Forecasting the Term Structure of Interest Rates with SPDE-Based Models

TL;DR

This paper introduces a novel SPDE-based extension to the DNS model for interest rate forecasting, capturing complex dependencies across time and maturity, and demonstrating improved forecast accuracy and economic utility.

Contribution

It develops a flexible SPDE residual modeling approach within the DNS framework, enabling scalable Bayesian inference and better capturing dependencies in yield curve data.

Findings

SPDE extensions improve forecast accuracy over benchmarks.

Forecasts yield significant utility gains in bond portfolio management.

Structured residual modeling reduces dependence in measurement errors.

Abstract

The Dynamic Nelson--Siegel (DNS) model is a widely used framework for term structure forecasting. We propose a novel extension that models DNS residuals as a Gaussian random field, capturing dependence across both time and maturity. The residual field is represented via a stochastic partial differential equation (SPDE), enabling flexible covariance structures and scalable Bayesian inference through sparse precision matrices. We consider a range of SPDE specifications, including stationary, non-stationary, anisotropic, and nonseparable models. The SPDE--DNS model is estimated in a Bayesian framework using the integrated nested Laplace approximation (INLA), jointly inferring latent DNS factors and the residual field. Empirical results show that the SPDE-based extensions improve both point and probabilistic forecasts relative to standard benchmarks. When applied in a mean--variance bond portfolio framework, the forecasts generate economically meaningful utility gains, measured as performance fees relative to a Bayesian DNS benchmark under monthly rebalancing. Importantly, incorporating the structured SPDE residual substantially reduces cross-maturity and intertemporal dependence in the remaining measurement error, bringing it closer to white noise. These findings highlight the advantages of combining DNS with SPDE-driven residual modeling for flexible, interpretable, and computationally efficient yield curve forecasting.