k-NN Estimation of Directed Information

Detection and estimation of causality relationships between two random processes is a fundamental problem in many natural and social sciences [1]. This task is in particular challenging as in many real-life scenarios one does not have a good underlying statistical model for the considered process, e.g., in the fields of neuroscience, financial markets, meteorology, etc. For such scenarios it is desirable to use a non-parametric estimator for the causal influence between two observed timeseries. This report discusses estimation of directed information (DI) [2, 3] as a measure of causal influence between two continuous-amplitude time series, when an underlying statistical model for the observed time-series is not available. When estimating statistical functionals it is common to assume that the underlying process are stationary and ergodic. In the rest of this report we build upon these assumptions without verifying their validity.