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ON M‐Estimation Under Long‐Range Dependence in Volatility

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  • Jan Beran

Abstract

. We consider M‐estimation of a location parameter for processes with zero autocorrelations but long‐range dependence in volatility. The observed process is the product of i.i.d. Gaussian observations and a long‐memory Gaussian process. For nonlinear estimators, the rate of convergence depends on the type of the ψ‐function. For skew‐symmetric ψ‐functions, a central limit theorem with ‐rate of convergence holds, under suitable regularity assumptions. This is not true in general for M‐estimators where the ψ‐function is not skewsymmetric.

Suggested Citation

  • Jan Beran, 2007. "ON M‐Estimation Under Long‐Range Dependence in Volatility," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(1), pages 138-153, January.
    • Handle: RePEc:bla:jtsera:v:28:y:2007:i:1:p:138-153
    DOI: 10.1111/j.1467-9892.2006.00506.x
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