The Nobel Memorial Prize for Robert F. Engle

and curvature. The correlations between the estimated factors and the empirical level, slope, and
curvature are pφ_1t,l_t) = 0.97, p(β_2t,s_t) = -0.99, and p(β_3t,c_t) = 0.99, where (l_t, st, ct) are the empirical
level, slope and curvature of the yield curve. In Table 3 and Figure 8 (left column) we present
descriptive statistics for the estimated factors. From the autocorrelations of the three factors, we can see
that the first factor is the most persistent, and that the second factor is more persistent than the third.
Augmented Dickey-Fuller tests suggest that β₁ and β₂ may have a unit roots, and that β₃ does not.¹¹
Finally, the pairwise correlations between the estimated factors are not large.

Modeling and Forecasting Yield Curve Level, Slope and Curvature

We model and forecast the Nelson-Siegel factors as univariate AR(1) processes. The AR(1)
models can be viewed as natural benchmarks determined a priori: the simplest great workhorse
autoregressive models. The yield forecasts based on underlying univariate AR(1) factor specifications

are:
where

¹¹ We use SIC to choose the lags in the augmented Dickey-Fuller unit-root test. The MacKinnon
critical values for rejection of hypothesis of a unit root are -3.4518 at the one percent level, -2.8704 at the
five percent level, and -2.5714 at the ten percent level.

¹² Note that we directly regress factors at t+h on factors at t, which is a standard method of
coaxing least squares into optimizing the relevant loss function, h-month-ahead RMSE, as opposed to the
usual 1-month-ahead RMSE. We estimate all competitor models in the same way, as described below.

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