In this study we examine the long term behavior of stock returns. The analysis reveals that negative autocorrelations of the returns exist for a super-long horizon as long as 10 years. This pattern, however, contrasts to predictions of previous stock price models which include random walks. We suggest the introduction of a fractionally integrated process into a nonstationary component of stock prices, and demonstrate empirically the existence of the process in NYSE stock returns. The predicted values of autocorrelation from our stock price model confirm the super-long term behavior of the returns observed in regression, indicating that inefficiency in the stock market could remain for a long time.