A Non - Parametric Test for Detecting theComplex - Valued Nature of Time

The emergence of complex-valued signals in natural sciences and engineering has been highlighted in the open literature, and in cases where the signals have complex-valued representations, the complex-valued approach is likely to exhibit advantages over the more convenient real-valued bivariate one. It remains unclear, however, whether and when the complex-valued approach should be preferred over the bivariate one, thus, clearly indicating the need for a criterion that addresses this issue. To this cause, we propose a statistical test, based on the local predictability in the complex-valued phase space, which discriminates between the bivariate or complex-valued nature of time series. This is achieved in the well-established surrogate data framework. Results on bothe the bec-nhmark and real-work IPIX complex radar data support the approach.