This paper proposes a piecewise autoregression for general integer-valued time series. The conditional mean of the process depends on parameter which is constant over time. We derive an inference procedure based penalized contrast that constructed from Poisson quasi-maximum likelihood model. consistency proposed estimator established. From practical applications, we data-driven slope heuristic ...

In the present article, we introduce a new true integer valued autoregressive model of order one TPDINAR(1) for data sets on Z and either positive or negative correlations based Poisson difference (Skellam) marginal distribution using random walk variable (It). Properties are derived. We consider several methods estimating unknown parameters model, their properties discussed. Simulations carrie...

The ring of integer-valued polynomials over a given subset S ℤ (or Int(S,ℤ)) is defined as the set in ℚ[x] which maps to ℤ. In factorization theory, it crucial check irreducibility polynomial. this article, we make Bhargava factorials our main tool polynomial f∈Int(S,ℤ)). We also generalize results arbitrary subsets Dedekind domain.