Inference for Model Misspecification in Interest Rate Term Structure using Functional Principal Component Analysis

TL;DR

This paper develops nonparametric tests to evaluate the adequacy of interest rate models, revealing occasional misspecification during rare events by comparing Nelson-Siegel basis with data-driven principal components.

Contribution

It introduces two novel nonparametric tests for model misspecification in interest rate models using functional principal components analysis.

Findings

High dispersion between bases during rare events

Occasional model misspecification detected

Nelson-Siegel basis may not always capture yield curve dynamics

Abstract

Level, slope, and curvature are three commonly-believed principal components in interest rate term structure and are thus widely used in modeling. This paper characterizes the heterogeneity of how misspecified such models are through time. Presenting the orthonormal basis in the Nelson-Siegel model interpretable as the three factors, we design two nonparametric tests for whether the basis is equivalent to the data-driven functional principal component basis underlying the yield curve dynamics, considering the ordering of eigenfunctions or not, respectively. Eventually, we discover high dispersion between the two bases when rare events occur, suggesting occasional misspecification even if the model is overall expressive.