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The merits of the modelling philosophy of Box \& Jenkins (1970) areillustrated with a summary of our recent work on seasonal river flowforecasting. Specifically, this work demonstrates that the principle ofparsimony, which has been questioned by several authors recently, is helpful inselecting the best model for forecasting seasonal river flow. Our work alsodemonstrates the importance of model adequacy. An adequate model for seasonalriver flow must incorporate seasonal periodic correlation. The usualautoregressive-moving average (ARMA) and seasonal ARMA models are not adequatein this respect for seasonal river flow time series. A new diagnostic check,for detecting periodic correlation in fitted ARMA models is developed in thispaper. This diagnostic check is recommended for routine use when fittingseasonal ARMA models. It is shown that this diagnostic check indicates thatmany seasonal economic time series also exhibit periodic correlation. Since thestandard forecasting methods are inadequate on this account, it can beconcluded 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 inadequatemodel did not improve the forecasts whereas combining the two forecasts of twoinadequate models did yield an improvement in forecasting performance. Thesefindings also support the model building philosophy of Box \& Jenkins. Thenon-intuitive findings of Newbold \& Granger (1974) and Winkler \& Makridakis(1983) that the apparent arbitrary combination of forecasts from similar modelswill lead to forecasting performance is not supported by our case study withriver flow forecasting.

Parsimony, model adequacy and periodic correlation in forecasting time series