Time-varying auto-regressive models for count time-series

TL;DR

This paper introduces two Bayesian time-varying models for count time series, especially for COVID-19 daily case data, demonstrating their effectiveness through simulations and real data analysis.

Contribution

It proposes novel Bayesian semiparametric AR(p) and INGARCH models with time-varying parameters for count data, including COVID-19 cases, with efficient HMC sampling and theoretical convergence analysis.

Findings

Models outperform existing methods in simulations

Effective for analyzing COVID-19 case data

Posterior contraction rates established

Abstract

Count-valued time series data are routinely collected in many application areas. We are particularly motivated to study the count time series of daily new cases, arising from COVID-19 spread. We propose two Bayesian models, a time-varying semiparametric AR(p) model for count and then a time-varying INGARCH model considering the rapid changes in the spread. We calculate posterior contraction rates of the proposed Bayesian methods with respect to average Hellinger metric. Our proposed structures of the models are amenable to Hamiltonian Monte Carlo (HMC) sampling for efficient computation. We substantiate our methods by simulations that show superiority compared to some of the close existing methods. Finally we analyze the daily time series data of newly confirmed cases to study its spread through different government interventions.