# Warped Dynamic Linear Models for Time Series of Counts

arXiv: https://arxiv.org/abs/2110.14790 · HTML: https://mlsanity.com/paper/2110.14790/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 55 references that are in the map.
- First posted on arXiv 27 Oct 2021.

## Builds on (most cited first, 12 of 12)

- [On Particle Methods for Parameter Estimation in State-Space Models](https://mlsanity.com/paper/1412.8695/) (2014)
- [Ensemble Kalman methods for high-dimensional hierarchical dynamic space-time models](https://mlsanity.com/paper/1704.06988/) (2017)
- [Approximate leave-future-out cross-validation for Bayesian time series models](https://mlsanity.com/paper/1902.06281/) (2019)
- [A closed-form filter for binary time series](https://mlsanity.com/paper/1902.06994/) (2019)
- [Latent Gaussian Count Time Series](https://mlsanity.com/paper/1811.00203/) (2018)
- [Simultaneous Transformation and Rounding (STAR) Models for Integer-Valued Data](https://mlsanity.com/paper/1906.11653/) (2019)
- [Nonparametric Bayes modeling of count processes](https://mlsanity.com/paper/1307.2822/) (2013)
- [Sequential Bayesian Analysis of Multivariate Count Data](https://mlsanity.com/paper/1602.01445/) (2016)
- [KFAS: Exponential Family State Space Models in R](https://mlsanity.com/paper/1612.01907/) (2016)
- [Bayesian forecasting of many count-valued time series](https://mlsanity.com/paper/1805.05232/) (2018)
- [Semiparametric count data regression for self-reported mental health](https://mlsanity.com/paper/2106.09114/) (2021)
- [Semiparametric discrete data regression with Monte Carlo inference and prediction](https://mlsanity.com/paper/2110.12316/) (2021)

## Abstract (arXiv)

Dynamic Linear Models (DLMs) are commonly employed for time series analysis due to their versatile structure, simple recursive updating, ability to handle missing data, and probabilistic forecasting. However, the options for count time series are limited: Gaussian DLMs require continuous data, while Poisson-based alternatives often lack sufficient modeling flexibility. We introduce a novel semiparametric methodology for count time series by warping a Gaussian DLM. The warping function has two components: a (nonparametric) transformation operator that provides distributional flexibility and a rounding operator that ensures the correct support for the discrete data-generating process. We develop conjugate inference for the warped DLM, which enables analytic and recursive updates for the state space filtering and smoothing distributions. We leverage these results to produce customized and efficient algorithms for inference and forecasting, including Monte Carlo simulation for offline analysis and an optimal particle filter for online inference. This framework unifies and extends a variety of discrete time series models and is valid for natural counts, rounded values, and multivariate observations. Simulation studies illustrate the excellent forecasting capabilities of the warped DLM. The proposed approach is applied to a multivariate time series of daily overdose counts and demonstrates both modeling and computational successes.