Time series chaos detection and assessment via scale dependent Lyapunov Exponent

Abstract

Many dynamical systems in a wide range of disciplines -- such as engineering, economy and biology -- exhibit complex behaviors generated by nonlinear components which might result in deterministic chaos. While in lab--controlled setups its detection and level estimation is in general a doable task, usually the same does not hold for many practical applications. This is because experimental conditions imply facts like low signal--to--noise ratios, small sample sizes and not--repeatability of the experiment, so that the performances of the tools commonly employed for chaos detection can be seriously affected. To tackle this problem, a combined approach based on wavelet and chaos theory is proposed. This is a procedure designed to provide the analyst with qualitative and quantitative information, hopefully conducive to a better understanding of the dynamical system the time series under investigation is generated from. The chaos detector considered is the well known Lyapunov Exponent. A real life application, using the Italian Electric Market price index, is employed to corroborate the validity of the proposed approach.</jats:p>