Robust clustering of COVID-19 cases across U.S. counties using mixtures of asymmetric time series models with time varying and freely indexed covariates

In this paper, we develop a mixture of autoregressive (MoAR) process model with time varying and freely indexed covariates under the flexible class of two-piece distributions using the scale mixtures of normal (TP-SMN) family. This novel family of time series (TP-SMN-MoAR) models was used to examine flexible and robust clustering of reported cases of Covid-19 across 313 counties in the U.S. The TP-SMN distributions allow for symmetrical/ asymmetrical distributions as well as heavy-tailed distributions providing for flexibility to handle outliers and complex data. Developing a suitable hierarchical representation of the TP-SMN family enabled the construction of a pseudo-likelihood function to derive the maximum pseudo-likelihood estimates via an EM-type algorithm.