Identification of Direction of Time in Vector Autoregressive Systems Using PC Algorithm

In this paper we study whether it is possible to identify the direction of time in vector autoregressive processes. We prove a result regarding time reversibility of such systems and propose an algorithm to identify the direction of time when the system is not reversible. We first show that it is possible to utilize the PC-algorithm to identify the directed acyclic graph corresponding to a vector autoregressive process. The identified directed acyclic graph is then used to determine the direction of time. We test our proposed algorithm both on simulated data and real data consisting of EEG recordings.