Multivariate statistical process monitoring (MSPM) has received a considerable amount of attention in terms of both academic research and industrial applications. Most of these efforts have been focused on fault detection and isolation, while root cause diagnosis has not yet been fully addressed. In recent years, data-driven causality analysis methods have been adopted in order to understand the faults triggering the alarms. Among them, the Granger causality (G-causality) test is complex relationship between process variables and to identify the causes of the a popular method of inferring causal associations between signals based on temporal precedence. Nevertheless, the conventional G-causality test applies only to stationary and linear time series. Additionally, it determines the relationships between the variable pairs and is not suited to multivariate cases. In this study, the use of statistical tests is proposed in order to assess whether the time series are nonstationary or nonlinear. For significant nonstationary or nonlinear signals, the Gaussian process regression (GPR) approach is integrated into the framework of the multivariate G-causality test in order to better indicate the causal relationships between the candidate process variables. The feasibility of the proposed scheme for root cause diagnosis is illustrated through case studies.