Delay Vector Variance method for real and complex signals

The Delay vector variance (DVV) method uses predictability of the signal in phase space to characterize the time series. Using the surrogate data methodology, so called DVV plots and DVV scatter diagrams can be generated using the DVV method, as a test statistic, to examine the determinism/stochastisity and linearity/nonlinearity within a signal simultaneously. In DVV scatter diagram, the target variance values of the original signal is plotted against the averaged variance values, calculated over a number of iAAFT surrogates. As a result, for linear signals, the scatter diagram coincides with the bisector line and conversely for nonlinear signals, the scatter diagram deviates from bisector lineas shown in the attached document. The DVV method has been successfully applied to analyse the nature of biometric signals (EEG and fMRI).

Further Reading + References

T. Gautama, D.P. Mandic, and M. M. Van Hulle, "The delay vector variance method for detecting determinism and nonlinearity in time series," Physica D, vol. 190, no. 3-4, pp. 167-176, 2004. [pdf]