PARSIMONY, MODEL ADEQUACY AND PERIODIC CORRELATION IN TIME-SERIES FORECASTING

The merits of the modelling philosophy of Box & Jenkins (1970) are ill ustrated with a summary of our recent work on seasonal river flow fore casting. Specifically, this work demonstrates that the principle of pa rsimony, which has been questioned by several authors recently, is hel pful in selecting the best model for forecasting seasonal river flow. Our work also demonstrates the important of model adequacy. An adequat e model for seasonal river flow must incorporate seasonal periodic cor relation. The usual autoregressive-moving average (ARMA) and seasonal ARMA models are not adequate in this respect for seasonal river flow t ime series. A new diagnostic check, for detecting periodic correlation in fitted ARMA models is developed in this paper. This diagnostic che ck is recommended for routine use when fitting seasonal ARMA models. I t is shown that this diagnostic check indicates that many seasonal eco nomic time series also exhibit periodic correlation. Since the standar d forecasting methods are inadequate on this account, it can be conclu ded that in many cases, the forecasts produced are sub-optimal. Finall y, a limitation of the arbitrary combination of forecasts is also illu strated. Combining forecasts from an adequate parsimonious model with an inadequate model did not improve the forecasts whereas combining th e two forecasts of two inadequate models did yield an improvement in f orecasting 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 arbit rary combination of forecasts from similar models will lead to forecas ting performance is not supported by our case study with river flow fo recasting.