Finite mixture model of hidden Markov regression with covariate dependence

In recent days, a combination of finite mixture model (FMM) and hidden Markov model (HMM) is becoming popular for partitioning heterogeneous temporal data into homogeneous groups (clusters) with homogeneous time points (regimes). The regression mixtures commonly considered in this approach can also accommodate for covariates present in data. The classical fixed covariate approach, however, may not always serve as a reasonable assumption as it is incapable of accounting for the contribution of covariates in cluster formation. This paper introduces a novel approach for detecting clusters and regimes in time series data in the presence of random covariates. The computational challenges related to the proposed model has been discussed, and several simulation studies are performed. An application to United States COVID-19 data yields meaningful clusters and regimes.