The periodogram at the Fourier frequencies

In the time series literature one can often find the claim that the periodo gram ordinates of an lid sequence at the Fourier frequencies behave like an lid standard exponential sequence. We review some results about functions of these periodogram ordinates, including the convergence of extremes, poin t processes, the empirical distribution function and the empirical process. We show when the analogy with an lid exponential sequence is valid and stu dy situations when it fails,Periodogram ordinates of an infinite variance l id sequence are also considered. (C) 2000 Elsevier Science B.V. All rights reserved.