Chaos Detection in Economic Time Series: Metric versus Topological Tools

From an empirical point of view, it is difficult to distinguish between fluctuations provoked by random shocks and endogenous fluctuations determined by the nonlinear nature of the relation between economic aggregates. For this purpose, chaos tests are developed to investigate the chaotic phenomena of basic features: nonlinearity, fractal attractor, and sensitivity to initial conditions. The application of these tests to economic and financial time series produced controversial results. Investigators found substantial evidence for nonlinearity but relatively weak evidence for chaos per se. The aim of the paper is twofold. In the first place, to compare the different techniques with which to analyse chaotic time series highlighting their potentiality and limitations. Secondly, to apply in an empirical exercise a topological tool - Recurrence Analysis - using data already analysed with metric tests in order to show whether the result of this analysis could change if performed with tools more appropriate for discovering chaos in short and noisy time series.