CHAPTER EIGHT

Model Diagnostic Checking

The model having been identified and the parameters estimated, diagnostic checks are then applied to the fitted model. 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 true. This method assumes that we can guess the direction in which the model is likely to be inadequate. Therefore, it is necessary to supplement this approach by less specific checks applied to the residuals from the fitted model. These allow the data themselves to suggest modifications to the model. We shall describe two such checks that employ (1) the autocorrelation function of the residuals and (2) the cumulative periodogram of the residuals.

8.1 CHECKING THE STOCHASTIC MODEL

8.1.1 General Philosophy

Suppose that using a particular time series, the model has been identified and the parameters estimated using the methods described in Chapters 6 and 7. The question remains of deciding whether this model is adequate. If there should be evidence of serious inadequacy, we shall need to know how the model should be modified in the next iterative cycle. What we are doing is described only partially by the words “testing goodness of fit.” We need to discover in what way a model is inadequate, so as to suggest appropriate modification. To illustrate, by reference to familiar procedures outside time series analysis, the scrutiny of residuals for the analysis of variance, described ...

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