Estimation of change‐point for a class of count time series models

Yunwei Cui, Rongning Wu and Qi Zheng

Scandinavian Journal of Statistics, 2021, vol. 48, issue 4, 1277-1313

Abstract: We apply a three‐step sequential procedure to estimate the change‐point of count time series. Under certain regularity conditions, the estimator of change‐point converges in distribution to the location of the maxima of a two‐sided random walk. We derive a closed‐form approximating distribution for the maxima of the two‐sided random walk based on the invariance principle for the strong mixing processes, so that the statistical inference for the true change‐point can be carried out. It is for the first time that such properties are provided for integer‐valued time series models. Moreover, we show that the proposed procedure is applicable for the integer‐valued autoregressive conditional heteroskedastic (INARCH) models with Poisson or negative binomial conditional distribution. In simulation studies, the proposed procedure is shown to perform well in locating the change‐point of INARCH models. And, the procedure is further illustrated with empirical data of weekly robbery counts in two neighborhoods of Baltimore City.

Date: 2021
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