Model-Free Tests for Series Correlation in Multivariate Linear Regression

TL;DR

This paper introduces new, robust, model-free tests for detecting series correlation in linear regression errors, applicable to both fixed and random designs, with proven asymptotic properties and validated by simulations.

Contribution

It develops simple, robust tests based on residuals and design matrices that do not rely on traditional model assumptions, extending diagnostic tools for regression analysis.

Findings

Tests perform well in simulations

Asymptotic distributions derived via joint CLT

Applicable to fixed and random design models

Abstract

Testing for series correlation among error terms is a basic problem in linear regression model diagnostics. The famous Durbin-Watson test and Durbin's h-test rely on certain model assumptions about the response and regressor variables. The present paper proposes simple tests for series correlation that are applicable in both fixed and random design linear regression models. The test statistics are based on the regression residuals and design matrix. The test procedures are robust under different distributions of random errors. The asymptotic distributions of the proposed statistics are derived via a newly established joint central limit theorem for several general quadratic forms and the delta method. Good performance of the proposed tests is demonstrated by simulation results.