How misleading can sample ACFs of stable MAs be? (Very!)

DOI10.1214/aoap/1029962814zbMath0959.62076OpenAlexW2073521040MaRDI QIDQ1578593

Fang Xue, Gennady Samorodnitsky, Sidney I. Resnick

Publication date: 4 September 2000

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

Full work available at URL: https://doi.org/10.1214/aoap/1029962814

zbMATH Keywords

heavy tailsinfinite variancestable processmoving averageARMA processessample correlation

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Extreme value theory; extremal stochastic processes (60G70) Statistics of extreme values; tail inference (62G32)

Related Items (11)

The supremum of a negative drift random walk with dependent heavy-tailed steps. ⋮ Growth rates of sample covariances of stationary symmetric \(\alpha \)-stable processes associated with null recurrent Markov chains ⋮ Limit theory for the sample autocovariance for heavy-tailed stationary infinitely divisible processes generated by conservative flows ⋮ The Extremal Dependence Measure and Asymptotic Independence ⋮ Empirical Testing Of The Infinite Source Poisson Data Traffic Model ⋮ Large sample theory for statistics of stable moving averages ⋮ Long memory and self-similar processes ⋮ Ruin probability with certain stationary stable claims generated by conservative flows ⋮ A method for fitting stable autoregressive models using the autocovariation function ⋮ Stable marked point processes ⋮ Null flows, positive flows and the structure of stationary symmetric stable processes

Cites Work

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• Heavy tail modeling and teletraffic data. (With discussions and rejoinder)
• Sample correlation behavior for the heavy tailed general bilinear process

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