slightly better than the random walk and slope regression forecasts, are indeed only very slightly better.
Finally, the Diebold-Mariano (1995) statistics reported in Table 7 indicate universal insignificance of the
RMSE differences between our 1-month-ahead forecasts and those from random walks or Fama-Bliss
regressions.
The 1-month-ahead forecast defects likely come from a variety of sources, some of which could
be eliminated. First, for example, pricing errors due to illiquidity may be highly persistent and could be
reduced by including variables that may explain mispricing. It is worth noting, moreover, that related
papers such as Bliss (1997b) and de Jong (2000) also find serially correlated forecast errors, often with
persistence much stronger than ours.
Matters improve radically, however, as the forecast horizon lengthens. Our model’s 6-month-
ahead forecasting results, reported in Table 5, are noticeably improved, and our model’s 12-month-ahead
forecasting results, reported in Table 6, are much improved. In particular, our model’s 12-month ahead
forecasts outperform those of all competitors at all maturities, often by a wide margin in both relative and
absolute terms. Seven of the ten Diebold-Mariano statistics in Table 7 indicate significant 12-month-
ahead RMSE superiority of our forecasts at the five percent level. The strong yield curve forecastability
at the 12-month-ahead horizon is, for example, very attractive from the vantage point of active bond
trading and the vantage point of credit portfolio risk management.15 Moreover, our 12-month-ahead
forecasts, like their 1- and 6-month-ahead counterparts, could be improved upon, because the forecast
errors remain serially correlated.16
It is worth noting that Duffee (2002) finds that even the simplest random walk forecasts dominate
those from the Dai-Singleton (2000) affine model, which therefore appears largely useless for
forecasting. Hence Duffee proposes a less-restrictive “essentially-affine” model and shows that it
forecasts better than the random walk in most cases, which is appropriately viewed as a victory. A
15 Note that Nelson-Siegel loadings imply a very smooth yield curve, which in turn suggests that
our model, although not arbitrage-free, would not likely generate extreme portfolio positions.
Competitors such as regression on principal components, in contrast, have no smooth cross-sectional
restrictions and may well generate extreme portfolio positions in practice. This is one important way in
which our approach is superior to directs regression on principal components, despite the fact that our
estimated factors are close to the first three principal components. (Four more are given below.)
16 We report 12-month-ahead forecast error serial correlation coefficients at displacements of 12
and 24 months, in contrast to those at displacements of 1 and 12 months reported for the 1-month-ahead
forecast errors, because the 12-month-ahead errors would naturally have moving-average structure even
if the forecasts were fully optimal, due to the overlap.
14