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Estimation of a linear regression model with stationary ARMA(p, q) errors

Authors
Journal
Journal of Econometrics
0304-4076
Publisher
Elsevier
Publication Date
Volume
47
Identifiers
DOI: 10.1016/0304-4076(91)90106-n
Disciplines
  • Computer Science
  • Mathematics

Abstract

Abstract It is well known that consistent estimation of a linear regression model with a stationary Gaussian ARMA process in the errors can be carried out by maximum likelihood or, alternatively, by two-stage procedures involving estimation of the nuisance parameters followed by feasible generalized least squares for the model parameters. We show that the estimators coincide up to O p(T − 3 2 ) and derive the variance to O( T −2), which up to terms of this order is the same for both estimators. Considering the form of the error covariance matrix for an ARMA( p,q) process allows us to examine a computationally convenient algorithm for estimation of the parameters of the regression model. Finally we provide a Monte Carlo comparison of the small-sample properties of OLS and two versions of the proposed estimator.

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