This article develops a set of inferential methods for functional factor models that have been extensively used in modelling yield curves. Our setting accommodates both temporal dependence and heteroskedasticity. First, we introduce an estimation approach based on minimizing the least-squares loss function and establish the consistency and asymptotic normality of the estimators. Second, we propose a goodness-of-fit test that allows us to determine whether a specific model fits the data. We derive the asymptotic distribution of the test statistics, and this leads to a significance test. A simulation study establishes the good finite-sample performance of our inferential methods. An application to US and UK yield curves demonstrates the generality of our framework, which can accommodate both sparsely and densely observed yield curves.

中文翻译：

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在功能因素模型中的推论与收益率曲线的应用

本文开发了一套功能因素模型的推理方法，这些方法已广泛用于建模收益率曲线。我们的设置同时适应时间依赖性和异方差。首先，我们引入了一种基于最小二乘损失函数的估计方法，并建立了估计量的一致性和渐近正态性。其次，我们提出了一个拟合优度检验，它允许我们确定特定模型是否适合数据。我们推导出检验统计量的渐近分布，这导致了显着性检验。一项模拟研究确定了我们的推理方法在有限样本中的良好性能。对美国和英国收益率曲线的应用证明了我们框架的普遍性，它可以适应稀疏和密集观察到的收益率曲线。