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Distribution of the ML Estimator of an MA(1) and a local level model

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  • Shephard, Neil

Abstract

Although considerable attention has recently been paid to the behavior of the maximum likelihood estimator of simple moving average models, little progress has been made in finding a good approximation to its distribution in cases where the process is close to being noninvertible. In this paper a method is produced that gives an excellent approximation to the distribution function, even in the case where the process is strictly noninvertible. Also studied is the related problem of the distribution of the maximum likelihood estimator of the signalto-noise ratio in the local level model.

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  • Shephard, Neil, 1993. "Distribution of the ML Estimator of an MA(1) and a local level model," Econometric Theory, Cambridge University Press, vol. 9(3), pages 377-401, June.
    • Handle: RePEc:cup:etheor:v:9:y:1993:i:03:p:377-401_00
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    1. Atkinson, A. C. & Koopman, S. J. & Shephard, N., 1997. "Detecting shocks: Outliers and breaks in time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 387-422, October.
    2. Hirano, Keisuke & Wright, Jonathan H., 2022. "Analyzing cross-validation for forecasting with structural instability," Journal of Econometrics, Elsevier, vol. 226(1), pages 139-154.
    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. Eddie Dekel & Michele Piccione, 1997. "On the Equivalence of Simultaneous and Sequential Binary Elections," Discussion Papers 1206, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Koop, Gary & Dijk, Herman K. Van, 2000. "Testing for integration using evolving trend and seasonals models: A Bayesian approach," Journal of Econometrics, Elsevier, vol. 97(2), pages 261-291, August.
    6. Solimene, L., 1994. "Total factor productivity in the Italian telecommunications industry," Discussion Paper Series In Economics And Econometrics 9401, Economics Division, School of Social Sciences, University of Southampton.
    7. Ulph, A., 1997. "Harmonisation, minimum standards and optimal international environmental policy under asymmetric information," Discussion Paper Series In Economics And Econometrics 9701, Economics Division, School of Social Sciences, University of Southampton.
    8. 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.
    9. Blackburn, K. & Mongiardino, A. & Sola, M., 1992. "Was there an "EMS Effect" in the European disinflation?," Discussion Paper Series In Economics And Econometrics 9201, Economics Division, School of Social Sciences, University of Southampton.
    10. James H. Stock & Mark W. Watson, 1996. "Asymptotically Median Unbiased Estimation of Coefficient Variance in a Time Varying Parameter Model," NBER Technical Working Papers 0201, National Bureau of Economic Research, Inc.
    11. Ulph, A. & Ulph, D., 1996. "Global warming, irreversibility and learning," Discussion Paper Series In Economics And Econometrics 9601, Economics Division, School of Social Sciences, University of Southampton.
    12. Dordonnat, Virginie & Koopman, Siem Jan & Ooms, Marius, 2012. "Dynamic factors in periodic time-varying regressions with an application to hourly electricity load modelling," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3134-3152.
    13. Beyer, A., 1995. "The causal link between money and prices in Germany," Discussion Paper Series In Economics And Econometrics 9501, Economics Division, School of Social Sciences, University of Southampton.
    14. Ismail, A.G., 1993. "Profit-sharing in the modelling of Islamic banks," Discussion Paper Series In Economics And Econometrics 9301, Economics Division, School of Social Sciences, University of Southampton.

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