Momentum, the strategy of capitalizing on the ongoing trend in the stock price movements, has been one of the most puzzling market anomalies in modern finance. This paper seeks to exploit the momentum profitability from the perspective of the excursion patterns in the stock price movements. A theoretical framework is developed for momentum strategy analysis and the long memory process in the financial markets. To test the null hypothesis of the Random Walk Hypothesis and the Efficient Market Hypothesis, we employ the Hurst exponent to detect the long-term memory existed in the stock return series. A time series with 0 < H < 0.5 shows negative correlations between points and a mean-reverting behavior, while a series with 0.5 < H < 1 indicates positive correlations and a long memory process. Basic momentum strategies are further applied to the past stock price data, and the back testing results show that there is a U-shaped relationship between the strategy returns and Hurst exponent. This paper also builds on earlier model of a rule-based naïve trading strategy using Hurst exponent as a signal. The strategy generates remarkably higher profitability compared with the benchmark returns. These findings provide new evidence against the random walk assumption and present challenges to a number of rational asset pricing theories.   ii