How long is the memory of the US stock market?

The Efficient Market Hypothesis (EMH), one of the most important hypothesis in financial economics, argues that return rates have no memory (correlation) which implies that agents cannot make abnormal profits in financial markets, due to the possibility of arbitrage operations. With return rates for the US stock market, we corroborate the fact that with a linear approach, return rates do not show evidence of correlation. However, linear approaches might not be complete or global, since return rates could suffer from nonlinearities. Using detrended cross-correlation analysis and its correlation coefficient, a methodology which analyzes long-range behavior between series, we show that the long-range correlation of return rates only ends in the 149th lag, which corresponds to about seven months. Does this result undermine the EMH?