What is the Effect of Restrictions Imposed by Principal Components Analysis on the Empirical Performance of Dynamic Term Structure Models?

This paper investigates the effect of restrictions imposed by principal components analysis (PCA) on the empirical performance of dynamic term structure models (DTSM). The application of PCA maximizes the explained variance of a linear combination of bond yields by selecting weights that are as uncorrelated as possible. In the context of factor construction, this choice of weights imposes orthogonality on the state variable bringing about restrictions on model estimation. We quantify the effect of these restrictions, measured through internal consistency equations, on the empirical performance of DTSM contained within linear-affine and linear-quadratic state space formulations (SSF) characterized by Gaussian and non-Gaussian transition dynamics for the state variable. When looking across DTSM, we find the smallest effect of restrictions imposed by PCA on empirical performance when it is used in the context of a linear-affine SSF, and the state transition dynamics are postulated based upon the conditional mean and variance. We also document that the magnitude of this effect is more pronounced when the probability distribution for the data is described by the first four moments relative to just the first two and the parameter dependencies defining the relationship between bond yields and factors are more analytically or computationally complicated (e.g., involves a special function like the Bessel function or cumbersome algebraic manipulations). Suggestions for future research are provided.