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Asymptotic Properties of the Maximum-Likelihood and Nonlinear Least-Squares Estimators for Noninvertible Moving Average Models

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  • Tanaka, Katsuto
  • Satchell, S.E.

Abstract

Dealing with noninvertible, infinite-order moving average (MA) models, we study the asymptotic properties of an estimator of the noninvertible coefficient. The estimator is constructed acting as if the data were generated from a Gaussian MA process. Allowing for two cases on the initial values of the error process, we first discuss the condition for the existence of a consistent estimator. We then compute the probability of the estimator occurring at the boundary of the invertibility region. Some approximations are also suggested to the limiting distribution of the normalized estimator.

Suggested Citation

  • Tanaka, Katsuto & Satchell, S.E., 1989. "Asymptotic Properties of the Maximum-Likelihood and Nonlinear Least-Squares Estimators for Noninvertible Moving Average Models," Econometric Theory, Cambridge University Press, vol. 5(3), pages 333-353, December.
    • Handle: RePEc:cup:etheor:v:5:y:1989:i:03:p:333-353_01
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    Cited by:

    1. 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.
    2. Luukkonen, Ritva & Saikkonen, Pentti, 1996. "Power of the Lagrange multiplier test for testing an autoregressive unit root," Economics Letters, Elsevier, vol. 51(1), pages 27-35, April.
    3. 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.
    4. Sutradhar, Brajendra C. & Kumar, Pranesh, 2001. "On the efficiency of extended generalized estimating equation approaches," Statistics & Probability Letters, Elsevier, vol. 55(1), pages 53-61, November.
    5. McKenzie, Michael & Satchell, Stephen & Wongwachara, Warapong, 2012. "Nonlinearity and smoothing in venture capital performance data," Journal of Empirical Finance, Elsevier, vol. 19(5), pages 782-795.
    6. 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.
    7. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2004. "Regular and Modified Kernel-Based Estimators of Integrated Variance: The Case with Independent Noise," Economics Papers 2004-W28, Economics Group, Nuffield College, University of Oxford.

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