Paper: arXiv 2405.07292

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.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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"]

Cited References (32)

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  2. Forecasting economic time series using targeted predictors (2008)
  3. Sufficient forecasting using factor models (2017)
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  5. The kernel trick for nonlinear factor modeling (2022)
  6. Forecasting using principal components from a large number of predictors (2002)
  7. Inferential theory for factor models of large dimensions (2003)
  8. Reducing the dimensionality of data with neural networks (2006)
and 24 more
  1. Empirical asset pricing via machine learning (2020)
  2. Kernel Methods in Machine Learning (2008)
  3. Principal components, sufficient dimension reduction, and envelopes (2018)
  4. Sufficient dimension reduction: Methods and applications with R (2018)
  5. High-dimensional statistics: A non-asymptotic viewpoint (2019)
  6. Nonlinear forecasting with many predictors using kernel ridge regression (2016)
  7. The kernel trick for nonlinear factor modeling (2022)
  8. Eigenvalue ratio test for the number of factors (2013)
  9. Are latent factor regression and sparse regression adequate? (2023)
  10. Forecasting economic time series using supervised factors and idiosyncratic elements (2024)
  11. Approximate factor models with weaker loadings (2023)
  12. Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets (1983)
  13. Spurious factor analysis (2021)
  14. Principal Component Analysis for Nonstationary Series (2024)
  15. Sufficient forecasting using factor models (2017)
  16. Econometrics of Machine Learning Methods in Economic Forecasting (2023) — link
  17. How is machine learning useful for macroeconomic forecasting? (2022)
  18. Forecasting using supervised factor models (2019)
  19. Scaled PCA: A new approach to dimension reduction (2022)
  20. The Arbitrage Theory of Capital Asset Pricing (1976)
  21. Macroeconomic forecasting using diffusion indexes (2002)
  22. Forecasting financial and macroeconomic variables using data reduction methods: New empirical evidence (2014)
  23. Confidence intervals for diffusion index forecasts and inference for factor-augmented regressions (2006)
  24. Inflation and unemployment forecasting with genetic support vector regression (2014)

0 of 32 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.