Granger causality based on vector time series and quaternion algebra with possible applications to molecular dynamics data analysis.

Causal analysis plays a significant role in physics, chemistry, and biology. Dynamics of complex (bio)molecular and nanosystems, from the microscopic to the macroscopic scale, are characterized by time-dependent vectors such as positions, forces, momenta, angular momenta, or torques. Identification and analysis of causal relationships between these time-dependent signals is an important problem in the multidimensional time-series analysis and is of great practical importance in describing the properties of such dynamical systems, and to understanding their functionality.