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Parameter estimation and dependence characterization of the MAR(1) process. (English) Zbl 1274.62587

Summary: Classical linear ARMA with normal distributed noises are not suitable for heavy tailed phenomena. MARMA processes obtained by replacing summation by the maximum operator are more appropriate. We consider unit FrĂ©chet first order MARMA, denoted MAR(1), and present a characterization based on ordinal autocorrelation. An estimator of the model’s parameter and respective consistency and asymptotic normality properties are also stated.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60G10 Stationary stochastic processes
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