Determinism test and noise estimate for a complex time series

Abstract

We address the issue of recognizing determinism in a time series. Specifically, we employ the method of singular-value decomposition (SVD) to derive the eigenvalue spectra of the trajectory matrices constructed from a number of scalar time series, mainly white noise and chaotic signals, where a very large embedding dimension is used. The results suggest that the SVD eigenvalue spectrum can be employed as a measure of determinism and an estimate for the strength of a noise contained in the time series can be deduced.