On the CLT for discrete Fourier transforms of functional time series

Clément Cerovecki, Siegfried Hörmann

Publikation: Beitrag in einer FachzeitschriftArtikel

Abstract

The purpose of this paper is to derive sharp conditions for the asymptotic normality of a discrete Fourier transform of a functional time series (Xt:t≥1) defined, for all θ∈(−π,π], by Sn(θ)=Xte−iθ+⋯+Xte−inθ. Assuming that the function space is a Hilbert space we prove that a Central Limit Theorem (CLT) holds for almost all frequencies θ if the process (Xt) is stationary, ergodic and purely non-deterministic. Under slightly stronger assumptions we formulate versions which provide a CLT for fixed frequencies as well as for Sn(θn), when θn→θ0 is a sequence of fundamental frequencies. In particular we also deduce the regular CLT (θ=0) under new and very mild assumptions. We show that our results apply to the most commonly studied functional time series.
Originalspracheenglisch
Seiten (von - bis)282-295
Seitenumfang14
FachzeitschriftJournal of multivariate analysis
Jahrgang154
PublikationsstatusVeröffentlicht - 2017

Fingerprint Untersuchen Sie die Forschungsthemen von „On the CLT for discrete Fourier transforms of functional time series“. Zusammen bilden sie einen einzigartigen Fingerprint.

Dieses zitieren