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Abstract:
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We introduce a novel methodology for count time series by warping a Gaussian Dynamic Linear Model. The warping function has two components: a transformation operator that provides distributional flexibility and a rounding operator that ensures the correct support for the discrete data-generating process. Importantly, 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 computing strategies 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.
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