In this section we consider forecasting using 3 different models, an AR model, an ARDL model, and an exponential smoothing model. The examples focus on short-term forecasting, typically up to 3 periods into the future.
Suppose that it is the 3rd quarter in 2009 and have estimated the AR(2) model of GDP growth using data up to and including 2009:3. In this section the use of an AR(2) model to forecast the next three periods is discussed and forecast confidence intervals are generated.
The AR(2) model in terms of its unknown coefficients
gt = S + digt-i + 92gt-2 + vt (9.14)
Denoting the last sample observation as gT, the task is to forecast gT+1, gT+2, and gT+з – The value of the next observation beyond the available sample is
gT+1 = S + ві gT + %t -1 + vt+1 (9.15)
Growth rates for the 2 most recent quarters are GT = G200g:3 = 0.8, and gT-1 = g2oo9:2 = -0.2, which with the estimated values of the parameters is used to make a forecast of gT+1 = g200g:4.
gT+1 =S + e1gT + e2gT-1
=0.46573 + 0.37700 x 0.8 + 0.24624 x (-0.2)
Once the model is estimated it is easy to compute this forecast.
1 open "@gretldirdatapoeokun. gdt"
2 ols g(0 to -2) const —robust —quiet
Using this model to forecast in gretl is very simple. The main decision you have to make at this point is how many periods into the future you want to forecast. In gretl you have to extend the sample to include future periods under study.