Empirical likelihood ratio test for autocorrelation in least squares regression

Abstract

Detecting autocorrelation in regression models is crucial for accurate estimation and testing procedures. Among the various methods available, the Durbin–Watson (D-W) test is commonly utilized. However, a notable limitation of the D-W test is its reliance on an indeterminate range due to the intractable distribution of the D-W statistic. Consequently, the test yields inconclusive results when the statistic falls within this range. This paper introduces a distribution-free Empirical Likelihood Ratio Test (ELRT) for detecting autocorrelation in regression models. A Monte Carlo simulation study is carried out to compare the performance of the proposed ELRT with the D-W test, ( a + b d U ) approximation and bootstrapped D-W test based on size and power. The results show that the proposed ELRT considerably outperforms the original D-W test and ( a + b d U ) approximation test irrespective of sample size, level of autocorrelation and number of regressors. The proposed test is competitor for bootstrapped D-W test in terms of maintaining the empirical size and power for large samples, n ≥ 100 . As a real-life application, the working of the proposed test is illustrated through air quality data of Delhi.