  Fractal analysis is carried out on the stock market indices of seven European
countries and the US. We find evidence of long range dependence in the log
return series of the Mibtel (Italy) and the PX Glob (Czech Republic). Long
range dependence implies that predictable patterns in the log returns do not
dissipate quickly, and may therefore produce potential arbitrage opportunities.
Therefore, these results are in contravention of the Efficient Market
Hypothesis. We show that correcting for short range dependence, or
prefiltering, may dispose of genuine long range dependence, suggesting that the
market is efficient in cases when it is not. Prefiltering does not reduce
significantly the power of the tests only for cases for which the Hurst
exponent (a measure of the long range dependence) lies well outside the
boundaries of no long range dependence. For borderline cases, the prefiltering
procedure reduces the power of the test. On the other hand, the absence of
prefiltering does not result in a test that is significantly oversized.
