Kernel Three Pass Regression Filter

TL;DR

This paper introduces the Kernel Three-Pass Regression Filter (K3PRF), a new efficient estimator that captures nonlinear relationships in high-dimensional time series forecasting, improving both short-term and long-term prediction accuracy.

Contribution

It extends the three-pass regression filter to nonlinear settings using kernel methods, enhancing forecasting efficiency and accuracy in high-dimensional data.

Findings

Performs comparably or better than existing models in short-term forecasts.

Shows significant improvements in long-term forecasting accuracy.

Computationally efficient for high-dimensional data.

Abstract

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.