be interpreted as factors. Unlike factor analysis, however, in which one estimates both the unobserved
factors and the factor loadings, the Nelson-Siegel framework imposes structure on the factor loadings.3
Doing so not only facilitates highly precise estimation of the factors, but, as we show, it also lets us
interpret the factors as level, slope and curvature. We propose and estimate autoregressive models for
the factors, and then we forecast the yield curve by forecasting the factors. Our results are encouraging;
in particular, our models produce one-year-ahead forecasts that are noticeably more accurate than
standard benchmarks.
Related work includes the factor models of Litzenberger, Squassi and Weir (1995), Bliss (1997a,
1997b), Dai and Singleton (2000), de Jong and Santa-Clara (1999), de Jong (2000), Brandt and Yaron
(2001) and Duffee (2002). Particularly relevant are the three-factor models of Balduzzi, Das, Foresi and
Sundaram (1996), Chen (1996), and especially the Andersen-Lund (1997) model with stochastic mean
and volatility, whose three factors are interpreted in terms of level, slope and curvature. We will
subsequently discuss related work in greater detail; for now, suffice it to say that little of it considers
forecasting directly, and that our approach, although related, is indeed very different.
We proceed as follows. In section 2 we provide a detailed description of our modeling
framework, which interprets and extends earlier work in ways linked to recent developments in multi-
factor term structure modeling, and we also show how it can replicate a variety of stylized facts about the
yield curve. In section 3 we proceed to an empirical analysis, describing the data, estimating the models,
and examining out-of-sample forecasting performance. In section 4 we offer interpretive concluding
remarks.
2. Modeling and Forecasting the Term Structure I: Methods
Here we introduce the framework that we use for fitting and forecasting the yield curve. We
argue that the well-known Nelson-Siegel (1987) curve is well-suited to our ultimate forecasting purposes,
and we introduce a novel twist of interpretation, showing that the three coefficients in the Nelson-Siegel
curve may be interpreted as latent level, slope and curvature factors. We also argue that the nature of the
factors and factor loadings implicit in the Nelson-Siegel model facilitate consistency with various
empirical properties of the yield curve that have been cataloged over the years. Finally, motivated by our
interpretation of the Nelson-Siegel model as a three-factor model of level, slope and curvature, we
contrast it to various multi-factor models that have appeared in the literature.
3 Classic unrestricted factor analyses include Litterman and Scheinkman (1991) and Knez,
Litterman and Scheinkman (1994).