This paper examines the long-run dynamics and the cyclical structure of the US stock market using fractional integration techniques, specifically a version of the tests of Robinson (1994a) which allows for unit (or fractional) roots both at the zero (long-run) and at the cyclical frequencies. We consider inflation, real risk-free rate, real stock returns, equity premium and price/dividend ratio, annually from 1871 to 1993. When focusing exclusively on the long-run frequency, the estimated order of integration varies considerably, but nonstationarity is found only for the price/dividend ratio. When the cyclical component is also taken into account, most series appear to be stationary and to exhibit long memory. Further, mean reversion occurs. Finally, the fractional (at zero and cyclical) models are shown to forecast more accurately than rival ones based on fractional and integer differentiation exclusively at the zero frequency.
stock market fractional cycles long memory Gegenbauer processes