Piecewise autoregression for general integer-valued time series

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 to calibrate penalty term contrast; and implementation carried out through dynamic programming algorithm, leads O(n2) complexity. Some simulation results are provided, as well applications US recession data number trades in stock Technofirst.