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On a method of estimating parameters in non-negative ARMA models. (English) Zbl 0882.62089
Summary: The purpose of this paper is to introduce a method of estimating parameters in nonnegative ARMA processes. The method is a generalization of the procedures which were derived for autoregressive and moving-average processes. The estimates are constructed in the form of minima of certain fractions or some functions of these minima. A theorem concerning the strong consistency of these estimates is proved and its applications to the models ARMA(1,1), ARMA(2,1) and \(\text{ARMA} (p,1)\), \(p>2\) are demonstrated.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F12 Asymptotic properties of parametric estimators
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References:
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