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Observation-driven models for discrete-valued time series. (English) Zbl 1493.62546

Summary: Statistical inference for discrete-valued time series has not been developed like traditional methods for time series generated by continuous random variables. Some relevant models exist, but the lack of a homogenous framework raises some critical issues. For instance, it is not trivial to explore whether models are nested and it is quite arduous to derive stochastic properties which simultaneously hold across different specifications. In this paper, inference for a general class of first order observation-driven models for discrete-valued processes is developed. Stochastic properties such as stationarity and ergodicity are derived under easy-to-check conditions, which can be directly applied to all the models encompassed in the class and for every distribution which satisfies mild moment conditions. Consistency and asymptotic normality of quasi-maximum likelihood estimators are established, with the focus on the exponential family. Finite sample properties and the use of information criteria for model selection are investigated throughout Monte Carlo studies. An empirical application to count data is discussed, concerning a test-bed time series on the spread of an infection.

MSC:

62M20 Inference from stochastic processes and prediction
62F12 Asymptotic properties of parametric estimators
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62J12 Generalized linear models (logistic models)

Software:

tscount; glarma
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Full Text: DOI Link

References:

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