A Quantile Nelson-Siegel model

2024-01-18

AI Summary

Traditional yield curve models—such as Nelson–Siegel—capture only the conditional mean, neglecting tail risk and distributional heterogeneity. Method: We propose a dynamic three-factor quantile regression model, the first to systematically embed quantile regression within the Nelson–Siegel framework, enabling joint modeling and forecasting of the entire conditional yield curve distribution—particularly at extreme quantiles. Our approach integrates dynamic factor structure, quantile regression, and Bayesian inference, and is empirically validated on U.S. Treasury data since the 1970s. Contribution/Results: We document significant quantile-specific heterogeneity in the effects of financial and macroeconomic variables; the Great Recession induced substantially stronger and more persistent shocks to the term structure than the COVID-19 pandemic. The model markedly improves predictive accuracy in the distributional tails and offers a novel interpretive lens for interest rate dynamics during crises.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

A widespread approach to modelling the interaction between macroeconomic variables and the yield curve relies on three latent factors usually interpreted as the level, slope, and curvature (Diebold et al., 2006). This approach is inherently focused on the conditional mean of the yields and postulates a dynamic linear model where the latent factors smoothly change over time. However, periods of deep crisis, such as the Great Recession and the recent pandemic, have highlighted the importance of statistical models that account for asymmetric shocks and are able to forecast the tails of a variable's distribution. A new version of the dynamic three-factor model is proposed to address this issue based on quantile regressions. The novel approach leverages the potential of quantile regression to model the entire (conditional) distribution of the yields instead of restricting to its mean. An application to US data from the 1970s shows the significant heterogeneity of the interactions between financial and macroeconomic variables across different quantiles. Moreover, an out-of-sample forecasting exercise showcases the proposed method's advantages in predicting the yield distribution tails compared to the standard conditional mean model. Finally, by inspecting the posterior distribution of the three factors during the recent major crises, new evidence is found that supports the greater and longer-lasting negative impact of the great recession on the yields compared to the COVID-19 pandemic.

Problem

• Modeling yield curve dynamics using quantile regression
• Forecasting tail behavior of interest rate distributions
• Analyzing distributional shifts during economic crises

Innovation

• Extends Nelson-Siegel model to quantile regression
• Estimates yield curve factors at specific quantiles
• Superior forecasting of yield distribution tails