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

In: Essays in Honor of Aman Ullah

Author

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  • Yong Bao

Abstract

I derive the finite-sample bias of the conditional Gaussian maximum likelihood estimator in ARMA models when the error follows some unknown non-normal distribution. The general procedure relies on writing down the score function and its higher order derivative matrices in terms of quadratic forms in the non-normal 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.

Suggested Citation

  • Yong Bao, 2016. "Finite-Sample Bias of the Conditional Gaussian Maximum Likelihood Estimator in ARMA Models," Advances in Econometrics, in: Essays in Honor of Aman Ullah, volume 36, pages 207-244, Emerald Group Publishing Limited.
    • Handle: RePEc:eme:aecozz:s0731-905320160000036015
    DOI: 10.1108/S0731-905320160000036015
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    More about this item

    Keywords

    ARMA; conditional Gaussian maximum likelihood estimator; bias; C32; C12;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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