A State-Space Approach to Estimate and Test Multifactor Cox-Ingersoll-Ross Models of the Term Structure

Abstract

The objective of this paper is to estimate and test multifactor versions of the Cox-Ingersoll-Ross (CIR) model of the nominal term structure of interest rates. The proposed state-space approach integrates time-series and cross-sectional aspects of the CIR model, is consistent with the underlying economic model, and can use information from all available points of the term structure. We recover estimates of the underlying factors that are consistent with the assumptions about the stochastic processes and compare them with factors obtained from standard factor analysis. We perform thorough diagnostic checking and thereby provide new evidence regarding conclusions about the adequacy of the CIR model. We present empirical results for U.S. Treasury market data. Although the specification of multifactor CIR models is sufficiently flexible for the shape of the term structure, we find strong evidence against the adequacy of the CIR model.

JEL Classification: G12