In this article, we introduce a multiplicative integer-valued time series model, which is defined as the product of unit-mean independent and identically distributed (i.i.d.) sequence, an dependent process. The latter binomial thinning operation its own past observed Furthermore, it combines some features GARCH (INGARCH), autoregressive conditional duration (ACD), integer autoregression (INAR) ...

Abstract Using numerous transaction data on the number of stock trades, we conduct a forecasting exercise with INGARCH models, governed by various conditional distributions; Poisson, linear and quadratic negative binomial, double Poisson generalized Poisson. The model parameters are estimated efficient Markov Chain Monte Carlo methods, while forecast evaluation is done calculating point density...

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...