Process Control for the Vector Autoregressive Model

Multivariate monitoring techniques for serially correlated observations have been widely used in various applications. This study examines several issues that have arisen in relation to the statistical quality control for the vector autoregressive (VAR) model, using a Monte Carlo approach. Different versions of the Hotelling T² statistic and control limits to monitor the VAR-type process for both Phase I and Phase II schemes can be specified for different sample sizes and configurations of the model. Our simulation study suggests that the Hotelling's T² statistic can be tested against the χ² critical values during Phase I, but should be tested against scaled F critical values during Phase II. An unbiased covariance estimate of residuals is also recommended during Phase II when sample size is typically small. By reanalyzing some real data examples, the authors offer new conclusions.