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Semibinomial conditionally nonlinear autoregressive models of discrete random sequences: probabilistic properties and statistical parameter estimation

  • Valeriy A. Voloshko EMAIL logo and Yuriy S. Kharin
Published/Copyright: December 11, 2020

Abstract

We introduce a new model P-CNAR(s) of sequences of discrete random variables with long memory determined by semibinomial conditionally nonlinear autoregression of order s ∈ ℕ with small number of parameters. Probabilistic properties of this model are studied. For parameters of the model P-CNAR a family of consistent asymptotically normal statistical FB-estimates is suggested and the existence of an efficient FB-estimate is proved. Computational advantages of FB-estimate w.r.t. maximum likelihood estimate are shown: less restrictive sufficient conditions for uniqueness, explicit form of FB-estimate, fast recursive computation algorithm under extension of the model P-CNAR. Subfamily of “sparse” FB-estimates that use some subset of frequencies of s-tuples is constructed, the asymptotic variance minimization problem within this subfamily is solved.


Note: Originally published in Diskretnaya Matematika (2019) 31,№1, 72–98 (in Russian).


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Received: 2018-12-01
Published Online: 2020-12-11
Published in Print: 2020-12-16

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