On the CLT for discrete Fourier transforms of functional time series

Clément Cerovecki, Siegfried Hörmann

Published 2015-06-02Version 1

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.