Hurst exponent dynamics of S&P 500 returns: Implications for market efficiency, long memory, multifractality and financial crises predictability by application of a nonlinear dynamics analysis framework

In this study, we conduct a rolling window approach to wavelet-filtered (denoised) S&P500 returns (2000−2020) to obtain time-varying Hurst exponents. We discuss implications of Hurst exponent dynamics such as the complete invalidity of the efficient market hypothesis (EMH), an explicative rationale for momentum crashes and potentials for crises predictability. We analyse the dynamics of the Hurst exponents by applying a novel nonlinear dynamics analysis framework for non-stationary and nonlinear time series. The latter framework includes statistical tests, a recurrence quantification analysis (RQA), a wavelet multi-resolution analysis (MRA) and a multifractal detrended fluctuation analysis (MFDFA) paired with subsequent multifractal analyses. Besides, we display empirical findings taken out of the academic literature and critically elaborate on the impact of our findings and future prospects. •Rolling window analysis of dynamics of time-varying Hurst exponents conducted.•Total invalidity of efficient markets hypothesis (EMH) shown.•Rationale for momentum crashes and potential crises predictions stated.•Multifractal and power-law analyses for Hurst exponents implemented.•Nonlinear dynamics analysis framework proposed.