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Why Do Noninvertible Estimated Moving Averages Occur?

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  • T. W. Anderson
  • Akimichi Takemura

Abstract

. The positive probability that an estimated moving average process is noninvertible is studied for maximum likelihood estimation of a university process. Upper and lower bounds for the probability in the first‐order case are obtained as well as limits when the sample size tends to infinity. Higher order moving average models and autoregressive moving average models are also treated.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:7:y:1986:i:4:p:235-254
    DOI: 10.1111/j.1467-9892.1986.tb00492.x
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    Cited by:

    1. Vougas, Dimitrios V., 2008. "New exact ML estimation and inference for a Gaussian MA(1) process," Economics Letters, Elsevier, vol. 99(1), pages 172-176, April.
    2. Giorgio Canarella & Luis A. Gil-Alana & Rangan Gupta & Stephen M. Miller, 2022. "Globalization, long memory, and real interest rate convergence: a historical perspective," Empirical Economics, Springer, vol. 63(5), pages 2331-2355, November.
    3. Kim, Chang-Jin & Kim, Jaeho, 2013. "The `Pile-up Problem' in Trend-Cycle Decomposition of Real GDP: Classical and Bayesian Perspectives," MPRA Paper 51118, University Library of Munich, Germany.
    4. Yabe, Ryota, 2017. "Asymptotic distribution of the conditional-sum-of-squares estimator under moderate deviation from a unit root in MA(1)," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 220-226.
    5. Monti, Anna Clara, 1996. "A new preliminary estimator for MA(1) models," Computational Statistics & Data Analysis, Elsevier, vol. 21(1), pages 1-15, January.
    6. Pollock, D.S.G., 1991. "On the criterion function for arma estimation," Serie Research Memoranda 0074, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    7. Michael A. Hauser, 1998. "Maximum Likelihood Estimators for ARMA and ARFIMA Models: A Monte Carlo Study," Econometrics 9809001, University Library of Munich, Germany.
    8. 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.
    9. Robert Paige & A. Trindade & R. Wickramasinghe, 2014. "Extensions of saddlepoint-based bootstrap inference," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 961-981, October.
    10. Consuelo Arellano & Sastry G. Pantula, 1995. "Testing For Trend Stationarity Versus Difference Stationarity," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(2), pages 147-164, March.
    11. Kohei Noda & Tomoyuki Shirai, 2023. "Expected Number of Zeros of Random Power Series with Finitely Dependent Gaussian Coefficients," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1534-1554, September.
    12. Yoonsuk Lee & B. Wade Brorsen, 2017. "Permanent Breaks and Temporary Shocks in a Time Series," Computational Economics, Springer;Society for Computational Economics, vol. 49(2), pages 255-270, February.
    13. Davis, Richard A. & Mikosch, Thomas, 1998. "Gaussian likelihood-based inference for non-invertible MA(1) processes with SS noise," Stochastic Processes and their Applications, Elsevier, vol. 77(1), pages 99-122, September.
    14. YABE, Ryota & 矢部, 竜太, 2014. "Asymptotic Distribution of the Conditional Sum of Squares Estimator Under Moderate Deviation From a Unit Root in MA(1)," Discussion Papers 2014-19, Graduate School of Economics, Hitotsubashi University.

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