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

TY - JOUR

T1 - Local Whittle Estimation of Long-Range Dependence for Functional Time Series

AU - Li, Degui

AU - Robinson, Peter M.

AU - Shang, Hanlin

N1 - © 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.

PY - 2021/10/1

Y1 - 2021/10/1

N2 - 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.

AB - 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.

U2 - 10.1111/jtsa.12577

DO - 10.1111/jtsa.12577

M3 - Article

SN - 0143-9782

VL - 42

SP - 685

EP - 695

JO - Journal of Time Series Analysis

JF - Journal of Time Series Analysis

IS - 5-6

ER -