We propose a flexible model for count time series which has potential uses for both underdispersed and overdispersed data. The model is based on the Conway-Maxwell-Poisson (COM-Poisson) distribution with parameters varying along time to take serial correlation into account. Model estimation is challenging however and require the application of recently proposed methods to deal with the intractable normalising constant as well as efficiently sampling values from the COM-Poisson distribution.
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