Abstract: This paper describes the dynamics of daily new cases arising from the Covid-19 pandemic using a long-range dependent model. A new long memory model, LFIGX (Log-linear zero-inflated generalized Poisson integer-valued Fractionally Integrated GARCH process with eXogenous covariates), is proposed to account for count time series data with a long-run dependent effect. It provides a novel unified framework for integer-valued processes with serial and long-range dependence (positive or negative), over-dispersion, zero-inflation, nonlinearity, and exogenous variable effects. We adopt an adaptive Bayesian Markov Chain Monte Carlo (MCMC) sampling scheme for parameter estimation. This new modeling is applied to the daily new confirmed cases of the Covid-19 pandemic in six countries including Japan, Vietnam, Italy, the United Kingdom, Brazil, and the United States. The LFIGX model provides insightful interpretations of the impacts of policy index and temperature and delivers good forecasting performance for the dynamics of the daily new cases in different countries.

Key words and phrases: Count time series, Covid-19, fractionally integrated INGARCHX, MCMC-based Bayesian, policy effects.