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

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.