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.

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