An Unobserved Components Model of the Yield Curve

We develop an unobserved component model in which the short‐term interest rate is composed of a stochastic trend and a stationary cycle. Using the Nelson–Siegel model of the yield curve as inspiration, we estimate an extremely parsimonious state‐space model of interest rates across time and maturity. The time‐series process suggests a specific functional form for the yield curve. We use the Kalman filter to estimate the time‐series process jointly with observed yield curves, greatly improving empirical identification. Our stochastic process generates a three‐factor model for the term structure. At the estimated parameters, trend and slope factors matter while the third factor is empirically unimportant. Our baseline model fits the yield curve well. Model generated estimates of uncertainty are positively correlated with estimated term premia. An extension of the model with regime switching identifies a high‐variance regime and a low‐variance regime, where the high‐variance regime occurs rarely after the mid‐1980s. The term premium is higher, and more so for yields of short maturities, in the high‐variance regime than in the low‐variance regime. The estimation results support our model as a simple and yet reliable framework for modeling the term structure.