Long Term Mean Reversion of Stock Prices Based on Fractional Integration

Abstract

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.

Keywords: mean reversion, stock price model, fractional integration, market inefficiency