An Integrated Modeling Framework for Multivariate Poisson Process with Temporal and Spatial Correlations

Multivariate Poisson (MP) counts are common in the course of manufacturing and service process. It is significant to monitor the MP counts and judge whether the process is in control or not. Most of the previous researches assumed that the variables of each univariate Poisson process are independent. Taking the temporal and spatial correlations into account, this article proposes an integrated model based on copula model and autoregressive (AR) process. Furthermore, the inference functions for margins (IFM) method and the expectation maximization (EM) algorithm accompanied by sequential importance resampling (SIR) method, provide satisfactory estimators in the proposed model.