‰h /1 (τ) ~yt (τ) = c^(τ) + ^(τ)('' (τ) y(3 (3)).
The forecasted yield change is obtained from a regression of historical yield changes on
yield curve slopes.
(3) Fama-Bliss forward rate regression:
yt+h / ( (τ) ~У( (τ) = c(τ) + y(τ)(f'th (τ) yyt (τ)),
where f↑(τ) is the forward rate contracted at time t for loans from time t+h to time
t+h + τ. Hence the forecasted yield change is obtained from a regression of historical
yield changes on forward spreads. Note that, because the forward rate is proportional to
the derivative of the discount function, the information used to forecast future yields in
forward rate regressions is very similar to that in slope regressions.
(4) Cochrane-Piazzesi (2002) forward curve regression:
9
yt.h /1 (τ) yt(t (τ) = c^(τ) + To(τ) yt(12) + ∑Tk(τ)ft12 k(12).
k=1
Note that the Fama-Bliss forward regression is a special case of the Cochrane-Piazzesi
forward regression.14
(5) AR(1) on yield levels:
yt+l, /1 (τ) = c^(τ) + τ yt (τ).
(6) VAR(1) on yield levels:
yt+h, /1 = c + г yt.
where yt ≡ [yt(3), yt(12), yt(36), yt(60), yt(120)]z.
(7) VAR(1) on yield changes:
zt.h /1 = c + Γ zt t
14 Note that this is an unrestricted version of the model estimated by Cochrane and Piazzesi.
Imposition of the Cochrane-Piazzesi restrictions produced qualitatively identical results.
12
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