Asymptotic equivalence for inference on the volatility from noisy observations

By Markus Reiß. 2011

98 citations recorded by the source corpus.

We consider discrete-time observations of a continuous martingale under measurement error. This serves as a fundamental model for high-frequency data in finance, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a Gaussian shift experiment in terms of the square root of the volatility function σ and a nonstandard noise level. As an application, new rate-optimal estimators of the volatility function and simple efficient estimators of the integrated volatility are constructed.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/20af2e98c954db5e52367b857a299e76b4a1234b

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Citations in the corpus

FAST CONVERGENCE RATES IN ESTIMATING LARGE VOLATILITY MATRICES USING HIGH-FREQUENCY FINANCIAL DATA (2013, background): “Theorem 1 indicates that the convergence rate for each element of the MSRVM estimator Γ̂ is n−1/4, which is the optimal convergence rate for estimating each element of Γ (see Gloter and Jacod, 2001; Reiss, 2011).”
Estimating the Spot Covariation of Asset Prices—Statistical Theory and Empirical Evidence (2014, unknown): “Related approaches for a univariate framework can be found in Hansen, Large, and Lunde (2008), Reiß (2011), and Curci and Corsi (2012).”
An estimator for the quadratic covariation of asynchronously observed Itô processes with noise: Asymptotic distribution theory (2011, background): “Gaussian noise, asymptotic equivalence in the Le Cam sense to a Gaussian shift experiment is shown in [26] and an asymptotically efficient estimator whose asymptotic variance equals the parametric efficiency bound is constructed.”
Modelling microstructure noise with mutually exciting point processes (2011, background): “It will also be interesting to consider non-parametric estimates of the kernel shapes (uij) along the line of the work of Reynaud-Bouret and Schbath (2010) and to consider various questions related to the well-known non-stationarity and long-range correlations of the volatility.”
Estimating the Quadratic Covariation Matrix from Noisy Observations: Local Method of Moments and Efficiency (2013, unknown): “1 in [22] for information on Hellinger distances between Gaussian measures and bounds with the Hilbert–Schmidt norm.”
OPTIMAL SPARSE VOLATILITY MATRIX ESTIMATION FOR HIGH-DIMENSIONAL ITÔ PROCESSES WITH MEASUREMENT ERRORS (2013, methodology): “In particular we may have any contemporaneous correlations between ε i ( t ℓ ) and ε j ( t ℓ ) as well as lagged serial auto-correlations for individual noise ε i ( · ) and lagged serial cross-correlations be-tween ε i ( ) and ε j ( ) with lags up to M .”
Econometrics of co-jumps in high-frequency data with noise (2015, methodology): “Our estimation method brings together the efficient spectral covariance estimator by Reiß (2011) and Bibinger and Reiß (2013) and the concept of truncation.”