A new look at time series of counts

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Some recent progress in count time series (2011, background): “Superpositioning independent copies of such processes yields to stationary series with binomial, Poisson, geometric or any other discrete marginal distribution [18].”
Count Time Series: A Methodological Review (2021, methodology): “Mimicking this idea, Blight (1989) and Cui and Lund (2009) attempt to construct series with the prescribed marginal distribution by combining correlated binary (Bernoulli) processes.”
Count Time Series Models (2012, methodology): “4 Renewal Process Models In a recent contribution by Cui and Lund (2009), the authors propose a new and simple model for stationary time series of integer counts.”