Warped Dynamic Linear Models for Time Series of Counts

TL;DR

This paper introduces a novel warped dynamic linear model for count time series that combines nonparametric transformation and rounding to improve flexibility and forecasting accuracy, with efficient recursive inference algorithms.

Contribution

It proposes a semiparametric warped DLM that unifies and extends existing models for count data, enabling flexible, recursive Bayesian inference and forecasting.

Findings

Excellent forecasting performance demonstrated in simulations.

Effective application to overdose count data.

Unified framework for various discrete time series models.

Abstract

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.