Maximum Likelihood Estimation for an Observation Driven Model for Poisson Counts

By Richard A. Davis, W. Dunsmuir, S. Streett. 2005

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Vector Multiplicative Error Models: Representation and Inference (2006, background): “4For other works related to GLARMA models see, among others, Li (1994), Davis et al. (2002).”
Count Time Series: A Methodological Review (2021, background): “Unfortunately, establishing strict stationarity and mixing for {αt} has only been done in special cases (Davis, Dunsmuir, and Streett 2003, 2005).”
First‐order integer valued AR processes with zero inflated poisson innovations (2012, background): “See for example, Latour (1997, 1998), McKenzie (2003), Davis et al. (2003, 2005) and Enciso-Mora et al. (2009) for more details and references therein.”
Count Time Series Models (2012, background): “The same phenomenon occurs for model (19) for the case p = 1; see Davis et al. (2005) who prove asymptotic normality of the maximum likelihood estimators when δ = 1 and β1 > 0, such that β1(1 + exp(β1 − β0))1/2 < 1.”
Some recent progress in count time series (2011, background): “[52] who prove asymptotic normality of the maximum-likelihood estimators when a = 1 and provided that β1 > 0 such that β1(1 + exp(β1 − β0)) < 1.”