Lower bounds for volatility estimation in microstructure noise models
2010 | book part
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Lower bounds for volatility estimation in microstructure noise models
Munk, A. & Schmidt-Hieber, J. (2010)
In:Berger, James O.; Cai, T. Tony; Johnstone, Iain M. (Eds.), Borrowing Strength: Theory Powering Applications – A Festschrift for Lawrence D. Brown pp. 43-55. Beachwood, Ohio, USA: Institute of Mathematical Statistics. DOI: https://doi.org/10.1214/10-IMSCOLL604
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Details
- Authors
- Munk, Axel ; Schmidt-Hieber, Johannes
- Editors
- Berger, James O.; Cai, T. Tony; Johnstone, Iain M.
- Abstract
- n this paper minimax lower bounds are derived for the estimation of the instantaneous volatility in three related high-frequency statistical models. These bounds are based on new upper bounds for the Kullback-Leibler divergence between two multivariate normal random variables along with a spectral analysis of the processes. A comparison with known upper bounds shows that these lower bounds are optimal. Our major finding is that the Gaussian microstructure noise introduces an additional degree of ill-posedness for each model, respectively.
- Issue Date
- 2010
- Publisher
- Institute of Mathematical Statistics
- Language
- English