The periodogram at the Fourier frequencies
The authors consider an iid sequence (\(Z_t\)) of random variables with \(Z=Z_0\), \(EZ=0\) and \(EZ^2=1\). They give a review of the asymptotic properties of the periodogram ordinates of the iid sequence at the Fourier frequencies and investigate the limit behaviour of various functions of these periodogram ordinates. In some cases (extremes, point processes, empirical distribution functions) an analogy was found with an iid standard exponential sequence, whereas in other cases (empirical processes, weighted sums) the analogy failed. Periodogram ordinates of an infinite variance iid sequence were also considered.
scientific article; zbMATH DE number 2000161
scientific article