On the CLT for discrete Fourier transforms of functional time series

2015/06/02 by Clément Cerovecki, Cerovecki, Clément, Siegfried Hörmann +1
Mathematics · #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST) #math.PR #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1506.00970

arxiv created 2015/12/04 · arxiv updated 2015/12/07

Abstract

We consider a strictly stationary and ergodic sequence of random elements taking values in some Hilbert space. Our target is to study the weak convergence of the discrete Fourier transforms under sharp conditions. As a side-result we obtain the regular CLT for partial sums under mild assumptions.

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