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16.2 Multiperiod Forecasts 689

These VAR equations can be used to perform Granger causality tests. The
F-statistic testing the null hypothesis that the coefficients on TSpreadt−1 and
TSpreadt−2 are zero in the GDP growth rate equation [Equation (16.5)] is 5.91,
which has a p-value less than 0.001. Thus the null hypothesis is rejected, so we can
conclude that the term spread is a useful predictor of the growth rate of GDP,
given lags in the growth rate of GDP (that is, the term spread rate Granger-causes
the growth rate of GDP). The F-statistic testing the hypothesis that the coeffi-
cients on the two lags of GDPGRt are zero in the term spread equation [Equation
(16.6)] is 3.48, which has a p-value of 0.03. Thus the growth rate of GDP Granger-
causes the term spread at the 5% significance level.

Forecasts of the growth rate of GDP and the term spread one period ahead are
obtained exactly as discussed in Section 14.4. The forecast of the growth rate of
GDP for 2013:Q1, based on Equation (16.5), is GDP2013:Q102012:Q4 = 1.7 percentage
point. A similar calculation using Equation (16.6) gives a forecast of the term spread
2013:Q1, based on data through 2012:Q4 of TSpread2013:Q102012:Q4 = 1.7%. The
actual values for 2013:Q1 are GDPGR2013:Q1 = 1.1% and TSpread2013:Q1 = 1.9%.

16.2 Multiperiod Forecasts

The discussion of forecasting so far has focused on making forecasts one period
in advance. Often, however, forecasters are called upon to make forecasts further
into the future. This section describes two methods for making multiperiod fore-
casts. The usual method is to construct “iterated” forecasts, in which a one-period-
ahead model is iterated forward one period at a time, in a way that is made precise
in this section. The second method is to make “direct” forecasts by using a regres-
sion in which the dependent variable is the multiperiod variable that one wants to
forecast. For reasons discussed at the end of this section, in most applications, the
iterated method is recommended over the direct method.

Iterated Multiperiod Forecasts

The essential idea of an iterated forecast is that a forecasting model is used to
make a forecast one period ahead, for period T + 1, using data through period T.
The model then is used to make a forecast for date T + 2, given the data through
date T, where the forecasted value for date T + 1 is treated as data for the pur-
pose of making the forecast for period T + 2. Thus the one-period-ahead forecast
(which is also referred to as a one-step-ahead forecast) is used as an intermediate