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Matematicheskie Zametki, 2008, Volume 83, Issue 4, Pages 552–558
DOI: https://doi.org/10.4213/mzm4575 (Mi mzm4575) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Statistical Analysis of First-Order MARMA Processes

A. V. Lebedev

M. V. Lomonosov Moscow State University
Full-text PDF (430 kB) Citations (8)
References:
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DOI: https://doi.org/10.4213/mzm4575
Abstract: In this paper, we consider processes of the MARMA type that can be derived from the classical ARMA processes by replacing summation by the maximum operation. It is assumed that the innovations and the values of the process have the standard Fréchet distribution. For simple MARMA processes of first order, certain numerical characteristics are calculated. Sign tests and rank statistical methods for parameter estimation are developed. The characterization relations that can be used for the identification of models are justified.
Keywords: MARMA and ARMA processes, moving maximum, sign test, rank test, estimation of parameters, random variable, Fréchet distribution, Pearson correlation coefficient.
Received: 20.03.2007
English version:
Mathematical Notes, 2008, Volume 83, Issue 4, Pages 506–511
DOI: https://doi.org/10.1134/S0001434608030243
Bibliographic databases:
UDC: 519.246
Language: Russian
Citation: A. V. Lebedev, “Statistical Analysis of First-Order MARMA Processes”, Mat. Zametki, 83:4 (2008), 552–558; Math. Notes, 83:4 (2008), 506–511
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm/v83/i4/p552
    • This publication is cited in the following 8 articles:
    1. A. V. Lebedev, “Multivariate Extremes of Random Scores of Particles in Branching Processes with Max-Linear Inheritance”, Math. Notes, 105:3 (2019), 376–384  mathnet  crossref  crossref  mathscinet  isi  elib
    2. A. V. Lebedev, “Statisticheskii analiz maksimum-lineinykh sluchainykh protsessov”, Sistemy i sredstva inform., 27:2 (2017), 16–28  mathnet  crossref  elib
    3. Ferreira M., “the Lawrence-Lewis Pareto Process: An Extremal Approach”, Electron. J. Appl. Stat. Anal., 9:1 (2016), 68–82  crossref  mathscinet  isi  scopus
    4. Ferreira M., Ferreira H., “Extremes of Multivariate Armax Processes”, Test, 22:4 (2013), 606–627  crossref  mathscinet  zmath  isi  scopus
    5. Ferreira M., “On the extremal behavior of a Pareto process: an alternative for ARMAX modeling”, Kybernetika (Prague), 48:1 (2012), 31–49  mathscinet  zmath  isi
    6. M. Ferreira, “On Tail Dependence: A Characterization for First-Order Max-Autoregressive Processes”, Math. Notes, 90:6 (2011), 882–893  mathnet  crossref  crossref  mathscinet  isi
    7. Ferreira M., “Estimation of the parameter of a pARMAX model”, REVSTAT, 8:2 (2010), 139–149  mathscinet  zmath  isi
    8. A. V. Lebedev, “Nonlinear Prediction in Max-Autoregressive Processes”, Math. Notes, 85:4 (2009), 602–606  mathnet  crossref  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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