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arXiv · 1811.00203

Latent Gaussian Count Time Series

Yisu Jia·Stefanos Kechagias·James Livsey·Robert Lund·Vladas Pipiras
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Abstract

This paper develops the theory and methods for modeling a stationary count time series via Gaussian transformations. The techniques use a latent Gaussian process and a distributional transformation to construct stationary series with very flexible correlation features that can have any pre-specified marginal distribution, including the classical Poisson, generalized Poisson, negative binomial, and binomial structures. Gaussian pseudo-likelihood and implied Yule-Walker estimation paradigms, based on the autocovariance function of the count series, are developed via a new Hermite expansion. Particle filtering and sequential Monte Carlo methods are used to conduct likelihood estimation. Connections to state space models are made. Our estimation approaches are evaluated in a simulation study and the methods are used to analyze a count series of weekly retail sales.

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Yisu Jia, Stefanos Kechagias, James Livsey, Robert Lund, Vladas Pipiras. 2018-11-01. Latent Gaussian Count Time Series. https://doi.org/10.1080/01621459.2021.1944874

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