# Latent Gaussian Count Time Series

arXiv: https://arxiv.org/abs/1811.00203 · HTML: https://mlsanity.com/paper/1811.00203/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2018.

## Built on by (most cited first, 4 of 4)

- [Laplace Matching for fast Approximate Inference in Latent Gaussian Models](https://mlsanity.com/paper/2105.03109/) (2021)
- [Semiparametric discrete data regression with Monte Carlo inference and prediction](https://mlsanity.com/paper/2110.12316/) (2021)
- [Warped Dynamic Linear Models for Time Series of Counts](https://mlsanity.com/paper/2110.14790/) (2021)
- [Hierarchical Count Echo State Network Models with Application to Graduate Student Enrollments](https://mlsanity.com/paper/2501.14698/) (2025)

## Abstract (arXiv)

This paper develops the theory and methods for modeling a stationary count time series via Gaussian transformations. The techniques use a latent Gaussian process and a distributional transformation to construct stationary series with very flexible correlation features that can have any pre-specified marginal distribution, including the classical Poisson, generalized Poisson, negative binomial, and binomial structures. Gaussian pseudo-likelihood and implied Yule-Walker estimation paradigms, based on the autocovariance function of the count series, are developed via a new Hermite expansion. Particle filtering and sequential Monte Carlo methods are used to conduct likelihood estimation. Connections to state space models are made. Our estimation approaches are evaluated in a simulation study and the methods are used to analyze a count series of weekly retail sales.