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Nonstationary fractionally integrated functional time series

Li, Degui, Robinson, Peter M. and Shang, Han Lin (2023) Nonstationary fractionally integrated functional time series. Bernoulli, 29 (2). 1505 - 1526. ISSN 1350-7265

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Identification Number: 10.3150/22-BEJ1508


We study a functional version of nonstationary fractionally integrated time series, covering the functional unit root as a special case. The time series taking values in an infinite-dimensional separable Hilbert space are projected onto a finite number of sub-spaces, the level of nonstationarity allowed to vary over them. Under regularity conditions, we derive a weak convergence result for the projection of the fractionally integrated functional process onto the asymptotically dominant sub-space, which retains most of the sample information carried by the original functional time series. Through the classic functional principal component analysis of the sample variance operator, we obtain the eigenvalues and eigenfunctions which span a sample version of the dominant sub-space. Furthermore, we introduce a simple ratio criterion to consistently estimate the dimension of the dominant sub-space, and use a semiparametric local Whittle method to estimate the memory parameter. Monte-Carlo simulation studies are given to examine the finite-sample performance of the developed techniques.

Item Type: Article
Official URL:
Additional Information: © 2023 ISI/BS.
Divisions: Economics
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics
Date Deposited: 09 Mar 2023 14:09
Last Modified: 16 Jun 2024 16:45

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