Kernel Three Pass Regression Filter

ArXiv ID: 2405.07292 “View on arXiv”

Authors: Unknown

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.

Keywords: factor models, time series forecasting, kernel methods, dimensionality reduction, latent factors

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper presents advanced mathematical concepts including kernel methods, feature space transformation, and stochastic order notation, indicating high mathematical complexity. It also includes empirical performance claims against established models and mentions computational efficiency, suggesting strong data and implementation focus.

  flowchart TD
    A["Research Goal:<br>Forecast single time series<br>using high-dimensional predictors"] --> B["Data Inputs:<br>Y Target & X Predictors<br>shared latent dynamics"]
    B --> C["Methodology: Kernel 3-Pass<br>Regression Filter K3PRF<br>extends linear factor models"]
    C --> D["Computational Process:<br>1. Extract latent factors<br>2. Apply kernel methods for nonlinearity<br>3. Supervised regression filter"]
    D --> E["Key Findings/Outcomes:<br>Efficient dimensionality reduction<br>Superior long-term forecasts<br>Matches/exceeds short-term performance"]