On the asymptotic behavior of the Durbin-Watson statistic for ARX processes in adaptive tracking

Bernard Bercu 1, 2 Bruno Portier 3 V. Vazquez 1
2 ALEA - Advanced Learning Evolutionary Algorithms
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
Abstract : 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.
Type de document :
Article dans une revue
International Journal of Adaptive Control and Signal Processing, Wiley, 2013, 27, pp.1-25. 〈10.1002/acs.2424〉
Liste complète des métadonnées

Littérature citée [27 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00915951
Contributeur : Bernard Bercu <>
Soumis le : lundi 9 décembre 2013 - 15:11:21
Dernière modification le : vendredi 15 décembre 2017 - 23:20:14
Document(s) archivé(s) le : dimanche 9 mars 2014 - 23:46:16

Fichier

BPVDW2013RV.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

Bernard Bercu, Bruno Portier, V. Vazquez. On the asymptotic behavior of the Durbin-Watson statistic for ARX processes in adaptive tracking. International Journal of Adaptive Control and Signal Processing, Wiley, 2013, 27, pp.1-25. 〈10.1002/acs.2424〉. 〈hal-00915951〉

Partager

Métriques

Consultations de la notice

239

Téléchargements de fichiers

332