Count Data Time Series Models Based on Expectation Thinning
Rong Zhu, Harry Joe · Stochastic Models · 2010
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.