The distribution of the maximum of an ARMA(1,1) process

DOI10.5802/CRMATH.111zbMath1455.62184arXiv1312.7150OpenAlexW3108562854MaRDI QIDQ2214476

Christopher S. Withers, Saralees Nadarajah

Publication date: 8 December 2020

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.7150

zbMATH Keywords

eigenvaluescumulative distribution functionFredholm kernelARMA(1,1) process

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Order statistics; empirical distribution functions (62G30) Characterization and structure theory of statistical distributions (62E10) Large deviations (60F10) Approximation by operators (in particular, by integral operators) (41A35) Fredholm integral equations (45B05)

Cites Work

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• The distribution of the maximum of a first order moving average: the continuous case
• The distribution of the maximum of a first order autoregressive process: The continuous case
• Extreme value theory for moving average processes
• A note on bias reduction
• The rate of convergence of extremes of stationary normal sequences

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