Diffusions with measurement errors. II. Optimal estimators

By Arnaud Gloter, Jean Jacod. 2001

99 citations recorded by the source corpus.

Subfields: Finance, Modeling and Simulation, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8d087ffb6b76e9aff8c73b0aa732d566a7e9c1f6

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Citations in the corpus

Fact or friction: jumps at ultra high frequency (2014, unknown): “The N − 1 / 4 rate of convergence is slow compared to the noiseless case, but it is the fastest possible that can be achieved in noisy diﬀusion models (see Gloter and Jacod, 2001a,b). is in proportion to the eﬃcient price variation.”
Microstructure Noise in the Continuous Case: The Pre-Averaging Approach ∗ (2008, background): “In practice we do not know how to choose µ in an optimal way (this is the drawback of all previously quoted papers as well, and especially for the e‐cient estimator of Gloter and Jacod (2001) ).”
Efficient Estimation of Stochastic Volatility Using Noisy Observations: A Multi-Scale Approach (2004, unknown): “Interestingly, the n 1=4 rate of convergence in our new estimator is the same as that in parametric estimation for volatility, when the true process is Markov (see Gloter and Jacod 2000a, 2000b).”
VOLATILITY AND COVARIATION ESTIMATION WHEN MICROSTRUCTURE NOISE AND TRADING TIMES ARE ENDOGENOUS (2012, background): “The more usual type is the case of an additive noise that is independent of the ecient price ([3], [4], [5], [15], [ 16 ], [35], [37]).”
Designing Realised Kernels to Measure the Ex-Post Variation of Equity Prices in the Presence of Noise (2008, background): “(7) The slow rate of convergence of σ̂2ML is a familiar result from the work of, for example, Stein (1987) and Gloter and Jacod (2001a, 2001b).”
Microstructure Noise, Realized Variance, and Optimal Sampling (2008, unknown): “Parametric likelihood-based identi…cation in the presence of noise is also studied in work by Gloter and Jacod (2001a, 2001b).”
OPTIMAL SPARSE VOLATILITY MATRIX ESTIMATION FOR HIGH-DIMENSIONAL ITÔ PROCESSES WITH MEASUREMENT ERRORS (2013, methodology): “…bivariate continuous Itˆo processes are observed with measurement errors at n discrete time points, the optimal convergence rates for estimating a univariate integrated volatility or a bivariate integrated co-volatility are n − 1 / 4 [Gloter and Jacod (2001a, 2001b), Reiß (2011), and Xiu (2010)].”
Statistical Properties of Microstructure Noise (2013, unknown): “Gloter and Jacod (2001), Li and Mykland (2007) and Rosenbaum (2009) studied the case when the noise is of specific form such as roundoff errors or round-off errors on top of additive white noise.”
A blocking and regularization approach to high dimensional realized covariance estimation (2012, unknown): “ofn1=4 for realized covariance estimators (see Gloter and Jacod, 2001; Kinnebrock and Podolskij, 2008).”
Asymptotic equivalence for inference on the volatility from noisy observations (2011, methodology): “Note that Gloter and Jacod (2001a) merely require α≥ 1/4 for their LAN-result, but our counterexample is excluded by their parametric setting.”
Pre-Averaging Estimators of the Ex-Post Covariance Matrix in Noisy Diffusion Models with Non-Synchronous Data (2010, background): “In the optimal case, called balanced pre-averaging, this leads to an efficient n−1/4 rate of convergence, which is known to be the fastest attainable (see, e.g., Gloter and Jacod, 2001a,b).”
Limit theorems for moving averages of discretized processes plus noise (2010, background): “[6] for a comprehensive theory in the parametric setting).”
Realised quantile-based estimation of the integrated variance (2010, background): “First, the rate of convergence in Theorem 5 is N−1/4, which is known to be optimal in the noisy diffusion model (Gloter and Jacod, 2001a,b).”
Edgeworth Expansions for Realized Volatility and Related Estimators (2011, background): “and Jacod (1997) in the context of rounding, and by Gloter and Jacod (2001) in the context of additive error.”