A Durbin-Watson serial correlation test for ARX processes via excited   adaptive tracking
  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. 
Bernard Bercu (IMB), Bruno Portier, Victor Vazquez (IMB)
math.PR math.ST stat.TH