The delay vector variance method for detecting determinism and nonlinearity in time series

Abstract

A novel ‘delay vector variance’ (DVV) method for detecting the presence of determinism and nonlinearity in a time series is introduced. The method is based upon the examination of local predictability of a signal. Additionally, it spans the complete range of local linear models due to the standardisation to the distribution of pairwise distances between delay vectors. This provides consistent and easy-to-interpret diagrams, which convey information about the nature of a time series. In order to gain further insight into the technique, a DVV scatter diagram is introduced, which plots the DVV curve against that for a globally linear model (surrogate data). This way, the deviation from the bisector line represents a qualitative measure of nonlinearity, which can be used additionally for constructing a quantitative measure for statistical testing. The proposed method is compared to existing methods on synthetic, as well as standard real-world signals, and is shown to provide more consistent results overall, compared to other, established nonlinearity analysis methods.