Forecasting Macroeconomic Variables With High‐Frequency Predictors: A Supervised Nonlinear Mixed‐Frequency Factor Approach

ABSTRACT This study develops a forecasting framework that improves the signal extraction ability of traditional methods when high‐frequency monthly predictors are used to forecast low‐frequency quarterly macroeconomic variables by modelling nonlinear relationships between predictors and the target variable. Conventional approaches to extracting information from high‐frequency predictors suffer from two major limitations. First, not all common factors extracted from the predictor set contain predictive information for the target variable, and retaining the full factor set may introduce noise, thereby reducing forecasting efficiency. Second, existing standard methods typically impose linear relationships between predictors and latent factors. The first limitation can be addressed by incorporating supervised information extraction mechanisms, as exemplified by the mixed‐frequency three‐pass regression filter (3PRF). Building on this framework, this paper further extends the methodology by proposing a new estimator that allows for latent nonlinear dependence structures—the mixed‐frequency kernel 3PRF (MF‐K3PRF)—thereby effectively overcoming the second limitation. The MF‐K3PRF estimator captures nonlinear relationships between predictors and the target variable through kernel mappings while maintaining high computational efficiency. We establish the predictive consistency of the estimator as both the time series sample size and the cross‐sectional dimension increase. The simulation results demonstrate that compared with existing methods, the MF‐K3PRF has superior finite‐sample performance. Finally, we demonstrate the superiority of the MF‐K3PRF in forecasting quarterly macroeconomic variables using high‐frequency monthly data through a series of empirical applications.