A Durbin–Watson serial correlation test for ARX processes via excited adaptive tracking

Abstract

We propose a new statistical test for the residual autocorrelation in ARX adaptive tracking. The introduction of a persistent excitation in the adaptive tracking control allows us to build a bilateral statistical test based on the well-known Durbin–Watson statistic. We establish the almost sure convergence and the asymptotic normality for the Durbin–Watson statistic leading to a powerful serial correlation test. Numerical experiments illustrate the good performances of our statistical test procedure.

Keywords:

• Durbin–Watson statistic
• estimation
• adaptive tracking control
• persistent excitation
• almost sure convergence
• asymptotic normality
• statistical test for serial autocorrelation

2000 Mathematics Subject Classification:

• primary: 62G05
• secondary: 93C40
• 62F05
• 60F15
• 60F05

Acknowledgements

The authors would like to thank the three anonymous reviewers for their constructive comments which helped to improve the paper substantially.

Disclosure statement

No potential conflict of interest was reported by the authors.