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Regression of spectral estimators with fractionally integrated time series. (English) Zbl 0782.62085

Summary: Assuming a normal distribution we supplement the proof of periodogram regression suggested by J. Geweke and S. Porter-Hudak [ibid. 4, 221-238 (1983; Zbl 0534.62062)] in order to estimate and test the difference parameter of fractionally integrated autoregressive moving- average models. The procedure proposed by R. L. Kashyap and K.-B. Eom [ibid. 9, 35-41 (1988; Zbl 0635.62085)] arises as a special case and is found to be correct if the true parameter value is negative. Regression of the smoothed periodogram yields estimators for the difference parameter with much faster vanishing variance; no asymptotic distribution can be derived, however. In computer experiments we find that the smoothed periodogram regression may be superior to pure periodogram regression when we have to discriminate between autoregression and fractional integration.
[Edit. remark: A corrigendum to this paper appeared in ibid., No. 5, 549 (1993)].

MSC:

62M15 Inference from stochastic processes and spectral analysis
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References:

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