  Factor modeling is a powerful statistical technique that permits to capture
the common dynamics in a large panel of data with a few latent variables, or
factors, thus alleviating the curse of dimensionality. Despite its popularity
and widespread use for various applications ranging from genomics to finance,
this methodology has predominantly remained linear. This study estimates
factors nonlinearly through the kernel method, which allows flexible
nonlinearities while still avoiding the curse of dimensionality. We focus on
factor-augmented forecasting of a single time series in a high-dimensional
setting, known as diffusion index forecasting in macroeconomics literature. Our
main contribution is twofold. First, we show that the proposed estimator is
consistent and it nests linear PCA estimator as well as some nonlinear
estimators introduced in the literature as specific examples. Second, our
empirical application to a classical macroeconomic dataset demonstrates that
this approach can offer substantial advantages over mainstream methods.
