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Mathematical Methods of Statistics

, Volume 27, Issue 4, pp 268–293 | Cite as

Asymptotic Distribution of Least Squares Estimators for Linear Models with Dependent Errors: Regular Designs

  • E. CaronEmail author
  • S. Dede
Article
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Abstract

We consider the usual linear regression model in the case where the error process is assumed strictly stationary.We use a result of Hannan, who proved a Central Limit Theorem for the usual least squares estimator under general conditions on the design and the error process.We show that for a large class of designs, the asymptotic covariance matrix is as simple as in the independent and identically distributed (i.i.d.) case.We then estimate the covariance matrix using an estimator of the spectral density whose consistency is proved under very mild conditions.

Keywords

linear model least squares estimator short memory processes spectral density 

2000 Mathematics Subject Classification

62F12 62J05 62M10 62M15 
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Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Ecole Centrale NantesLaboratoire de Mathématiques Jean Leray UMRNantesFrance
  2. 2.Lycée StanislasParisFrance

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