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On location estimation for LARCH processes

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  • Beran, Jan
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    Abstract

    We consider location estimation when the error process is a stationary LARCH process with long memory in the second moments. The asymptotic distribution of the sample mean and nonlinear M-estimators of the location parameter are derived. Essential assumptions for obtaining asymptotic normality with -rate of convergence are symmetry of the innovation distribution and skew-symmetry of the [psi]-function.

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    File URL: http://www.sciencedirect.com/science/article/B6WK9-4J2W09T-2/2/669775a2ae0106302b292220dce8c7e0
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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 97 (2006)
    Issue (Month): 8 (September)
    Pages: 1766-1782

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    Handle: RePEc:eee:jmvana:v:97:y:2006:i:8:p:1766-1782

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    Related research

    Keywords: Long memory M-estimator LARCH process Volatility Central limit theorem Location estimation;

    References

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    1. Chen, Shijie & Mukherjee, Kanchan, 1999. "Asymptotic uniform linearity of some robust statistics under exponentially subordinated strongly dependent models," Statistics & Probability Letters, Elsevier, vol. 44(2), pages 137-146, August.
    2. Liudas Giraitis & Remigijus Leipus & Peter M Robinson & Donatas Surgailis, 2003. "LARCH, Leverage and Long Memory," STICERD - Econometrics Paper Series /2003/460, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus, 2000. "Stationary Arch Models: Dependence Structure And Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 16(01), pages 3-22, February.
    4. Koul, Hira L., 1992. "M-estimators in linear models with long range dependent errors," Statistics & Probability Letters, Elsevier, vol. 14(2), pages 153-164, May.
    5. Peter M Robinson, 2001. "The Memory of Stochastic Volatility Models," STICERD - Econometrics Paper Series /2001/410, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    6. Jan Beran & Yuanhua Feng, 1999. "Local Polynomial Estimation with a FARIMA-GARCH Error Process," CoFE Discussion Paper 99-08, Center of Finance and Econometrics, University of Konstanz.
    7. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
    8. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    9. Giraitis, Liudas & Koul, Hira L. & Surgailis, Donatas, 1996. "Asymptotic normality of regression estimators with long memory errors," Statistics & Probability Letters, Elsevier, vol. 29(4), pages 317-335, September.
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    Cited by:
    1. Christian Francq & Jean-Michel Zakoïan, 2010. "Inconsistency of the MLE and inference based on weighted LS for LARCH models," Post-Print peer-00732536, HAL.
    2. Francq, Christian & Zakoian, Jean-Michel, 2009. "Inconsistency of the QMLE and asymptotic normality of the weighted LSE for a class of conditionally heteroscedastic models," MPRA Paper 15147, University Library of Munich, Germany.

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