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Diskr. Mat., 2019, Volume 31, Issue 1, Pages 72–98 (Mi dm1561)  

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

V. A. Voloshko, Yu. S. Kharin

Research Institute of Applied Problems of Mathematics and Informatics, Belarusian State University, Minsk

Abstract: We introduce a new wide class of long memory discrete random sequences determined by a new parsimonious model $\mathscr{P}-\mathrm{CNAR}(s)$ of semibinomial conditionally nonlinear autoregression of order $s\in\mathbb N$. Probabilistic properties of the model $\mathscr{P}-\mathrm{CNAR}$ are being studied. A new family of consistent asymptotically normal statistical FB-estimators is built for parameters of the model $\mathscr{P}-\mathrm{CNAR}$ and the existence of an efficient estimator within FB-family is proved. Computational advantages of FB-estimator w.r.t. maximum likelihood estimator are shown: less restrictive sufficient conditions for uniqueness; explicit form of FB-estimator; fast recursive computation algorithm under extension of the model $\mathscr{P}-\mathrm{CNAR}$. Subfamily of “sparse” FB-estimators that use some subset of $s$-tuples frequencies is constructed. The asymptotic variance minimization problem is solved within subfamily of “sparse” FB-estimators.

Keywords: discrete random sequence, parsimonious model, long memory, efficient estimator, exponential family.

DOI: https://doi.org/10.4213/dm1561

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Document Type: Article
UDC: 519.233.2
Received: 01.12.2018

Citation: V. A. Voloshko, Yu. S. Kharin, “Semibinomial conditionally nonlinear autoregressive models of discrete random sequences: probabilistic properties and statistical parameter estimation”, Diskr. Mat., 31:1 (2019), 72–98

Citation in format AMSBIB
\Bibitem{VolKha19}
\by V.~A.~Voloshko, Yu.~S.~Kharin
\paper Semibinomial conditionally nonlinear autoregressive models of
discrete random sequences: probabilistic properties and statistical
parameter estimation
\jour Diskr. Mat.
\yr 2019
\vol 31
\issue 1
\pages 72--98
\mathnet{http://mi.mathnet.ru/dm1561}
\crossref{https://doi.org/10.4213/dm1561}
\elib{http://elibrary.ru/item.asp?id=37045015}


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