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Piecewise autoregression for general integer-valued time series. (English) Zbl 1455.62170
Summary: 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.
##### MSC:
 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62G10 Nonparametric hypothesis testing 62P20 Applications of statistics to economics
##### Software:
CAPUSHE; basta; wbs
Full Text:
##### References:
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