Under-reported time-varying MINAR(1) process for modeling multivariate count series

A time-varying multivariate integer-valued autoregressive of order one (tvMINAR(1)) model is introduced for the non-stationary time series of correlated counts when under-reporting is likely present. A non-diagonal autoregression probability network is structured to preserve the cross-correlation of multivariate series, provide a necessary condition to ease model-fittings computations, and derive the full likelihood using the Viterbi algorithm. The motivating construction applies to fully under-reported counts that rely on a mixture presentation of the random thinning operator. Simulation studies are conducted to examine the proposed model, and the analysis of COVID-19 daily cases is accomplished to highlight its usefulness in applications. Finally, the comparison of models is presented using the posterior predictive checking method.