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Computationally Efficient Poisson Time-Varying Autoregressive Models through Bayesian Lattice Filters

Author

Listed:
  • Yuelei Sui

    (Amazon.com, Inc., New York, NY 10001, USA)

  • Scott H. Holan

    (Department of Statistics, University of Missouri, Columbia, MO 65211-6100, USA
    Office of the Associate Director for Research and Methodology, Research and Methodology Directorate, U.S. Census Bureau, Washington, DC 20233-9100, USA)

  • Wen-Hsi Yang

    (School of Agriculture and Food Sciences, The University of Queensland, St Lucia, QLD 4072, Australia
    School of Mathematics and Physics, The University of Queensland, St Lucia, QLD 4072, Australia)

Abstract

Estimation of time-varying autoregressive models for count-valued time series can be computationally challenging. In this direction, we propose a time-varying Poisson autoregressive (TV-Pois-AR) model that accounts for the changing intensity of the Poisson process. Our approach can capture the latent dynamics of the time series and therefore make superior forecasts. To speed up the estimation of the TV-AR process, our approach uses the Bayesian Lattice Filter. In addition, the No-U-Turn Sampler (NUTS) is used, instead of a random walk Metropolis–Hastings algorithm, to sample intensity-related parameters without a closed-form full conditional distribution. The effectiveness of our approach is evaluated through model-based and empirical simulation studies. Finally, we demonstrate the utility of the proposed model through an example of COVID-19 spread in New York State and an example of US COVID-19 hospitalization data.

Suggested Citation

  • Yuelei Sui & Scott H. Holan & Wen-Hsi Yang, 2023. "Computationally Efficient Poisson Time-Varying Autoregressive Models through Bayesian Lattice Filters," Stats, MDPI, vol. 6(4), pages 1-16, October.
    • Handle: RePEc:gam:jstats:v:6:y:2023:i:4:p:65-1052:d:1256118
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    References listed on IDEAS

    as
    1. Brandt, Patrick T. & Williams, John T., 2001. "A Linear Poisson Autoregressive Model: The Poisson AR(p) Model," Political Analysis, Cambridge University Press, vol. 9(2), pages 164-184, January.
    2. Rosen, Ori & Stoffer, David S. & Wood, Sally, 2009. "Local Spectral Analysis via a Bayesian Mixture of Smoothing Splines," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 249-262.
    3. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    4. René Ferland & Alain Latour & Driss Oraichi, 2006. "Integer‐Valued GARCH Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 923-942, November.
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