1. Introduction
The last twenty-five years have produced major advances in theoretical models of the term
structure as well as their econometric estimation. Two popular approaches to term structure modeling
are no-arbitrage models and equilibrium models. The no-arbitrage tradition focuses on perfectly fitting
the term structure at a point in time to ensure that no arbitrage possibilities exist, which is important for
pricing derivatives. The equilibrium tradition focuses on modeling the dynamics of the instantaneous
rate, typically using affine models, after which yields at other maturities can be derived under various
assumptions about the risk premium.1 Prominent contributions in the no-arbitrage vein include Hull and
White (1990) and Heath, Jarrow and Morton (1992), and prominent contributions in the affine
equilibrium tradition include Vasicek (1977), Cox, Ingersoll and Ross (1985), and Duffie and Kan
(1996).
Interest rate point forecasting is crucial for bond portfolio management, and interest rate density
forecasting is important for both derivatives pricing and risk management.2 Hence one wonders what the
modern models have to say about interest rate forecasting. It turns out that, despite the impressive
theoretical advances in the financial economics of the yield curve, surprisingly little attention has been
paid to the key practical problem of yield curve forecasting. The arbitrage-free term structure literature
has little to say about dynamics or forecasting, as it is concerned primarily with fitting the term structure
at a point in time. The affine equilibrium term structure literature is concerned with dynamics driven by
the short rate, and so is potentially linked to forecasting, but most papers in that tradition, such as de Jong
(2000) and Dai and Singleton (2000), focus only on in-sample fit as opposed to out-of-sample
forecasting. Moreover, those that do focus on out-of-sample forecasting, notably Duffee (2002),
conclude that the models forecast poorly.
In this paper we take an explicitly out-of-sample forecasting perspective, and we use neither the
no-arbitrage approach nor the equilibrium approach. Instead, we use the Nelson-Siegel (1987)
exponential components framework to distill the entire yield curve, period-by-period, into a three-
dimensional parameter that evolves dynamically. We show that the three time-varying parameters may
1 The empirical literature that models yields as a cointegrated system, typically with one
underlying stochastic trend (the short rate) and stationary spreads relative to the short rate, is similar in
spirit. See Diebold and Sharpe (1990), Hall, Anderson, and Granger (1992), Shea (1992), Swanson and
White (1995), and Pagan, Hall and Martin (1996).
2 For comparative discussion of point and density forecasting, see Diebold, Gunther and Tay
(1998) and Diebold, Hahn and Tay (1999).