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Stationary count time series models

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Abstract During the last 20–30 years, there was a remarkable growth in interest on approaches for stationary count time series. We consider popular classes of models for such time series, including thinning‐based models, conditional regression models, and Hidden‐Markov models. We review and compare important members of these model families, having regard to stochastic properties such as the dispersion and autocorrelation structure. Our survey covers univariate and multivariate count data, as well as unbounded and bounded counts. We also discuss an illustrative data example. Besides this critical presentation of the current state‐of‐the‐art, some existing challenges and opportunities for future research are identified. This article is categorized under: Statistical Models > Time Series Models Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms
Sales count time series: plot against time t in top row; plots of sample probability mass function against x as well as (partial) autocorrelation function against lag h in bottom row
[ Normal View | Magnified View ]
Road accidents count time series: plot of daytime (xt,1) and nighttime (xt,2) accidents against time t
[ Normal View | Magnified View ]
Monthly price stability count time series (2000–2006): plot against time t as well as autocorrelation function against lag h
[ Normal View | Magnified View ]

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Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms
Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods
Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data
Statistical Models > Time Series Models

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