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

ArXiv ID: 2601.04608 “View on arXiv”

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.

Keywords: Yield Curve Forecasting, Distributionally Robust Optimization, Factor Models, Random Forest, Expected Shortfall

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: 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.

  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"]