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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

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}