标题： 整数值时间序列的分段自回归模型 显示英文标题

标题： Piecewise autoregression for general integer-valued time series

摘要： 本文提出了一种适用于一般整数值时间序列的分段自回归模型。该过程的条件均值依赖于一个随时间分段常数的参数。我们基于从模型的泊松准最大似然构造的惩罚对比，推导出一种推理程序。所提出的估计量的一致性被建立起来。从实际应用出发，我们根据斜率启发式方法推导出一种数据驱动的程序来校准对比的惩罚项；实现通过动态规划算法完成，其时间复杂度为 $\mathcal{O}(n^2)$。提供了一些模拟结果，以及对美国经济衰退数据和Technofirst公司股票交易数量的应用。 显示英文摘要

摘要： 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 $\mathcal{O}(n^2)$ 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.