Abstract
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.
Highlights
For three decades, models akin to the Nelson–Siegel model have been used to quantify the term structure of various economic and financial variables, including yields, spot rates, and futures, with hundreds of papers using it in various contexts
For the sake of conserving space, the method of parameter estimation is demonstrated by the traditional Nelson–Siegel model, and other models can be estimated in the same manner
The general pattern is that more factor functions enable larger flexibility in the yield curve modelling, which results in fewer rejections by the goodness-of-fit test
Summary
Models akin to the Nelson–Siegel model have been used to quantify the term structure of various economic and financial variables, including yields, spot rates, and futures, with hundreds of papers using it in various contexts. It allows us to formulate results on consistency and asymptotic distribution of parameter estimators and derive a goodness-of-fit test This test permits us to evaluate the admissibility of a specific model over a specific time period within the Neyman–Pearson testing paradigm. The vector of coefficients cannot only follow an unknown time series model, but this model can change within the time period over which observations are available This approach substantially extends homoskedastic parametric models such as the AR(1) in Diebold et al (2006) and VAR(1) in Diebold and Li (2006). This theory is conditional on the availability of suitable long-run covariance estimators, which remain consistent under heteroskedastic errors. Online Supporting Information contains the proofs of the results stated in Sections 2 and 3, details of the numerical implementation of our methods, as well as additional results and figures
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