robust clustering of covariated time series models

In this paper, we develop a mixture of autoregressive (moar) process modelwith time varying and freely indexed covariates under the flexible class of two–piecedistributions using the scale mixtures of normal (tp-smn) family. this novel familyof time series (tp-smn-moar) models was used to examine flexible and robustclustering of reported cases of covid-19 across 313 counties in the u.s. the tp-smndistributions allow for symmetrical/ asymmetrical distributions as well as heavy-taileddistributions providing for flexibility to handle outliers and complex data. developinga suitable hierarchical representation of the tp-smn family enabled the constructionof a pseudo-likelihood function to derive the maximum pseudo-likelihood estimates viaan em-type algorithm.