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

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 the COVID-19 spread. First, we propose a Bayesian framework to study the time-varying semiparametric AR(p) model for the count and then extend it to a more sophisticated time-varying INGARCH model. We calculate posterior contraction rates of the proposed Bayesian methods with respect to the 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 existing methods that closely fit this setting. Finally, we analyze the daily time series data of newly confirmed cases in NYC to study the spread of COVID for three months.

Bayesian time‐varying autoregressive models of COVID‐19 epidemics

“…To calculate the posterior distribution from the previous expressions, we employ the gradient‐based. The Hamiltonian Monte Carlo (HMC) algorithm is similar to Roy and Karmakar ( 2021 ). Tuning of HMC parameters is necessary to obtain a good acceptance rate.…”

“…Unlike Agosto et al ( 2021), policy covariates have been introduced. The Bayesian framework instead introduces the time-varying models of Roy and Karmakar (2021) and evaluates their performances against the extended structure with time-varying policy covariates. Time constant coefficient models have also been added to have a direct comparison with Agosto et al (2021) in the Bayesian framework.…”

“…( 2021 ), Geir et al. ( 2022 ), and Roy and Karmakar ( 2021 ) with the inclusion of time‐varying policy covariates. And we also extend the causal contagion models recently proposed by Bo et al.…”

“…We contribute to fill the gap with a model that extends Fokianos et al (2008) within a time-varying coefficient framework. In doing so, we extend the timedependent contagion models recently proposed by Agosto et al (2021), Geir et al (2022), and Roy and Karmakar (2021) with the inclusion of time-varying policy covariates. And we also extend the causal contagion models recently proposed by Bo et al (2021) and Islam et al (2020) with the inclusion of time-varying covariate effects, which also allows to compare alternative time lags of policy measures.…”

Disentangling the effect of measures, variants and vaccines on SARS-CoV-2 Infections in England: A dynamic intensity model

“… 3 The dynamic INGARCH model was also used by Agosto and Giudici (2020), Roy and Karmakar (2021) and Giudici et al (2021) to model COVID-19 infections in U.S and Italy, though without accounting for overdispersion. The first study assumes stationarity and constant parameters, therefore not accounting for NPIs.…”