The Autocorrelated Liu-Type Estimator: A Solution for Severe Multicollinearity and Autocorrelated Errors in Linear Regression Models

Abstract

The simultaneous existence of severe multicollinearity and autocorrelated errors in linear regression models poses substantial challenges for estimation precision and model stability. Although many studies have suggested solutions to tackle multicollinearity and autocorrelation simultaneously, such approaches are generally confined to mild or moderate instances of these problems and frequently underperform in more severe scenarios. Furthermore, Generalized Least Squares (GLS), while proficient at mitigating autocorrelation, fails to rectify multicollinearity. This paper presents the Autocorrelated Liu-Type Estimator (ALTE). This innovative biased estimating technique combines the shrinkage benefits of the Liu-Type estimator with the efficiency improvements of GLS in the context of autoregressive error processes. Theoretical characteristics of ALTE, including expectation, variance, and Mean Squared Error (MSE), are derived using canonical transformation and eigenvalue decomposition. Empirical validation using two real-world manufacturing datasets demonstrates ALTE's superior performance, consistently achieving lower MSE compared to GLS, Auto-Ridge Estimator (ARE), Auto-Liu, and Auto-Two-Parameter estimators. Additionally, a comprehensive Monte Carlo simulation study encompassing diverse sample sizes (n = 20, 50, 250), multicollinearity levels (γ² = 0.70, 0.80, 0.99), autocorrelation strengths (ρ = 0.3, 0.6, 0.9), and model dimensions (p = 2, 3, 5) substantiates ALTE's pronounced superiority, with Relative Efficiency (RE) improvements varying from 1.2 to almost 3.0. Assessments using RMSE and MAPE metrics support ALTE's practical applicability by demonstrating substantial improvements in prediction accuracy, particularly under severe multicollinearity and autocorrelation. These findings establish ALTE as a versatile and reliable tool for applied researchers addressing complex regression problems where traditional methods often fail.