Geodesic
Semibinomial conditionally nonlinear autoregressive models of discrete random sequences: probabilistic properties and statistical parameter estimation
Diskretnaya Matematika, Tome 31 (2019) no. 1, pp. 72-98

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We introduce a new model $\mathscr{P}\text{-}\mathrm{CNAR}(s)$ of sequences of discrete random variables with long memory determined by semibinomial conditionally nonlinear autoregression of order $s\in\N$ with small number of parameters. Probabilistic properties of this model are studied. For parameters of the model $\mathscr{P}\text{-}\mathrm{CNAR}(s)$ 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 $\mathscr{P}\text{-}\mathrm{CNAR}(s)$. 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.
Keywords: sequence of discrete random variables, parsimonious model, long memory, efficient estimate, exponential family. 
@article{DM_2019_31_1_a4,
     author = {V. A. Voloshko and Yu. S. Kharin},
     title = {Semibinomial conditionally nonlinear autoregressive models of discrete random sequences: probabilistic properties and statistical parameter estimation},
     journal = {Diskretnaya Matematika},
     pages = {72--98},
     publisher = {mathdoc},
     volume = {31},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2019_31_1_a4/}
}
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V. A. Voloshko; Yu. S. Kharin. Semibinomial conditionally nonlinear autoregressive models of discrete random sequences: probabilistic properties and statistical parameter estimation. Diskretnaya Matematika, Tome 31 (2019) no. 1, pp. 72-98. http://geodesic.mathdoc.fr/item/DM_2019_31_1_a4/