MODELS FOR PREDICTION AND CONTROL. VI. DIAGNOSTIC CHECKING.
WISCONSIN UNIV MADISON DEPT OF STATISTICS
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The report shows that one useful method of checking a model is to overfit, that is to estimate the parameters in a model somewhat more general than that which we believe to be ture. However, this method assumes that one knows the direction in which the model is likely to be inadequate. It is necessary therefore to supplement this approach by less specific tests applied to the residuals from the fitted model. These tests are more flexible than overfitting and allow the data themselves to suggest modifications to the model. Two such tests are described based on 1 the autocorrelation function of the residuals, and 2 the cumulative periodogram of the residuals. It is then shown how the autocorrelation function of the residuals can be used to identify a new model which can then be fitted and checked diagnostically. Finally, it is shown how tracking signals can be constructed which can be used to check when the parameters in the model need to be updated.
- Operations Research