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A goodness-of-fit test for Poisson count processes. (English) Zbl 1327.62455
Summary: We are studying a novel class of goodness-of-fit tests for parametric count time series regression models. These test statistics are formed by considering smoothed versions of the empirical process of the Pearson residuals. Our construction yields test statistics which are consistent against Pitman’s local alternatives and they converge weakly at the usual parametric rate. To approximate the asymptotic null distribution of the test statistics, we propose a parametric bootstrap method and we study its properties. The methodology is applied to simulated and real data.

MSC:
62M07 Non-Markovian processes: hypothesis testing
62F40 Bootstrap, jackknife and other resampling methods
60G10 Stationary stochastic processes
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