Electronic Journal of Statistics

A goodness-of-fit test for Poisson count processes

Konstantinos Fokianos and Michael H. Neumann

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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.

Article information

Electron. J. Statist., Volume 7 (2013), 793-819.

First available in Project Euclid: 25 March 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Autoregression conditional mean ergodicity goodness-of-fit test integer-valued processes local alternatives


Fokianos, Konstantinos; Neumann, Michael H. A goodness-of-fit test for Poisson count processes. Electron. J. Statist. 7 (2013), 793--819. doi:10.1214/13-EJS790. https://projecteuclid.org/euclid.ejs/1364220671

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