Fractional Integration and Mean Reversion in Stock Prices

The Efficient Market Hypothesis (EMH) is frequently tested by measuring the degree of mean reversion in stock prices, since highly predictable changes might indicate that investors are not fully rational. Existing studies often rely on statistical tests which impose too restrictive assumptions on the time series behaviour of the series of interest, and have very low power. This paper uses a test for unit roots and other nonstationary (and stationary) hypotheses recently developed by Robinson (1994) which allows for fractional alternatives and outperforms rival statistics. Its application to US real stock returns suggests that there is no permanent component in stock prices, since the series examined is close to being I(0). The key question then becomes whether there exists an autocorrelated structure, which would imply that the series is perfectly predictable, and hence that the market might not be efficient.