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Limit Theory for M-Estimates in an Integrated Infinite Variance

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  • Knight, Keith

Abstract

We consider the limiting distributions of M-estimates of an “autoregressive” parameter when the observations come from an integrated linear process with infinite variance innovations. It is shown that M-estimates are, asymptotically, infinitely more efficient than the least-squares estimator (in the sense that they have a faster rate of convergence) and are conditionally asymptotically normal.

Suggested Citation

  • Knight, Keith, 1991. "Limit Theory for M-Estimates in an Integrated Infinite Variance," Econometric Theory, Cambridge University Press, vol. 7(2), pages 200-212, June.
    • Handle: RePEc:cup:etheor:v:7:y:1991:i:02:p:200-212_00
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    Cited by:

    1. Serttas, Fatma Ozgu, 2010. "Essays on infinite-variance stable errors and robust estimation procedures," ISU General Staff Papers 201001010800002742, Iowa State University, Department of Economics.
    2. Lima Luiz Renato & Xiao Zhijie, 2010. "Testing Unit Root Based on Partially Adaptive Estimation," Journal of Time Series Econometrics, De Gruyter, vol. 2(1), pages 1-34, June.
    3. Galvao Jr., Antonio F., 2009. "Unit root quantile autoregression testing using covariates," Journal of Econometrics, Elsevier, vol. 152(2), pages 165-178, October.
    4. Uwe Hassler & Paulo M.M. Rodrigues & Antonio Rubia, 2016. "Quantile Regression for Long Memory Testing: A Case of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 14(4), pages 693-724.
    5. Hasan, Mohammad N., 2001. "Rank tests of unit root hypothesis with infinite variance errors," Journal of Econometrics, Elsevier, vol. 104(1), pages 49-65, August.
    6. Phillips, Peter C.B., 1995. "Robust Nonstationary Regression," Econometric Theory, Cambridge University Press, vol. 11(5), pages 912-951, October.
    7. Jungjun Choi & In Choi, 2019. "Maximum likelihood estimation of autoregressive models with a near unit root and Cauchy errors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1121-1142, October.
    8. Pierre Perron & Eduardo Zorita & Iliyan Georgiev & Paulo M. M. Rodrigues & A. M. Robert Taylor, 2017. "Unit Root Tests and Heavy-Tailed Innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(5), pages 733-768, September.
    9. Magda Peligrad & Hailin Sang, 2013. "Central Limit Theorem for Linear Processes with Infinite Variance," Journal of Theoretical Probability, Springer, vol. 26(1), pages 222-239, March.
    10. Chan, Ngai Hang & Zhang, Rong-Mao, 2009. "Quantile inference for near-integrated autoregressive time series under infinite variance and strong dependence," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4124-4148, December.
    11. Christis Katsouris, 2023. "Quantile Time Series Regression Models Revisited," Papers 2308.06617, arXiv.org, revised Aug 2023.
    12. Serguei Zernov & Victoria Zindle-Walsh & John Galbraith, 2006. "Asymptotics For Estimation Of Truncated Infinite-Dimensional Quantile Regressions," Departmental Working Papers 2006-16, McGill University, Department of Economics.
    13. Alain Hecq & Li Sun, 2019. "Identification of Noncausal Models by Quantile Autoregressions," Papers 1904.05952, arXiv.org.
    14. Bravo, Francesco & Li, Degui & Tjøstheim, Dag, 2021. "Robust nonlinear regression estimation in null recurrent time series," Journal of Econometrics, Elsevier, vol. 224(2), pages 416-438.
    15. Zernov, Serguei & Zinde-Walsh, Victoria & Galbraith, John W., 2009. "Asymptotics for estimation of quantile regressions with truncated infinite-dimensional processes," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 497-508, March.
    16. Phillips, Peter C B & McFarland, James W & McMahon, Patrick C, 1996. "Robust Tests of Forward Exchange Market Efficiency with Empirical Evidence from the 1920s," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(1), pages 1-22, Jan.-Feb..
    17. Xiao, Zhijie, 2004. "Estimating average economic growth in time series data with persistency," Journal of Macroeconomics, Elsevier, vol. 26(4), pages 699-724, December.
    18. Lucas, Andre, 1995. "An outlier robust unit root test with an application to the extended Nelson-Plosser data," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 153-173.
    19. D. M. Mahinda Samarakoon & Keith Knight, 2009. "A Note on Unit Root Tests with Infinite Variance Noise," Econometric Reviews, Taylor & Francis Journals, vol. 28(4), pages 314-334.
    20. Hoek, Henk & Lucas, Andre & van Dijk, Herman K., 1995. "Classical and Bayesian aspects of robust unit root inference," Journal of Econometrics, Elsevier, vol. 69(1), pages 27-59, September.
    21. Horváth, Lajos & Kokoszka, Piotr, 2003. "A bootstrap approximation to a unit root test statistic for heavy-tailed observations," Statistics & Probability Letters, Elsevier, vol. 62(2), pages 163-173, April.

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