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On covariance function tests used in system identification. (English) Zbl 0714.93056

Summary: Tests on the autocovariance function of the residuals of an estimated model, or on the cross-covariance function between the model residuals and the past values of the input signal are frequently used in system identification for model validation purposes. Usually, the threshold of such a test is derived under the assumption that the model and the identified system coincide.
The present paper shows that this simplifying assumption leads to a risk of overfitting less than expected and, accordingly, to a greater risk of underfitting. The correct test threshold is problem dependent and cannot be determined easily in the general case. However, it can be shown to lie in a certain interval; and to be equal to one of the bounds defining this interval under certain (sufficient) conditions. The implication of these results for model validation based on covariance tests is discussed and illustrated by means of some numerical examples.

MSC:

93E12 Identification in stochastic control theory
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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