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On location estimation for LARCH processes

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  • Beran, Jan

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.

Suggested Citation

  • Beran, Jan, 2006. "On location estimation for LARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1766-1782, September.
  • Handle: RePEc:eee:jmvana:v:97:y:2006:i:8:p:1766-1782
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Liudas Giraitis, 2004. "LARCH, Leverage, and Long Memory," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(2), pages 177-210.
    8. Robinson, P. M., 2001. "The memory of stochastic volatility models," Journal of Econometrics, Elsevier, vol. 101(2), pages 195-218, April.
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    1. repec:hal:journl:peer-00732536 is not listed on IDEAS
    2. Francq, Christian & Zakoïan, Jean-Michel, 2010. "Inconsistency of the MLE and inference based on weighted LS for LARCH models," Journal of Econometrics, Elsevier, vol. 159(1), pages 151-165, November.
    3. 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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