Finite-Sample Bias of the Conditional Gaussian Maximum Likelihood Estimator in ARMA Models

Advances in Econometrics, 2016, 36, 207–244. https://doi.org/10.1108/S0731-905320160000036015

Posted: 27 Feb 2016 Last revised: 21 Sep 2022

Date Written: October 19, 2015

Abstract

I derive the finite-sample bias of the conditional Gaussian maximum likelihood estimator in ARMA models when the error follows some unknown nonnormal distribution. The general procedure relies on writing down the score function and its higher-order derivative matrices in terms of quadratic forms in the nonnormal error vector with the help of matrix calculus. Evaluation of the bias can then be straightforwardly conducted. I give further simplified bias results for some special cases and compare with the existing results in the literature. Simulations are provided to confirm my simplified bias results.

Keywords: ARMA, conditional Gaussian maximum likelihood estimator, Bias

JEL Classification: C32, C12

Suggested Citation

Bao, Yong, Finite-Sample Bias of the Conditional Gaussian Maximum Likelihood Estimator in ARMA Models (October 19, 2015). Advances in Econometrics, 2016, 36, 207–244. https://doi.org/10.1108/S0731-905320160000036015, Available at SSRN: https://ssrn.com/abstract=2738162

Yong Bao (Contact Author)

Purdue University ( email )

Department of Economics
West Lafayette, IN 47907
United States

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