Quantifying the randomness of the stock markets

Randomness has been mathematically defined and quantified in time series using algorithms such as Approximate Entropy (ApEn). Even though ApEn is independent of any model and can be used with any time series, as the markets have different statistical values, it cannot be applied directly to make comparisons between series of financial data. In this paper, we develop further the use of Approximate Entropy to quantify the existence of patterns in evolving data series, defining a measure to allow comparisons between time series and epochs using a maximum entropy approach. We apply the methodology to the stock markets as an example of its application, showing that the number of patterns changed for the six analyzed markets depending on the economic situation, in agreement with the Adaptive Markets Hypothesis.