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

TL;DR

This paper introduces a new statistical test for residual autocorrelation in ARX adaptive tracking systems, leveraging persistent excitation to enhance the Durbin-Watson test's effectiveness.

Contribution

It develops a novel bilateral Durbin-Watson-based test for ARX processes using excited adaptive tracking, with proven convergence and normality properties.

Findings

Test demonstrates strong performance in numerical experiments.

Provides a reliable method for detecting serial correlation in ARX models.

Enhances existing autocorrelation testing techniques with adaptive control insights.

Abstract

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.