Forecasting the U.S. Treasury Yield Curve: A Distributionally Robust Machine Learning Approach

Paper: arXiv 2601.04608

Authors: Jinjun Liu, Ming-Yen Cheng

Abstract

We study U.S. Treasury yield curve forecasting under distributional uncertainty and recast forecasting as an operations research and managerial decision problem. Rather than minimizing average forecast error, the forecaster selects a decision rule that minimizes worst case expected loss over an ambiguity set of forecast error distributions. To this end, we propose a distributionally robust ensemble forecasting framework that integrates parametric factor models with high dimensional nonparametric machine learning models through adaptive forecast combinations. The framework consists of three machine learning components. First, a rolling window Factor Augmented Dynamic Nelson Siegel model captures level, slope, and curvature dynamics using principal components extracted from economic indicators. Second, Random Forest models capture nonlinear interactions among macro financial drivers and lagged Treasury yields. Third, distributionally robust forecast combination schemes aggregate heterogeneous forecasts under moment uncertainty, penalizing downside tail risk via expected shortfall and stabilizing second moment estimation through ridge regularized covariance matrices. The severity of the worst case criterion is adjustable, allowing the forecaster to regulate the trade off between robustness and statistical efficiency. Using monthly data, we evaluate out of sample forecasts across maturities and horizons from one to twelve months ahead. Adaptive combinations deliver superior performance at short horizons, while Random Forest forecasts dominate at longer horizons. Extensions to global sovereign bond yields confirm the stability and generalizability of the proposed framework.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematical concepts like distributionally robust optimization, moment-based ambiguity sets, and expected shortfall, indicating high math complexity. It also details a comprehensive empirical study with monthly data from 2006-2025, out-of-sample testing across multiple horizons, and extension to global sovereign bond yields, demonstrating substantial data and implementation rigor.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Forecast Treasury Yields<br>under Distributional Uncertainty"] --> B["Data Inputs:<br>Monthly U.S. Treasury Yields<br>Macroeconomic Indicators"]
  B --> C["Methodology:<br>1. Rolling Factor Augmented<br>Dynamic Nelson Siegel Model<br>2. Random Forest Model"]
  C --> D["Distributionally Robust<br>Forecast Combination:<br>Minimizes Worst-case Expected Loss<br>Adaptive Weights & Ridge Covariance"]
  D --> E["Computational Process:<br>Out-of-Sample Evaluation<br>1-12 Month Horizons"]
  E --> F{"Key Findings/Outcomes"}
  F --> G["Short Horizons: Adaptive<br>Combination Dominates"]
  F --> H["Long Horizons: Random Forest<br>Dominates"]
  F --> I["Generalizability: Robust<br>Performance on Global Bonds"]

Cited References (35)

1. Parsimonious Modeling of Yield Curves (1987)
2. Forecasting the Term Structure of Government Bond Yields (2006)
3. A Dynamic N elson– S iegel Model with Forward-Looking Macroeconomic Factors for the Yield Curve in the US (2019) — link
4. Random Forests (2001)
5. The Limited Virtue of Complexity in a Noisy World (2025)
6. Predicting the Yield Curve Using Forecast Combinations (2016) — link
7. Improved Methods of Combining Forecasts (1984)
8. Thick Modeling (2004)

0 of 35 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.