Diffusions with measurement errors. I. Local Asymptotic Normality

By Arnaud Gloter, Jean Jacod. 2001

149 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0d4399d52ad88d3c264def49dab9d28426a5faf4

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Citations in the corpus

How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise (2005, background): “Harris (1990b) notes that in practice there are sources of noise other than just the bid-ask spread, and studies their effect on the Roll model and its estimators.”
Variation, jumps, market frictions and high frequency data in financial econometrics (2005, unknown): “Note Gloter and Jacod (2001a) and Gloter and Jacod (2001b) also study what happens if Var(Uδi) varies with δ. F1 implies, for example, that [U ]t = ∞ which is inconvenient mathematically.”
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.”
Quasi-maximum likelihood estimation of volatility with high frequency data (2010, background): “In addition, other studies have shed light on its central limit theory, such as Jacod (1994) and Barndorff-Nielsen and Shephard (2002).”
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.”
Regular and Modified Kernel-Based Estimators of Integrated Variance: The Case with Independent Noise (2004, background): “This shows that the maximum likelihood estimator ofIV converges at the same rate,m1/4, as the modified kernel estimator, which indeed has been show to be the optimal rate of convergence in this context, see Gloter & Jacod (2001a, 2001b).”
Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps (2007, unknown): “The same assumption has already been used in Gloter and Jacod [13,14].”
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).”
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).”
High-dimensional minimum variance portfolio estimation based on high-frequency data (2020, unknown): “In fact, the optimal rate in estimating the integrated volatility in the noisy case is O(n1/4) (Gloter and Jacod (2001)), as is compared with the rate of O(n1/2) in the noiseless case.”
Integrated volatility and round-off error (2009, background): “We denote by Ck(I) the set of k times continuously differentiable functions on I ⊆ R.”
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).”
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 efficient price (Gloter and Jacod 2001a,b; Aı̈t-Sahalia, Mykland, and Zhang 2005a,b; Bandi and Russel 2005; Zhang, Mykland, and Aı̈t-Sahalia 2005; Zhang 2006a).”