Warped Dynamic Linear Models for Time Series of Counts
This work addresses a specific modeling gap for count time series in statistics, offering a novel semiparametric approach that unifies and extends discrete models, though it is incremental in building upon existing dynamic linear models.
The authors tackled the problem of modeling count time series, which are limited by existing Gaussian or Poisson-based dynamic linear models, by introducing a warped dynamic linear model that combines a nonparametric transformation and rounding operator for discrete data. The result is a flexible framework with analytic inference and efficient algorithms, validated through simulations and an application to daily overdose counts.
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.