comparison of our results and Duffee’s, however, reveals that our three-factor model produces larger
percentage reductions in out-of-sample RMSE relative to the random walk than does Duffee’s best
essentially-affine model. Our forecasting success is particularly notable in light of the fact that Duffee
forecasts only the smoothed yield curve, whereas we forecast the actual yield curve.17
Finally, we note that although our approach is closely related to direct principal components
regression, neither our approach nor our results are identical. Interestingly, there is reason to prefer our
approach on both empirical and theoretical grounds. Empirically, our results indicate that our approach
has superior forecasting performance on our sample of yields. Theoretically, other methods, including
regression on principal components and regression on ad hoc empirical level, slope and curvature, often
have unappealing features, including:
(1) they can not be used to produce yields at maturities other than those observed in the data,
(2) they do not guarantee a smooth yield curve and forward curve,
(3) they do not guarantee positive forward rates at all horizons, and
(4) they do not guarantee that the discount function starts at 1 and approaches 0 as maturity
approaches infinity.
4. Concluding Remarks
We have re-interpreted the Nelson-Siegel yield curve as a modern three-factor dynamic model of
level, slope and curvature, and we have explored the model’s performance in out-of-sample yield curve
forecasting. Although the 1-month-ahead forecasting results are no better than those of random walk and
other leading competitors, the 1-year-ahead results are much superior.
A number of authors have proposed extensions to Nelson-Siegel to enhance flexibility, including
Bliss (1997b), Soderlind and Svensson (1997), Bjork and Christensen (1999), Filipovic (1999, 2000),
Bjork (2000), Bjork and Landén (2000) and Bjork and Svensson (2001). From the perspective of interest
rate forecasting accuracy, however, the desirability of the above generalizations of Nelson-Siegel is not
obvious, which is why we did not pursue them here. For example, although the Bliss and Soderlind-
Svensson extensions can have in-sample fit no worse than that of Nelson-Siegel, because they include
Nelson-Siegel as a special case, there is no guarantee of better out-of-sample forecasting performance.
Indeed, accumulated experience suggest that parsimonious models are often more successful for out-of-
17 We note, however, that our enthusiasm must be tempered by the fact that our in-sample and
out-of-sample periods are not identical to Duffee’s, so definitive comparisons can not be made.
15