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.

The relationships between accounting earnings and stock prices, as well as between unexpected earnings and returns, have received substantial attention in the empirical literature. Several theoretical models predict the shapes of these relationships. However, a comprehensive empirical description that could be used to evaluate these predictions is lacking. By integrating recent advances in statistics and machine learning with findings in the accounting literature, we develop an empirical method to identify the relationships, which is consistent with the firm-specific and nonlinear features of the theoretical models. Our approach provides a clear description of stylized and robust patterns in the relationships that are relevant to distinguish between existing models and to aid future theory development. The findings are consistent with recently proposed dynamic option models for both the earnings-price and unexpected earnings-returns relationships. Data availability: Data are available from the public sources cited in the text. A summary of the R code used in the article is available in Starica and Marton (2024).