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Local Whittle Estimation of Long-Range Dependence for Functional Time Series

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JournalJournal of Time Series Analysis
DateAccepted/In press - 3 Dec 2020
DateE-pub ahead of print (current) - 12 Dec 2020
Number of pages11
Early online date12/12/20
Original languageEnglish

Abstract

This paper studies stationary functional time series with long-range dependence, and estimates the memory parameter involved. Semiparametric local Whittle estimation is used, where periodogram is constructed from the approximate first score, which is an inner product of the functional observation and estimated leading eigenfunction. The latter is obtained via classical functional principal component analysis. Under the restrictive condition of constancy of the memory parameter over the function support, and other conditions which include rather unprimitive ones on the first score, the estimate is shown to be consistent and asymptotically normal with asymptotic variance free of any unknown parameter, facilitating inference, as in the scalar time series case. Although the primary interest lies in long-range dependence, our methods and theory are relevant to short-range dependent or negative dependent functional time series. A Monte-Carlo study of finite sample performance and an empirical example are included.

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© 2020 John Wiley & Sons Ltd. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

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