Dynamic Term Structure Models Using Principal Components Analysis Near the Zero Lower Bound

Abstract

This chapter examines the empirical performance of dynamic Gaussian affine term structure models (DGATSMs) at the zero lower bound (ZLB) when principal components analysis (PCA) is used to extract factors. We begin by providing a comprehensive review of DGATSM when PCA is used to extract factors highlighting its numerous auspicious qualities; it specifies bond yields to be a simple linear function of underlying Gaussian factors. This is especially favorable since, in principle, PCA works best when the model is linear and the first two moments are sufficient to describe the data, among other characteristics. DGATSM have a strong theoretical foundation grounded in the absence of arbitrage. DGATSM produce reasonable cross-sectional fits of the yield curve. Both of these qualities are inherited into the model when PCA is used to extract the state vector. Additionally, the implementation of PCA is simple in that it takes a matter of seconds to estimate factors and is convenient to include in estimation as most software packages have ready-to-use algorithms to compute the factors immediately. The results from our empirical investigation lead us to conclude that DGATSM, when PCA is employed to extract factors, perform very poorly at the ZLB. It frequently crosses the ZLB enroot to producing negative out-of-sample forecasts for bond yields. The main implication in this study is that despite its numerous positive characteristics, DGATSM when PCA is used to extract factors produce poor empirical forecasts around the ZLB.