The effect of long memory in volatility on location estimation

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2008
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Schützner, Martin
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Zusammenfassung

We consider the question in how far long memory in volatility affects the asymptotic distribution of location estimators. Specifically, we consider Mestimation for models with finite moments. Under symmetry assumptions, the asymptotic distribution turns out to be the same as under independence, even if a nonlinear estimator is used. However, for nonlinear estimators, deviations from these assumptions can imply a slower rate of convergence and hence asymptotic efficiency zero compared to the sample mean. This means that for long-memory volatility models, estimators that are robust with respect to bias, turn out to be extremely sensitive with respect to the variance. Simulations and data examples illustrate the results by comparing the asymptotic behaviour of the sample mean, the median and a Huber estimator with an intermediate tuning parameter.

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Fachgebiet (DDC)
510 Mathematik
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M-estimator, long memory, location estimation, Appell polynomials, central limit theorem, Hermite process, volatility
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ISO 690BERAN, Jan, Martin SCHÜTZNER, 2008. The effect of long memory in volatility on location estimation. In: Sankhya. 2008, 70(1), pp. 84-112. ISSN 0976-8386. eISSN 0976-8394
BibTex
@article{Beran2008effec-794,
  year={2008},
  title={The effect of long memory in volatility on location estimation},
  number={1},
  volume={70},
  issn={0976-8386},
  journal={Sankhya},
  pages={84--112},
  author={Beran, Jan and Schützner, Martin}
}
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