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

Mohsen Maleki; Hamid Bidram; Darren Wraith

doi:10.1080/02664763.2021.2019688

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

J Appl Stat. 2022 Jan 1;50(11-12):2648-2662. doi: 10.1080/02664763.2021.2019688. eCollection 2023.

Authors

Mohsen Maleki¹, Hamid Bidram¹, Darren Wraith²

Affiliations

¹ Department of Statistics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, Iran.
² School of Public Health & Social Work and Centre for Data Science, Queensland University of Technology (QUT), Brisbane, Australia.

Abstract

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.

Keywords: EM-algorithm; covariates; mixture of autoregressive models; model-based clustering; scale mixtures of normal distributions; two-piece distributions.