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Abstract:
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Time-ordered and count-valued data present numerous challenges for forecasting and inference. In addition to complex dynamic dependences, these discrete data exhibit distributional features including zero-inflation, skewness, over- or under-dispersion, and may be bounded or censored. To meet these challenges, we propose a simple yet powerful framework for modeling count time series data. The data-generating process is defined by Simultaneously Transforming and Rounding a Dynamic Linear Model (STAR-DLM). STAR-DLMs inherit the dynamics and interpretability of Gaussian DLMs while providing the modeling flexibility to describe the aforementioned distributional features of count data. Unlike competing approaches, the exact forecasting, filtering, and smoothing distributions are obtained in closed form, which admits fast Monte Carlo-based posterior inference. STAR-DLMs are amenable to significant model generalizations, while the accompanying computational burden is met by an optimal particle filter for forecasting and inference. Empirical results for real and synthetic datasets demonstrate excellent modeling, forecasting, and computational performance.
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