Geodesic
Statistical Analysis of First-Order MARMA Processes
Matematičeskie zametki, Tome 83 (2008) no. 4, pp. 552-558

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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, rank test, estimation of parameters, random variable, Pearson correlation coefficient.
Mots-clés : sign test, Fréchet distribution 
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     author = {A. V. Lebedev},
     title = {Statistical {Analysis} of {First-Order} {MARMA} {Processes}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {552--558},
     publisher = {mathdoc},
     volume = {83},
     number = {4},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_4_a7/}
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A. V. Lebedev. Statistical Analysis of First-Order MARMA Processes. Matematičeskie zametki, Tome 83 (2008) no. 4, pp. 552-558. http://geodesic.mathdoc.fr/item/MZM_2008_83_4_a7/