Count data time series models based on expectation thinning

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Count data time series models based on expectation thinning

TitleCount data time series models based on expectation thinning
Publication TypeJournal Article
Year of Publication2010
AuthorsZhu, R, Joe, H
JournalStochastic Models
PaginationPII 925211404
Type of Articlearticle
KeywordsAutoregressive, Birth-death process, Continuous-time Markov process, Expectation thinning, Generalized discrete self-decomposability, overdispersion, Self-generalizability, Sojourn time
AbstractMotivated 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.