# A Conway-Maxwell-Poisson GARMA Model for Count Data

## TL;DR

This paper introduces a flexible count time series model based on the Conway-Maxwell-Poisson distribution, capable of handling both underdispersed and overdispersed data with serial correlation.

## Contribution

It develops a novel COM-Poisson GARMA model for count data, addressing estimation challenges with new methods for intractable normalising constants and sampling.

## Key findings

- Model effectively captures serial dependence in count data.
- Handles both underdispersed and overdispersed datasets.
- Proposes estimation techniques for complex COM-Poisson models.

## Abstract

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.