  The merits of the modelling philosophy of Box \& Jenkins (1970) are
illustrated with a summary of our recent work on seasonal river flow
forecasting. Specifically, this work demonstrates that the principle of
parsimony, which has been questioned by several authors recently, is helpful in
selecting the best model for forecasting seasonal river flow. Our work also
demonstrates the importance of model adequacy. An adequate model for seasonal
river flow must incorporate seasonal periodic correlation. The usual
autoregressive-moving average (ARMA) and seasonal ARMA models are not adequate
in this respect for seasonal river flow time series. A new diagnostic check,
for detecting periodic correlation in fitted ARMA models is developed in this
paper. This diagnostic check is recommended for routine use when fitting
seasonal ARMA models. It is shown that this diagnostic check indicates that
many seasonal economic time series also exhibit periodic correlation. Since the
standard forecasting methods are inadequate on this account, it can be
concluded that in many cases, the forecasts produced are sub-optimal. Finally,
a limitation of the arbitrary combination of forecasts is also illustrated.
Combining forecasts from an adequate parsimonious model with an inadequate
model did not improve the forecasts whereas combining the two forecasts of two
inadequate models did yield an improvement in forecasting performance. These
findings also support the model building philosophy of Box \& Jenkins. The
non-intuitive findings of Newbold \& Granger (1974) and Winkler \& Makridakis
(1983) that the apparent arbitrary combination of forecasts from similar models
will lead to forecasting performance is not supported by our case study with
river flow forecasting.
