Parsimony, model adequacy and periodic correlation in forecasting time series

Abstract

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.