Estimating the Maximum Lyapunov Exponent with Denoised Data to Test for Chaos in the German Stock Market

BenSaïda and Litimi (Chaos Solitions Fractals 54:90–95, 2013) suggest testing for deterministic chaos in a noisy time series context via neural networks, by choosing the parameters combination, from a given set, that maximizes the estimated Lyapunov exponent. First, we show that this strategy may dramatically reduce the power of the chaos test, compared to the more conservative approach of choosing the parameters combination that minimizes the Bayesian Information Criterion (BIC). Next, once selected the parameters combination that controls for size and power, we compare the results achieved on the German individual stock market returns with the 0–1 test to those achieved computing the maximum Lyauponov computed with wavelet-denoised data. The results are compatible with deterministic chaos in individual stock returns. Additional evidence in alternative indices and time periods is found.