A Novel Method for Determining the Nature of Time Series

Abstract

The delay vector variance (DVV) method, which analyzes the nature of a time series with respect to the prevalence of deterministic or stochastic components, is introduced. Due to the standardization within the DVV method, it is possible both to statistically test for the presence of nonlinearities in a time series, and to visually inspect the results in a DVV scatter diagram. This approach is convenient for interpretation as it conveys information about the linear or nonlinear nature, as well as about the prevalence of deterministic or stochastic components in the time series, thus unifying the existing approaches which deal either with only deterministic versus stochastic, or the linear versus nonlinear aspect. The results on biomedical time series, namely heart rate variability (HRV) and functional Magnetic Resonance Imaging (fMRI) time series, illustrate the applicability of the proposed DVV-method.