Affiliations: [a] Laboratorium voor Neuro- en Psychofysiologie, K.U.Leuven, Campus Gasthuisberg, Herestraat 49 B-3000 Leuven, Belgium | [b] Department of Electrical and Electronic Engineering, Imperial College of Science, Technology and Medicine, Exhibition Road, SW7 2BT, London, UK
Abstract: Although the emergence of multivariate signals in natural sciences and engineering has emphasised the problem of signal representation, that is, whether signals are by their nature a set of independent observations or multidimensional vectorial quantities, little research has been conducted on detecting the true nature of such signals. It remains unclear, therefore, when the complex-valued approach is to be preferred over the bivariate one, thus, clearly indicating the need for a criterion that addresses this issue. To this cause, we propose a nonparametric statistical test, based on the local predictability in the complex-valued phase space, which discriminates between the bivariate and complex-valued nature of time series. This is achieved in the well-established surrogate data framework. Results on both benchmark and real-world IPIX radar data support the approach.
