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Modelling Count Data Time Series with Markov Processes Based on Binomial Thinning
Author(s) -
Zhu Rong,
Joe Harry
Publication year - 2006
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2006.00485.x
Subject(s) - count data , mathematics , negative binomial distribution , series (stratigraphy) , thinning , binomial (polynomial) , covariate , statistics , univariate , time series , binomial distribution , negative multinomial distribution , markov chain , poisson distribution , multivariate statistics , beta binomial distribution , paleontology , ecology , biology
. 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.