Dynamical characteristics of global stock markets based on time dependent Tsallis non-extensive statistics and generalized Hurst exponents

We perform non-linear analysis on stock market indices using time-dependent extended Tsallis statistics. Specifically, we evaluate the q-triplet for particular time periods with purpose of demonstrating temporal dependence characteristics underlying dynamics. apply daily close price timeseries four major global markets (S&P 500, Tokyo-NIKKEI, Frankfurt-DAX, London-LSE). For comparison, also compute Generalized Hurst Exponents (GHE) Hq GHE method, thus estimating evolution multiscaling index focus before and after critical events such as bubbles (2000 dot.com bubble, Japanese 1990 2008 US real estate crisis) find that trends values significantly differ among these indicating in rising period a bubble break, statistics dynamics strongly deviates from purely stochastic behavior, whereas, breakdown, it gradually converges to Gaussian-like behavior which is characteristic an efficient market. conclude relative variation patterns can be connected different aspects reveals useful information about conditions especially those development bubble. found specific distinguish just stock-market break. Differences between endogenous exogenous crises are captured by changes q-triplet. Finally, introduce two new empirical metrics (Q-metrics) functions