Wavelet based sample entropy analysis: A new method to test weak form market efficiency

In this article, we analyze informational efficiency in daily returns of NASDAQ, DJIA and S&P 500 indices ranging from 04-01-1980 to 12-09-2013.We replace the traditional coarse graining method used in multi-scale entropy analysis by a Maximal Overlap Discreet Wavelet Transform decomposition and extract Sample entropy measure across different timescales. To compare against efficient market behavior, we simulate an i.i.d. normal series with the same mean and variance of the underlying series and repeat the procedure. Next, we plot both of these estimates to see how the values differ from each other across the scales. It is found that the three markets under study are not weak form efficient at high to medium frequencies (up to semi-annual period). They are informationally efficient in the long run (annual-biannual period). Here, efficiency of a financial market is closely related with the time horizons under which the agents operate. As time horizon increases, the markets move towards an informationally efficient state. It could be due to the fact that agents with a long investment horizon make use of the information set available in a comparatively efficient manner due to their comparatively high tolerance for price fluctuations as opposed to their high-frequency counterparts.