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

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  • Kyriakopoulou, Dimitra
  • Demos, Antonis

Abstract

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.

Suggested Citation

  • Kyriakopoulou, Dimitra & Demos, Antonis, 2010. "Edgeworth and Moment Approximations: The Case of MM and QML Estimators for the MA (1) Models," MPRA Paper 122393, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:122393
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    Cited by:

    1. Arvanitis Stelios & Demos Antonis, 2018. "On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Inference Estimators," Journal of Econometric Methods, De Gruyter, vol. 7(1), pages 1-38, January.
    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. Demos Antonis & Kyriakopoulou Dimitra, 2019. "Finite-Sample Theory and Bias Correction of Maximum Likelihood Estimators in the EGARCH Model," Journal of Time Series Econometrics, De Gruyter, vol. 11(1), pages 1-20, January.
    4. Stelios Arvanitis & Antonis Demos, 2015. "A class of indirect inference estimators: higher‐order asymptotics and approximate bias correction," Econometrics Journal, Royal Economic Society, vol. 18(2), pages 200-241, June.
    5. Antonis Demos & Stelios Arvanitis, 2010. "A New Class of Indirect Estimators and Bias Correction," DEOS Working Papers 1023, Athens University of Economics and Business.
    6. Veiga, Helena, 2015. "Model uncertainty and the forecast accuracy of ARMA models: A survey," DES - Working Papers. Statistics and Econometrics. WS ws1508, Universidad Carlos III de Madrid. Departamento de Estadística.

    More about this item

    Keywords

    Edgeworth expansion; moving average process; method of moments; Quasi Maximum Likelihood; autocorrelation; asymptotic properties;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • Y1 - Miscellaneous Categories - - Data: Tables and Charts

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