ABSTRACT
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 r for m chains consisting of s possible states to gather parsimony with realism. It can capture negative and positive associations among the chains with only a reduced number of parameters, rm2s2+2, remarkably lower than msrm+1 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.