Application of Multiscale entropy analysis to verification of the applicability of Efficient Market Hypothesis

Traditional entropy based algorithms used in the analysis of time series data quantify the regularity of the time series. But there is no straight forward correspondence between regularity and complexity. Neither completely predictable (e.g. periodic) signal, which have minimum entropy, nor completely unpredictable (e.g. uncorrelated random) signals which have maximum entropy, are truly complex, since they can be described very compactly. Entropy increases with disorder, however, an increase in entropy may not always be associated be with increase in dynamic complexity. Thus the traditional algorithms may generate misleading results because the algorithms are based on single time scale .However, the multiscale entropy (MSE) approach measures the complexity of the system taking into account the multiple time scales. This computational tool can be quite effectively used to quantify the complexity of a given time series. In this paper the behavior of Indian stock market index NIFTY is studied using MSE approach and it is shown that the market exhibits different MSE patterns at different level of information received. However this difference in MSE profile disappears when the time scale is increased. Since the complexity of the market changes with information this approach can be used to verify the applicability of Efficient Market Hypothesis(EMH) and to test the time scales above (below) which market behave efficiently( inefficiently).