Researchers have constantly asked whether stock returns can be predicted by some macroeconomic data. However, it is known that macroeconomic data may exhibit nonstationarity and/or heavy tails, which complicates existing testing procedures for predictability. In this paper we propose novel empirical likelihood methods based on some weighted score equations to test whether the monthly CRSP value-weighted index can be predicted by the log dividend-price ratio or the log earnings-price ratio. The new methods work well both theoretically and empirically regardless of the predicting variables being stationary or nonstationary or having an infinite variance.
"Predictive regressions for macroeconomic data." Ann. Appl. Stat. 8 (1) 577 - 594, March 2014. https://doi.org/10.1214/13-AOAS708