The maximum of the periodogram for a heavy-tailed sequence.

DOI10.1214/aop/1019160264zbMath1044.62097OpenAlexW2079450975MaRDI QIDQ1872524

Gennady Samorodnitsky, Thomas Mikosch, Sidney I. Resnick

Publication date: 6 May 2003

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1019160264

zbMATH Keywords

linear processdiscrete Fourier transforminfinite varianceperiodogramstable processstochastic integralpoint process convergencestable random variable

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Inference from stochastic processes and spectral analysis (62M15) Statistics of extreme values; tail inference (62G32)

Related Items (7)

An empirical likelihood approach for symmetric \(\alpha\)-stable processes ⋮ Trimmed stable AR(1) processes ⋮ Weak convergence of the function-indexed integrated periodogram for infinite variance processes ⋮ The periodogram at the Fourier frequencies ⋮ Empirical likelihood approach toward discriminant analysis for dynamics of stable processes ⋮ Cramér-type moderate deviation for the maximum of the periodogram with application to simultaneous tests in gene expression time series ⋮ Robust causality test of infinite variance processes

Cites Work

• Spectral estimates and stable processes
• The empirical distribution of Fourier coefficients
• Time series: theory and methods.
• The maximum of the periodogram of a non-Gaussian sequence.
• On the asymptotic distributions of maxima of trigonometric polynomials with random coefficients
• Point processes, regular variation and weak convergence
• The empirical distribution of the fourier coefficients of a sequence of independent, identically distributed long-tailed random variables
• THE DISTRIBUTION OF PERIODOGRAM ORDINATES
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