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Linear least squares estimation of the first order moving average parameter

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  • Emili Valdero Mora

    (Universitat de Barcelona)

Abstract

We propose an iterative procedure to minimize the sum of squares function which avoids the nonlinear nature of estimating the rst order moving average parameter and provides a closed form of the estimator. The asymptotic properties of the method are discussed and the consistency of the linear least squares estimator is proved for the invertible case. We perform various Monte Carlo experiments in order to compare the sample properties of the linear least squares estimator with its nonlinear counterpart for the conditional and unconditional cases. Some examples are also discussed.

Suggested Citation

  • Emili Valdero Mora, 2002. "Linear least squares estimation of the first order moving average parameter," Working Papers in Economics 80, Universitat de Barcelona. Espai de Recerca en Economia.
    • Handle: RePEc:bar:bedcje:200280
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    References listed on IDEAS

    as
    1. Davidson, James E. H., 1981. "Problems with the estimation of moving average processes," Journal of Econometrics, Elsevier, vol. 16(3), pages 295-310, August.
    2. Nelson, Charles R., 1974. "The first-order moving average process : Identification, estimation and prediction," Journal of Econometrics, Elsevier, vol. 2(2), pages 121-141, July.
    3. Sargan, J D & Bhargava, Alok, 1983. "Maximum Likelihood Estimation of Regression Models with First Order Moving Average Errors When the Root Lies on the Unit Circle," Econometrica, Econometric Society, vol. 51(3), pages 799-820, May.
    4. Dent, Warren & Min, An-Sik, 1978. "A Monte Carlo study of autoregressive integrated moving average processes," Journal of Econometrics, Elsevier, vol. 7(1), pages 23-55, February.
    5. T. W. Anderson & Akimichi Takemura, 1986. "Why Do Noninvertible Estimated Moving Averages Occur?," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(4), pages 235-254, July.
    6. Ansley, Craig F. & Newbold, Paul, 1980. "Finite sample properties of estimators for autoregressive moving average models," Journal of Econometrics, Elsevier, vol. 13(2), pages 159-183, June.
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    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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