The paper outlines a methodology for analyzing daily stock returns that relinquishes the assumption of global stationarity. Giving up this common working hypothesis reflects our belief that fundamental features of the financial markets are continuously and significantly changing. Our approach approximates the nonstationary data locally by stationary models. The methodology is applied to the S&P 500 series of returns covering a period of over seventy years of market activity. We find most of the dynamics of this time series to be concentrated in shifts of the unconditional variance. The forecasts based on our nonstationary unconditional modeling were found to be superior to those obtained in a stationary long-memory framework and to those based on a stationary Garch(1, 1) data-generating process.

We give the theoretical basis of a possible explanation for two stylized facts observed in long log-return series: the long-range dependence (LRD) in volatility and the integrated GARCH (IGARCH). Both these effects can be explained theoretically if one assumes that the data are nonstationary.