Independent Component Analysis With Heavy Tails Using Distance Covariance

Independent Component Analysis (ICA) is a popular tool used for blind source separation and has found application in fields such as financial time series, signal processing, feature extraction, and brain imaging. Inspired by modeling a macroeconomic time series that has components with heavy tails, we consider the ICA problem with an infinite variance source. Many of the ICA procedures require the existence of a finite second or even fourth moment. Distance covariance is a measure of dependence that has become an increasingly popular choice as an objective function in the ICA setting. Unfortunately, the standard weight function used in distance covariance requires a finite variance assumption when applied in the ICA framework. The objective of this paper is to derive consistency when using the distance covariance applied to the infinite variance case. Extensions to the ICA model with noise, which has a direct application to time series models when testing independence of residuals based on their estimated counterparts, are also considered.