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)

1 IMB - Institut de Mathématiques de Bordeaux
2 ALEA - Advanced Learning Evolutionary Algorithms
3 LMI - Laboratoire de Mathématiques de l'INSA de Rouen Normandie

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.

Domaines: Probabilités [math.PR]

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, 2013, 27, pp.1-25. ⟨10.1002/acs.2424⟩. ⟨hal-00915951⟩