A Note on the Asymptotic Properties of the GLS Estimator in Multivariate Regression with Heteroskedastic and Autocorrelated Errors

Paper: arXiv 2503.13950

Abstract

We study the asymptotic properties of the GLS estimator in multivariate regression with heteroskedastic and autocorrelated errors. We derive Wald statistics for linear restrictions and assess their performance. The statistics remains robust to heteroskedasticity and autocorrelation.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is highly theoretical, focusing on asymptotic properties, deriving Wald statistics, and presenting complex multivariate regression models with extensive LaTeX formulas, resulting in high mathematical complexity. However, it lacks any backtesting, code, or empirical data implementation, relying instead on simulation experiments for performance assessment, which suggests low empirical readiness.

Research Flowchart

  flowchart TD
  A["Research Goal: Analyze GLS estimator asymptotics<br>in multivariate regression with HAC errors"] --> B["Methodology: Asymptotic theory derivation"]
  B --> C["Data/Inputs: Multivariate regression model<br>with Heteroskedastic & Autocorrelated Errors"]
  C --> D["Computational Process: Derive Wald statistics<br>for linear restrictions"]
  D --> E["Key Findings: Statistics remain robust<br>to Heteroskedasticity & Autocorrelation"]