Premium
A Goodness‐of‐Fit Test for Integer‐Valued Autoregressive Processes
Author(s) -
Schweer Sebastian
Publication year - 2016
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12138
Subject(s) - mathematics , autoregressive model , goodness of fit , estimator , test statistic , asymptotic distribution , series (stratigraphy) , star model , central limit theorem , statistics , parametric statistics , asymptotic analysis , statistical hypothesis testing , time series , autoregressive integrated moving average , paleontology , biology
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.