@article { ISI:000280675100006,
	title = {Count data time series models based on expectation thinning},
	journal = {Stochastic Models},
	volume = {26},
	number = {3},
	year = {2010},
	pages = {PII 925211404},
	publisher = {Taylor \& Francis Inc},
	type = {article},
	abstract = {Motivated by modelling of unequally spaced count data time series, we propose the construction of a class of continuous-time first-order Markov processes based on the self-generalized expectation thinning operations. Properties of families of random variables leading to self-generalized expectation thinning operations are obtained. Characterization results are obtained for stationary marginal distributions, the innovation random variables and the infinitesimal innovation. The transition matrix and distribution of sojourn time are also derived. Particular families of self-generalized random variables are given to make the theory concrete for modelling count data that are overdispersed relative to Poisson. We also show that the self-generalizability condition is important in order to get nice properties for the Markov processes.},
	keywords = {Autoregressive, Birth-death process, Continuous-time Markov process, Expectation thinning, Generalized discrete self-decomposability, overdispersion, Self-generalizability, Sojourn time},
	issn = {1532-6349},
	doi = {10.1080/15326349.2010.498318},
	author = {Zhu, Rong and Joe, Harry}
}
@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}
}
