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Abstract:
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We propose a three-step sequential procedure to estimate the change-point of integer-valued time series. Under mild regularity conditions, not only is the asymptotic normality of the model estimators established, but also the estimator of the location of change-point is shown to converge in distribution to the location of the maxima of a double-sided random walk. We verify that the proposed method is applicable for the first order integer-valued generalized autoregressive conditional heteroskedastic (INGARCH(1, 1)) models with Poisson or negative binomial conditional distributions.
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