Time-varying Hurst–Hölder exponents and the dynamics of (in)efficiency in stock markets

Abstract The increasing empirical evidence against the paradigm that stock markets behave efficiently suggests to relax the too restrictive dichotomy between efficient and inefficient markets. Starting from the idea that financial prices evolve in a continuum of equilibria and disequilibria, we use the Hurst–Holder exponent to quantify the pointwise degree of (in)efficiency and introduce the notion of α -efficiency. We then define and study the properties of two functions which are used to build indicators providing timely information about the market efficiency. We apply our tools to the analysis of four stock indexes representative of U.S., Europe and Asia.