A generalized mixture integer-valued GARCH model. (English) Zbl 1458.62205
Summary: We propose a generalized mixture integer-valued generalized autoregressive conditional heteroscedastic model to provide a more flexible modeling framework. This model includes many mixture integer-valued models with different distributions already studied in the literature. The conditional and unconditional moments are discussed and the necessary and sufficient first- and second-order stationary conditions are derived. We also investigate the theoretical properties such as strict stationarity and ergodicity for the mixture process. The conditional maximum likelihood estimators via the EM algorithm are derived and the performances of the estimators are studied via simulation. The model can be selected in terms of both the number of mixture regimes and the number of orders in each regime by several different criteria. A real-life data example is also given to assess the performance of the model.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62H30 | Classification and discrimination; cluster analysis (statistical aspects) |
| 60G10 | Stationary stochastic processes |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
Software:
tscountReferences:
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