Dynamic Factor Models with Smooth Loadings for Analyzing the Term Structure of Interest Rates

We propose a new approach to the modelling of the term structure of interest rates. We consider the general dynamic factor model and show how to impose smoothness restrictions on the factor loadings. We further present a statistical procedure based on Wald tests that can be used to find a suitable set of such restrictions. We present these developments in the context of term structure models, but they are also applicable in other settings. We perform an empirical study using a data set of unsmoothed Fama-Bliss zero yields for US treasuries of different maturities. The general dynamic factor model with and without smooth loadings is considered in this study together with models that are associated with Nelson-Siegel and arbitrage-free frameworks. These existing models can be regarded as special cases of the dynamic factor model with restrictions on the model parameters. For all model candidates, we consider both stationary and nonstationary autoregressive processes (with different numbers of lags) for the latent factors. Finally, we perform statistical hypothesis tests to verify whether the restrictions imposed by the models are supported by the data. Our main conclusion is that smoothness restrictions can be imposed on the loadings of dynamic factor models for the term structure of US interest rates but that the restrictions implied by a number of popular term structure models are rejected.