  We forecast a single time series using a high-dimensional set of predictors.
When these predictors share common underlying dynamics, an approximate latent
factor model provides a powerful characterization of their co-movements
Bai(2003). These latent factors succinctly summarize the data and can also be
used for prediction, alleviating the curse of dimensionality in
high-dimensional prediction exercises, see Stock & Watson (2002a). However,
forecasting using these latent factors suffers from two potential drawbacks.
First, not all pervasive factors among the set of predictors may be relevant,
and using all of them can lead to inefficient forecasts. The second shortcoming
is the assumption of linear dependence of predictors on the underlying factors.
The first issue can be addressed by using some form of supervision, which leads
to the omission of irrelevant information. One example is the three-pass
regression filter proposed by Kelly & Pruitt (2015). We extend their framework
to cases where the form of dependence might be nonlinear by developing a new
estimator, which we refer to as the Kernel Three-Pass Regression Filter
(K3PRF). This alleviates the aforementioned second shortcoming. The estimator
is computationally efficient and performs well empirically. The short-term
performance matches or exceeds that of established models, while the long-term
performance shows significant improvement.
