Effective Model Complexity in Equity-Premium Forecasting

This article is concerned with the concept of model complexity in macro-financial return prediction, emphasizing the distinction between nominal dimensionality and meaningful forecasting flexibility. Using the Goyal–Welch macro-financial predictors in a rolling out-of-sample equity-premium forecasting design, the article compares regularized linear models, Random Fourier Feature ridge regressions, and exact Gaussian Radial Basis Function kernel ridge regressions. The results show that raw feature count is an incomplete measure of model complexity. Economically relevant complexity is shaped by feature geometry, kernel bandwidth, sample size, spectral concentration, and regularization strength. Spectral diagnostics reveal that nonlinear feature maps can redistribute variance across many directions, but an expanded geometry is not sufficient for better forecasting performance; any benefit depends on whether the induced directions are stable, regularized, and aligned with persistent predictive structure. Furthermore, given the monthly frequency of the data, exact kernel ridge regression is preferable to Random Fourier Features as a nonlinear benchmark: With a total number of samples of order 10³ and rolling training windows smaller still, exact kernel systems are typically feasible to solve directly while avoiding the approximation noise introduced by finite random-feature expansions. Regularized linear models also remain competitive, reflecting the low signal-to-noise ratio of aggregate return prediction. The practical question is therefore not whether more complex models are inherently better but when additional representational capacity converts the existing predictor information into usable forecasting directions rather than unstable nominal dimensionality.