# Asymptotic normality of the time-domain generalized least squares estimator for linear regression models

## TL;DR

This paper proves that the time-domain generalized least squares estimator is asymptotically normal for a broad class of error dependence models in linear regression, extending previous results limited to specific structures.

## Contribution

It establishes the asymptotic normality of the time-domain IGLS estimator under general dependence models, broadening the scope beyond prior frequency domain results.

## Key findings

- Asymptotic normality of time-domain IGLS estimator proven for general dependence models
- Extends previous results limited to specific error structures
- Provides theoretical foundation for inference with misspecified GLS in time domain

## Abstract

In linear models, the generalized least squares (GLS) estimator is applicable when the structure of the error dependence is known. When it is unknown, such structure must be approximated and estimated in a manner that may lead to misspecification. The large-sample analysis of incorrectly-specified GLS (IGLS) estimators requires careful asymptotic manipulations. When performing estimation in the frequency domain, the asymptotic normality of the IGLS estimator, under the so-called Grenander assumptions, has been proved for a broad class of error dependence models. Under the same assumptions, asymptotic normality results for the time-domain IGLS estimator are only available for a limited class of error structures. We prove that the time-domain IGLS estimator is asymptotically normal for a general class of dependence models.