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Ergodicity of observation-driven time series models and consistency of the maximum likelihood estimator. (English) Zbl 1285.62104

Summary: This paper deals with a general class of observation-driven time series models with a special focus on time series of counts. We provide conditions under which there exist strict-sense stationary and ergodic versions of such processes. The consistency of the maximum likelihood estimators is then derived for well-specified and misspecified models.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62B10 Statistical aspects of information-theoretic topics
62F10 Point estimation
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