The importance of unspanned macroeconomic variables for Dynamic Term Structure Models has been intensively discussed in the literature. To our best knowledge the earlier studies considered only linear interactions between the economy and the real-world dynamics of interest rates in DTSMs. We propose a generalized modelling setup for Gaussian DTSMs which allows for unspanned nonlinear associations between the two and we exploit it in forecasting. Specifically, we construct a custom sequential Monte Carlo estimation and forecasting scheme where we introduce Gaussian Process priors to model nonlinearities. Sequential scheme we propose can also be used with dynamic portfolio optimization to assess the potential of generated economic value to investors. The methodology is presented using US Treasury data and selected macroeconomic indices. Namely, we look at core inflation and real economic activity. We contrast the results obtained from the nonlinear model with those stemming from an application of a linear model. Unlike for real economic activity, in case of core inflation we find that, compared to linear models, application of nonlinear models leads to statistically significant gains in economic value across considered maturities.

翻译：文献中已深入讨论了未被经济变量覆盖的宏观变量对动态期限结构模型的重要性。据我们所知，早期研究仅考虑了经济与利率实际动态在动态期限结构模型中的线性交互关系。我们提出了一种针对高斯动态期限结构模型的广义建模框架，该框架允许两者之间存在未被覆盖的非线性关联，并将其应用于预测。具体而言，我们构建了一个自定义的序贯蒙特卡洛估计与预测方案，其中引入高斯过程先验来建模非线性关系。所提出的序贯方案还可与动态投资组合优化结合使用，以评估为投资者产生的经济价值潜力。该方法采用美国国债数据和选定的宏观指数进行展示。具体而言，我们考察了核心通胀与实际经济活动。我们将非线性模型所得结果与线性模型应用结果进行对比。与实际经济活动不同，在核心通胀案例中，我们发现与线性模型相比，非线性模型的应用在多个到期期限上带来了统计显著的经济价值增益。