Empirical likelihood estimation for linear regression models with AR(p) error terms with numerical examples.

Area of Science:

• Statistics
• Econometrics
• Data Analysis

Background:

• Linear regression models are widely used but often assume independent errors.
• Conditional Maximum Likelihood (CML) is common for correlated errors but requires distributional assumptions.
• These assumptions may not hold in real-world data.

Purpose of the Study:

• To propose and evaluate the Empirical Likelihood (EL) method for parameter estimation in linear regression models with autoregressive errors.
• To offer a distribution-free alternative to existing methods like CML.

Main Methods:

• The study proposes using the Empirical Likelihood (EL) method, a non-parametric approach.
• Parameter estimation is performed for linear regression models with autoregressive error terms.
• A simulation study compares EL with the Conditional Maximum Likelihood (CML) method.

Main Results:

• The Empirical Likelihood (EL) method significantly outperformed the Conditional Maximum Likelihood (CML) method.
• EL estimators showed lower mean squared errors (MSE) and bias compared to CML estimators.
• Findings were validated through numerical and real-data examples.

Conclusions:

• The Empirical Likelihood (EL) method is a robust and effective approach for linear regression with autoregressive errors.
• EL provides a valuable distribution-free alternative when error term assumptions are uncertain.
• This method offers improved accuracy in parameter estimation for time-series and related data.