Are Financial Markets Stochastic: A Test for Noisy Chaos

As opposed to stochastic dynamics, recent studies suggested that financial markets might be governed by chaotic dynamics. Models that tried to explain market behavior are based on the stochastic hypothesis, which is observed when adding the perturbation error. However, stochastic models provide poor forecasts of the market, so far, which raises the question about the validity of the stochastic hypothesis. This paper presents a practical framework to test chaotic dynamics even for noisy systems as opposed to stochastic dynamics. It elaborates an easy-to-use and comprehensive algorithm to build a program to test chaos based on theoretical studies. Monte-Carlo simulations have confirmed that this test is powerful in detecting chaotic dynamics. The applications have confirmed that stock index returns S&P 500, Nikkei 225 and CAC 40 are stochastic and not chaotic