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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.
A general class of time-varying regression models is considered in this paper. We estimate the regression coefficients by using local linear M-estimation. For these estimators, weak Bahadur representations are obtained and are used to construct simul
The meningitis belt is a region in sub-Saharan Africa where annual outbreaks of meningitis occur, with large epidemics observed cyclically. While we know that meningitis is heavily dependent on seasonal trends (in particular, weather), the exact path
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Many existing mortality models follow the framework of classical factor models, such as the Lee-Carter model and its variants. Latent common factors in factor models are defined as time-related mortality indices (such as $kappa_t$ in the Lee-Carter m
We propose a nonparametric method to explicitly model and represent the derivatives of smooth underlying trajectories for longitudinal data. This representation is based on a direct Karhunen--Lo`eve expansion of the unobserved derivatives and leads t