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We introduce a new modelP${\mathscr{P}}$   -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 modelP${\mathscr{P}}$   -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 modelP${\mathscr{P}}$   -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.

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