Model validity tests for non-linear signal processing applications

Time series model validity tests based on general correlations are presented in this paper. It is shown that the tests Φ xi xi (τ), Φ xi xi 2 (τ) and Φ xi xi xi (τ 1 , t 2 ) can only detect a subset of any possible unmodelled terms in the residuals, whereas Φ xi 2 xi 2 (τ) detects all possible terms...

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Bibliographic Details
Published in:International journal of control 1991-07, Vol.54 (1), p.157-194
Main Authors: BILLINGS, S. A., TAO, Q. H.
Format: Article
Language:English
Subjects:
Applied sciences
Exact sciences and technology
Information, signal and communications theory
Signal processing
Telecommunications and information theory
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Summary:Time series model validity tests based on general correlations are presented in this paper. It is shown that the tests Φ xi xi (τ), Φ xi xi 2 (τ) and Φ xi xi xi (τ 1 , t 2 ) can only detect a subset of any possible unmodelled terms in the residuals, whereas Φ xi 2 xi 2 (τ) detects all possible terms. These basic results are then extended to include functions of process or residual terms as entries in the correlation. Simulation studies are included to demonstrate the effectiveness of the tests when applied to estimated models of both simulated and real data sequences.
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179108934155