increments, extending the results of Robinson (1995) for stationary and invertible Gaussian processes. We generalize the definition of the memory parameter d for non-stationary processes in terms of the (successively) differentiated series. We obtain that the log-periodogram estimate is asymptotically normal for dE[1/2, 3/4) and still consistent for dE[1/2, 1). We show that with adequate data tapers, a modified estimate is consistent and asymptotically normal distributed for any d, including both non-stationary and non-invertible processes. The estimates are invariant to the presence of certain deterministic trends, without any need of estimation.
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Non-stationary time series, Log-periodogram regression, Semiparametric inference, Tapering
Bibliographic citation
Journal of Econometrics. 1999, vol. 91, nº 2, p. 325-371