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Edgeworth and Moment Approximations: The Case of MM and QML Estimators for the MA(1) Models


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  • Dimitra Kyriakopoulou


  • Antonis Demos



Extending the results in Sargan (1976) and Tanaka (1984), we derive the asymptotic expansions, of the Edgeworth and Nagar type, of the MM and QML estimators of the 1^{st} order autocorrelation and the MA parameter for the MA(1) model. It turns out that the asymptotic properties of the estimators depend on whether the mean of the process is known or estimated. A comparison of the Nagar expansions, either in terms of bias or MSE, reveals that there is not uniform superiority of neither of the estimators, when the mean of the process is estimated. This is also confirmed by simulations. In the zero-mean case, and on theoretical grounds, the QMLEs are superior to the MM ones in both bias and MSE terms. The results presented here are important for deciding on the estimation method we choose, as well as for bias reduction and increasing the efficiency of the estimators.

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Bibliographic Info

Paper provided by Athens University of Economics and Business in its series DEOS Working Papers with number 1003.

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Date of creation: 06 Apr 2008
Date of revision: 03 May 2010
Handle: RePEc:aue:wpaper:1003

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Related research

Keywords: Edgeworth expansion; moving average process; method of moments; Quasi Maximum Likelihood; autocorrelation; asymptotic properties.;

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Cited by:
  1. Antonis Demos & Stelios Arvanitis, 2010. "A New Class of Indirect Estimators and Bias Correction," DEOS Working Papers 1023, Athens University of Economics and Business.
  2. Antonis Demos & Stelios Arvanitis, 2012. "On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Estimators (Extended Revised Appendix)," DEOS Working Papers 1230, Athens University of Economics and Business.
  3. Stelios Arvanitis & Antonis Demos, 2014. "On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Inference Estimators," DEOS Working Papers 1406, Athens University of Economics and Business.


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