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Bias reduction of the maximum-likelihood estimator for a conditional Gaussian MA(1) model

Author

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  • Takeshi Kurosawa
  • Kohei Noguchi
  • Fumiaki Honda

Abstract

In this paper, we consider an estimation for the unknown parameters of a conditional Gaussian MA(1) model. In the majority of cases, a maximum-likelihood estimator is chosen because the estimator is consistent. However, for small sample sizes the error is large, because the estimator has a bias of O(n− 1). Therefore, we provide a bias of O(n− 1) for the maximum-likelihood estimator for the conditional Gaussian MA(1) model. Moreover, we propose new estimators for the unknown parameters of the conditional Gaussian MA(1) model based on the bias of O(n− 1). We investigate the properties of the bias, as well as the asymptotical variance of the maximum-likelihood estimators for the unknown parameters, by performing some simulations. Finally, we demonstrate the validity of the new estimators through this simulation study.

Suggested Citation

  • Takeshi Kurosawa & Kohei Noguchi & Fumiaki Honda, 2017. "Bias reduction of the maximum-likelihood estimator for a conditional Gaussian MA(1) model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(17), pages 8588-8602, September.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:17:p:8588-8602
    DOI: 10.1080/03610926.2016.1185119
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