Long range dependence in G7 stock markets return rates using mutual information and detrended cross-correlation analysis

According to theory, return rates are expected to have no memory, meaning that return rates do not show autocorrelation. Most studies find evidence of absence of linear autocorrelations, although other types of dependence exist. This paper analyzes the existence of long range dependence in G7 stock markets, applying two different methodologies which allow nonlinear behavior of return rates: mutual information and the correlation coefficient calculated from detrended cross-correlation analysis. We apply these methodologies to stock markets, calculating them for the first ten lags of each time series. It is possible to conclude on the existence of nonlinearity and long-term dependence in return rates for the seven indexes studied.