Rescaled Range (R/S) of returns of Bulgarian Stock Exchange index SOFIX and Bucharest Stock Exchange index BET

Rescaled Range analysis of the Bulgarian stock exchange index SOFIX and Bucharest stock exchange index BET for the period November 2010-August 2013 (daily observations) reveals that SOFIX return shows characteristics of long memory, while BET return is closer to random walk. Long memory feature contradicts efficient market hypothesis. When return series show long memory characteristics, it means the returns are not independent over time, ie past returns can help predict future returns, thereby violating the market efficiency hypothesis. Briefly, Rescaled Range calculates Hurst exponent (H exponent), which has the following values: H<0.5 is mean reverting characteristics of the return series, while H=0.5 is random walk and H>0.5 is long memory (persistence area). We can however divide the interval 0.0 to 1.0 into thirds, ie from 0-0.33 is the mean-reverting area, 0.34-0.67 is the random walk area and 0.68-1.0 is the persistence area. In the case of SOFIX Hurst exponent is 0.73 and for the same period the Hurst exponent of BET is 0.58. It should however be noted that during the different time frames, the indexes characteristics change - SOFIX return was random walk at some point of time and BET return was persistent. There are of course other indicators of long memory (as GPH, KPSS for instance); additionally the time period considered is short. The idea is just to show some insight. The analysis follows Jason Voss publication on S&P 500 in Enterprising Investor blog in Feb 2013.