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16.2 Multiperiod Forecasts 691

­iterated multivariate forecast is that the two-step-ahead (period T + 2) forecast
of one variable depends on the forecasts of all variables in the VAR in period
T + 1. For example, to compute the forecast of the growth rate of GDP in period
T + 2 using a VAR with the variables GDPGRt and TSpreadt, one must forecast
both GDPGRT+1 and TSpreadT+1, using data through period T as an intermediate
step in forecasting GDPGRT+2. More generally, to compute multiperiod iterated
VAR forecasts h periods ahead, it is necessary to compute forecasts of all vari-
ables for all intervening periods between T and T + h.

As an example, we will compute the iterated VAR forecast of GDPGR2013:Q2
based on data through 2012:Q4, using the VAR(2) for GDPGRt and TSpreadt in
Section 16.1 [Equations (16.5) and (16.6)]. The first step is to compute the one-
quarter-ahead forecasts GDPGR2013:Q1∙2012:Q4 and TSpread2013:Q1∙2012:Q4 from that
VAR. These one-period-ahead forecasts were computed in Section 16.1 based on
Equations (16.5) and (16.6). The forecasts were GDPGR2013:Q1∙2012:Q4 = 1.7 and
TSpread2013:Q1∙2012:Q4 = 1.7. In the second step, these forecasts are substituted
into Equations (16.5) and (16.6) to produce the two-quarter-ahead forecast:

GDPGR2013:Q2∙2012:Q4 = 0.52 + 0.29 GDPGR2013:Q1∙2012:Q4 + 0.22GDPGR2012:Q4
- 0.90 TSpread2013:Q1∙2012:Q4 + 1.33TSpread2012:Q4

= 0.52 + 0.30 * 1.7 + 0.22 * 0.15
- 0.90 * 1.7 + 1.33 * 1.6 = 1.7. (16.9)

Thus the iterated VAR(2) forecast, based on data through the fourth quarter of
2012, is that the growth rate of GDP will be 1.7% in the second quarter of 2013.

Iterated multiperiod forecasts are summarized in Key Concept 16.2.

Direct Multiperiod Forecasts

Direct multiperiod forecasts are computed without iterating by using a single
regression in which the dependent variable is the multiperiod-ahead variable to
be forecasted and the regressors are the predictor variables. Forecasts computed
this way are called direct forecasts because the regression coefficients can be used
directly to make the multiperiod forecast.

The direct multiperiod forecasting method. Suppose that you want to make a
forecast of YT + 2 using data through time T. The direct multivariate method takes
the ADL model as its starting point but lags the predictor variables by an addi-
tional time period. For example, if two lags of the predictors are used, then the