A Quantile Nelson-Siegel model

Abstract

We propose a novel framework for modeling the yield curve from a quantile perspective. Building on the dynamic Nelson-Siegel model of Diebold et al. (2006), we extend its traditional mean-based approach to a quantile regression setting, enabling the estimation of yield curve factors - level, slope, and curvature - at specific quantiles of the conditional distribution. A key advantage of our framework is its ability to characterize the entire conditional distribution of the yield curve across maturities and over time. In an empirical analysis of the U.S. term structure of interest rates, our method demonstrates superior out-of-sample forecasting performance, particularly in capturing the tails of the yield distribution - an aspect increasingly emphasized in the recent literature on distributional forecasting. In addition to its forecasting advantages, our approach reveals rich distributional features beyond the mean. In particular, we find that the dynamic changes in these distributional features differ markedly between the Great Recession and the COVID-19 pandemic period, highlighting a fundamental shift in how interest rate markets respond to distinct economic shocks.