The periodogram at the Fourier frequencies
In the time series literature one can often find the claim that the periodogram ordinates of an iid sequence at the Fourier frequencies behave like an iid standard exponential sequence. We review some results about functions of these periodogram ordinates, including the convergence of extremes, point processes, the empirical distribution function and the empirical process. We show when the analogy with an iid exponential sequence is valid and study situations when it fails. Periodogram ordinates of an infinite variance iid sequence are also considered.
Year of publication: |
2000
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Authors: | Kokoszka, Piotr ; Mikosch, Thomas |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 86.2000, 1, p. 49-79
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Publisher: |
Elsevier |
Keywords: | Periodogram Fourier frequency iid sequence Asymptotic normality Empirical process Point process Weyl's theorem Infinite variance process Stable distribution Asymptotic expansion Functional CLT |
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