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 a parameter which is piecewise constant over time. We derive an inference procedure based on a penalized contrast that is constructed from the Poisson quasi-maximum likelihood of the model. The consistency of the proposed estimator is established. From practical applications, we derive a data-driven procedure based on the slope heuristic to calibrate the penalty term of the contrast; and the implementation is carried out through the dynamic programming algorithm, which leads to a procedure of O(n(2)) time complexity. Some simulation results are provided, as well as the applications to the US recession data and the number of trades in the stock of Technofirst. (C) 2020 Elsevier B.V. All rights reserved.