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Piecewise autoregression for general integer-valued time series
Journal of Statistical Planning and Inference ( IF 0.9 ) Pub Date : 2021-03-01 , DOI: 10.1016/j.jspi.2020.07.003
Mamadou Lamine Diop , William Kengne

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.

中文翻译:

一般整数值时间序列的分段自回归

本文提出了一般整数值时间序列的分段自回归。该过程的条件均值取决于随时间分段恒定的参数。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推理过程。建立了建议的估计量的一致性。从实际应用中,我们推导出基于斜率启发式的数据驱动程序来校准对比度的惩罚项;并且通过动态规划算法实现,这导致了$\mathcal{O}(n^2)$时间复杂度的过程。提供了一些模拟结果,以及对美国经济衰退数据和Technofirst股票交易数量的应用。
更新日期:2021-03-01
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