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Microstructure noise in the continuous case: the pre-averaging approach. (English) Zbl 1166.62078

Summary: This paper presents a generalized pre-averaging approach for estimating the integrated volatility, in the presence of noise. This approach also provides consistent estimators of other powers of volatility; in particular, it gives feasible ways to consistently estimate the asymptotic variance of the estimator of the integrated volatility. We show that our approach, which possesses an intuitive transparency, can generate rate optimal estimators (with convergence rate \(n^{ - 1/4}\)).

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
60G44 Martingales with continuous parameter
62M09 Non-Markovian processes: estimation
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60G42 Martingales with discrete parameter
62G20 Asymptotic properties of nonparametric inference
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