A Goodness‐of‐Fit Test for Integer‐Valued Autoregressive Processes |
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| Authors: | Sebastian Schweer |
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| Affiliation: | Institute of Applied Mathematics, University of Heidelberg, Heidelberg, Germany |
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| Abstract: | For autoregressive count data time series, a goodness‐of‐fit test based on the empirical joint probability generating function is considered. The underlying process is contained in a general class of Markovian models satisfying a drift condition. Asymptotic theory for the test statistic is provided, including a functional central limit theorem for the non‐parametric estimation of the stationary distribution and a parametric bootstrap method. Connections between the new approach and existing tests for count data time series based on moment estimators appear in limiting scenarios. Finally, the test is applied to a real data set. |
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| Keywords: | Goodness‐of‐fit test integer‐valued time series probability generating function parametric bootstrap drift condition |
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