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

Bernard Bercu (1) , Bruno Portier (2) , Victor Vazquez (1)

1 IMB - Institut de Mathématiques de Bordeaux
2 INSA Rouen Normandie - Institut national des sciences appliquées Rouen Normandie

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.

Domaines: Probabilités [math.PR]; Statistiques [math.ST]; Théorie [stat.TH]

Bernard Bercu, Bruno Portier, Victor Vazquez. A Durbin-Watson serial correlation test for ARX processes via excited adaptive tracking. 2014. ⟨hal-01023598⟩