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690 Chapter 16 Additional Topics in Time Series Regression

step to make the two-period-ahead forecast. This process repeats, or iterates, until
the forecast is made for the desired forecast horizon h.

The iterated AR forecast method: AR(1). An iterated AR(1) forecast uses an
AR(1) for the one-period-ahead model. For example, consider the first-order
autoregression for GDPGR [Equation (14.7)]:

GDPGRt = 1.99 + 0.34 GDPGRt - 1. (16.7)
(0.35) (0.08)

The first step in computing the two-quarter-ahead forecast of GDPGR2013:Q2
based on Equation (16.7) using data through 2012:Q4 is to compute the one-

quarter-ahead forecast of GDPGR2013:Q1 based on data through 2012:Q4:
GDPGR2013:Q102012:Q4 = 1.99 + 0.34 GDPGR2012:Q4 = 1.99 + 0.34 * 0.15 = 2.0.
The second step is to substitute this forecast into Equation (16.7) so that

GDPGR2013:Q202012:Q4 = 1.99 + 0.34 GDPGR2013:Q102012:Q4 = 1.99 + 0.34 * 2.0 =
2.7. Thus, based on information through the fourth quarter of 2012, this forecast

states that the growth rate of GDP will be 2.7% in the second quarter of 2013.

The iterated AR forecast method: AR(p). The iterated AR(1) strategy is extended
to an AR(p) by replacing YT + 1 with its forecast, Yn T + 10T, and then treating that
forecast as data for the AR(p) forecast of YT + 2. For example, consider the iter-
ated two-period-ahead forecast of the growth rate of GDP based on the AR(2)

model from Section 14.3 [Equation (14.13)]:

GDPGRt = 1.63 + 0.28 GDPGRt - 1 + 0.18 GDPGRt - 2. (16.8)
(0.40) (0.08) (0.08)

The forecast of GDPGR2013:Q1 based on data through 2012:Q4 using this AR(2),
computed in Section 14.3, is GDPGR2013:Q102012:Q4 = 2.1. Thus the two-quarter-
ahead iterated forecast based on the AR(2) is GDPGR2013:Q202012:Q4 =
1.63 + 0.28 GDPGR2013:Q102012:Q4 + 0.18 GDPGR2012:Q4 = 1.63 + 0.28 * 2.1 + 0.18
× 0.15 = 2.2. According to this iterated AR(2) forecast, based on data through

the fourth quarter of 2012, the growth rate of GDP is predicted to be 2.2 percent-

age points in the second quarter of 2013.

Iterated multivariate forecasts using an iterated VAR. Iterated multivariate fore-
casts can be computed using a VAR in much the same way as iterated univariate
forecasts are computed using an autoregression. The main new feature of an