کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5129435 | 1489646 | 2017 | 14 صفحه PDF | دانلود رایگان |
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:tâ¥1) defined, for all θâ(âÏ,Ï], by Sn(θ)=Xteâiθ+â¯+Xteâinθ. 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 θnâθ0 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.
Journal: Journal of Multivariate Analysis - Volume 154, February 2017, Pages 282-295