Growth rates of sample covariances of stationary symmetric \(\alpha \)-stable processes associated with null recurrent Markov chains

DOI10.1016/S0304-4149(99)00081-2zbMath0995.62083OpenAlexW2044015449MaRDI QIDQ1613597

Fang Xue, Gennady Samorodnitsky, Sidney I. Resnick

Publication date: 29 August 2002

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0304-4149(99)00081-2

zbMATH Keywords

heavy tailsstable processACFsample covariancenull recurrent Markov chains

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)

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Cites Work

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• Limit theory for moving averages of random variables with regularly varying tail probabilities
• Limit theory for the sample covariance and correlation functions of moving averages
• Time series: theory and methods.
• Sample correlations of infinite variance time series models: An empirical and theoretical study
• Classes of mixing stable processes
• Limit theory for bilinear processes with heavy-tailed noise
• Heavy tail modeling and teletraffic data. (With discussions and rejoinder)
• How misleading can sample ACFs of stable MAs be? (Very!)
• Pitfalls of fitting autoregressive models for heavy-tailed time series
• A discrete renewal theorem with infinite mean
• Sample correlation behavior for the heavy tailed general bilinear process
• Probability