@article { ISI:000276369000022,
	title = {Negative binomial time series models based on expectation thinning operators},
	journal = {Journal of Statistical Planning and Inference},
	volume = {140},
	number = {7},
	year = {2010},
	month = {JUL},
	pages = {1874-1888},
	publisher = {Elsevier Science BV},
	type = {Article},
	abstract = {The study of count data time series has been active in the past decade, mainly in theory and model construction. There are different ways to construct time series models with a geometric autocorrelation function, and a given univariate margin such as negative binomial. In this paper, we investigate negative binomial time series models based on the binomial thinning and two other expectation thinning operators, and show how they differ in conditional variance or heteroscedasticity. Since the model construction is in terms of probability generating functions, typically, the relevant conditional probability mass functions do not have explicit forms. In order to do simulations, likelihood inference, graphical diagnostics and prediction, we use a numerical method for inversion of characteristic functions. We illustrate the numerical methods and compare the various negative binomial time series models for a real data example. (C) 2010 Elsevier B.V. All rights reserved.},
	keywords = {Autoregressive, Binomial thinning, Generalized discrete self-decomposability, Inversion of characteristic function, Negative binomial time series, Self-generalizability},
	issn = {0378-3758},
	doi = {10.1016/j.jspi.2010.01.031},
	author = {Zhu, Rong and Joe, Harry}
}
@article { ISI:000239509800005,
	title = {Modelling count data time series with Markov processes based on binomial thinning},
	journal = {Journal of Time Series Analysis},
	volume = {27},
	number = {5},
	year = {2006},
	month = {SEP},
	pages = {725-738},
	publisher = {Blackwell Publishing},
	type = {Article},
	abstract = {We obtain new models and results for count data time series based on binomial thinning. Count data time series may have non-stationarity from trends or covariates, so we propose an extension of stationary time series based on binomial thinning such that the univariate marginal distributions are always in the same parametric family, such as negative binomial. We propose a recursive algorithm to calculate the probability mass functions for the innovation random variable associated with binomial thinning. This simplifies numerical calculations and estimation for the classes of time series models that we consider. An application with real data is used to illustrate the models.},
	keywords = {Binomial thinning, count data time series, discrete self-decomposability, higher order Markov dependence, overdispersion, time-varying mean},
	issn = {0143-9782},
	doi = {10.1111/j.1467-9892.2006.00485.x},
	author = {Zhu, Rong and Joe, Harry}
}
