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.

翻译：动态Nelson-Siegel（DNS）模型是广泛使用的期限结构预测框架。本文提出一种新颖的扩展方法，将DNS残差建模为高斯随机场，以捕捉跨时间和期限的依赖关系。该残差场通过随机偏微分方程（SPDE）表示，能够实现灵活的协方差结构，并借助稀疏精度矩阵实现可扩展的贝叶斯推断。我们考虑了一系列SPDE设定，包括平稳、非平稳、各向异性和不可分离模型。SPDE-DNS模型在贝叶斯框架下采用集成嵌套拉普拉斯近似（INLA）进行估计，可联合推断潜在DNS因子与残差场。实证结果表明，相较于标准基准模型，基于SPDE的扩展方法在点预测和概率预测方面均有改进。当应用于均值-方差债券投资组合框架时，该预测模型产生了具有经济意义的效用增益，具体表现为按月再平衡策略下相对于贝叶斯DNS基准模型的绩效费用。重要的是，引入结构化SPDE残差显著降低了剩余测量误差中跨期限和跨时期的依赖性，使其更接近白噪声。这些发现凸显了将DNS模型与SPDE驱动的残差建模相结合，在实现灵活、可解释且计算高效的收益率曲线预测方面的优势。