Data-driven analysis and monitoring of complex dynamical systems have been gaining popularity due to various reasons like ubiquitous sensing and advanced computation capabilities. A key rationale is that such systems inherently have high dimensionality and feature complex subsystem interactions due to which majority of the first-principle based methods become insufficient. We explore the family of a recently proposed probabilistic graphical modeling technique, called spatiotemporal pattern network (STPN) in order to capture the Granger causal relationships among observations in a dynamical system. We also show that this technique can be used for anomaly detection and root-cause analysis for real-life dynamical systems. In this context, we introduce the notion of Granger-STPN (G-STPN) inspired by the notion of Granger causality and introduce a new nonparametric technique to detect causality among dynamical systems observations. We experimentally validate our framework for detecting anomalies and analyzing root causes in a robotic arm platform and obtain superior results compared to when other causality metrics were used in previous frameworks.