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Mat. Zametki, 2008, Volume 83, Issue 4, Pages 552–558 (Mi mz4575)  

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

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

DOI: https://doi.org/10.4213/mzm4575

Full text: PDF file (430 kB)
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English version:
Mathematical Notes, 2008, 83:4, 506–511

Bibliographic databases:

UDC: 519.246
Received: 20.03.2007

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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\paper Statistical Analysis of First-Order MARMA Processes
\jour Mat. Zametki
\yr 2008
\vol 83
\issue 4
\pages 552--558
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\jour Math. Notes
\yr 2008
\vol 83
\issue 4
\pages 506--511
\crossref{https://doi.org/10.1134/S0001434608030243}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Lebedev, “Nonlinear Prediction in Max-Autoregressive Processes”, Math. Notes, 85:4 (2009), 602–606  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Ferreira M., “Estimation of the parameter of a pARMAX model”, REVSTAT, 8:2 (2010), 139–149  mathscinet  zmath  isi
    3. 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
    4. 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
    5. Ferreira M., Ferreira H., “Extremes of Multivariate Armax Processes”, Test, 22:4 (2013), 606–627  crossref  mathscinet  zmath  isi  scopus
    6. Ferreira M., “the Lawrence-Lewis Pareto Process: An Extremal Approach”, Electron. J. Appl. Stat. Anal., 9:1 (2016), 68–82  crossref  mathscinet  isi  scopus
    7. A. V. Lebedev, “Statisticheskii analiz maksimum-lineinykh sluchainykh protsessov”, Sistemy i sredstva inform., 27:2 (2017), 16–28  mathnet  crossref  elib
    8. 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  isi  elib
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