Are US stock prices mean reverting? Some new tests using fractional integration models with overlapping data and structural breaks

Using recently developed econometric models of fractional integration with overlapping data, this study examines the time series properties of real monthly U.S. stock returns over the period 1871-2003. Using 1-month and overlapping, long-horizon stock returns of 12, 24, and 36 months, we find that real U.S. stock returns are covariance stationary for this period before and after allowing for the presence of structural breaks. Our results imply that the permanent (random walk) component of stock prices overwhelms any temporary (mean reverting) component, producing a fractional d-value for returns indistinguishable from zero. We highlight the limitations of standard ACF models of overlapping returns, and suggest that the previously observed pattern of increasingly negative autocorrelations is largely an artifact of short-term ARMA dynamics. We confirm the result of Souza (J Time Ser Anal 28:701-722, 2007) that, holding the bandwidth constant, overlapping (and nonoverlapping) temporal aggregation should not affect semiparametric, frequency domain d-estimates such as the GPH and feasible exact local Whittle.