Notes to Tables
Notes to Table 1:
We present descriptive statistics for monthly yields at different maturities, and for the yield curve level,
slope and curvature, where we define the level as the 10-year yield, the slope as the difference between
the 10-year and 3-month yields, and the curvature as the twice the 2-year yield minus the sum of the 3-
month and 10-year yields. The last three columns contain sample autocorrelations at displacements of 1,
12, and 30 months. The sample period is 1985:01-2000:12.
Notes to Table 2:
We fit the three-factor model,
using monthly yield data 1985:01-2000:12, with t fixed at 0.0609, and we present descriptive statistics
for the corresponding residuals at various maturities. The last three columns contain residual sample
autocorrelations at displacements of 1, 12, and 30 months.
y( ω = βι t+ β21
1 λτ
1 -e t
λτ
\ t
3t
1 ^λtτ
1 -e t
--------e
t
-∙k,τ
Notes to Table 3:
We fit the three-factor Nelson-Siegel model using monthly yield data 1985:01-2000:12, with λt fixed at
0.0609, and we present descriptive statistics for the three estimated factors β1t, β2t, and |î3t. The last
column contains augmented Dickey-Fuller (ADF) unit root test statistics, and the three columns to its left
contain sample autocorrelations at displacements of 1, 12, and 30 months.
Notes to Table 4:
We present the results of out-of-sample 1-month-ahead forecasting using eight models, as described in
detail in the text. We estimate all models recursively from 1985:1 to the time that the forecast is made,
beginning in 1994:1 and extending through 2000:12. We define forecast errors at t +1 as
yt+1(τ) y yt+1/t (τ), and we report the mean, standard deviation and root mean squared errors of the forecast
errors, as well as their first and twelfth sample autocorrelation coefficients.
Notes to Table 5:
We present the results of out-of-sample 6-month-ahead forecasting using eight models, as described in
detail in the text. We estimate all models recursively from 1985:1 to the time that the forecast is made,
beginning in 1994:1 and extending through 2000:12. We define forecast errors at t +6 as
yt+6(τ) y Уt 61 (τ), and we report the mean, standard deviation and root mean squared errors of the forecast
errors, as well as their sixth and eighteenth sample autocorrelation coefficients.
Notes to Table 6:
We present the results of out-of-sample 12-month-ahead forecasting using twelve models, as described in
detail in the text. We estimate all models recursively from 1985:1 to the time that the forecast is made,
beginning in 1994:1 and extending through 2000:12. We define forecast errors at t +12 as
yt+12(τ) ~‰ 12/1 (τ), and we report the mean, standard deviation and root mean squared errors of the
forecast errors, as well as their twelfth and twenty-fourth sample autocorrelation coefficients.
Notes to Table 7:
We present Diebold-Mariano forecast accuracy comparison tests of our three-factor model forecasts
(using univariate AR(1) factor dynamics) against those of the Random Walk model (RW) and the Fama-
Bliss forward rate regression model (FB). The null hypothesis is that the two forecasts have the same
mean squared error. Negative values indicate superiority of our three-factor model forecasts, and
asterisks denote significance relative to the asymptotic null distribution at the ten percent level.