A combination of VAR estimation and state space model reduction techni
ques are examined by Monte Carlo methods in order to find good, simple
to use, procedures for determining models which have reasonable predi
ction properties. The presentation is largely graphical. This helps fo
cus attention on the aspects of the model determination problem which
are relatively important for forecasting. One surprising result is tha
t, for prediction purposes, knowledge of the true structure of the mod
el generating the data is not particularly useful unless parameter val
ues are also known. This is because the difficulty in estimating param
eters of the true model causes more prediction error than results from
a more parsimonious approximate model.