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On the asymptotic behavior of the Durbin–Watson statistic for ARX processes in adaptive tracking
Author(s) -
Bercu Bernard,
Portier Bruno,
Vazquez Victor
Publication year - 2014
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2424
Subject(s) - autoregressive model , autocorrelation , estimator , mathematics , statistic , asymptotic distribution , press statistic , asymptotic analysis , watson , convergence (economics) , statistics , test statistic , econometrics , statistical hypothesis testing , computer science , ancillary statistic , artificial intelligence , economics , economic growth
SUMMARY A wide literature is available on the asymptotic behavior of the Durbin–Watson statistic for autoregressive models. However, it is impossible to find results on the Durbin–Watson statistic for autoregressive models with adaptive control. Our purpose is to fill the gap by establishing the asymptotic behavior of the Durbin–Watson statistic for ARX models in adaptive tracking. On the one hand, we show the almost sure convergence as well as the asymptotic normality of the least squares estimators of the unknown parameters of the ARX models. On the other hand, we establish the almost sure convergence of the Durbin–Watson statistic and its asymptotic normality. Finally, we propose a bilateral statistical test for residual autocorrelation in adaptive tracking. Copyright © 2013 John Wiley & Sons, Ltd.