A novel high-order multivariate Markov model for spatiotemporal analysis with application to COVID-19 outbreak

We propose a new strategy for analyzing the evolution of random phenomena over time and space simultaneously based on the high-order multivariate Markov chains. We develop a novel Markov model of order [Formula: see text] for [Formula: see text] chains consisting of [Formula: see text] possible states to gather parsimony with realism. It can capture negative and positive associations among the chains with only a reduced number of parameters, [Formula: see text] , remarkably lower than [Formula: see text] required for the full parameterized model. Our model privileges are enhanced by a Monte Carlo simulation experiment, besides application to analyze the spatial–temporal dynamics for the risk level of a recently global pandemic (COVID-19) outbreak in world health organization (WHO) regions for predicting the risk state of epidemiological prevalence and monitoring infection control.