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An estimator for the quadratic covariation of asynchronously observed Itô processes with noise: Asymptotic distribution theory, Stochastic Process
 Appl
"... We consider estimation of the quadratic (co)variation of a semimartingale from discrete observations which are irregularly spaced under highfrequency asymptotics. In the univariate setting, results from Jacod (2008) are generalized to the case of irregular observations. In the twodimensional setup ..."
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Cited by 11 (6 self)
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We consider estimation of the quadratic (co)variation of a semimartingale from discrete observations which are irregularly spaced under highfrequency asymptotics. In the univariate setting, results from Jacod (2008) are generalized to the case of irregular observations. In the twodimensional setup under nonsynchronous observations, we derive a stable central limit theorem for the estimator by Hayashi and Yoshida (2005) in the presence of jumps. We reveal how idiosyncratic and simultaneous jumps affect the asymptotic distribution. Observation times generated by Poisson processes are explicitly discussed.
ESTIMATING THE QUADRATIC COVARIATION MATRIX FROM NOISY OBSERVATIONS: LOCAL METHOD OF MOMENTS AND EFFICIENCY
, 1303
"... An efficient estimator is constructed for the quadratic covariation or integrated covolatility matrix of a multivariate continuous martingale based on noisy and nonsynchronous observations under highfrequency asymptotics. Our approach relies on an asymptotically equivalent continuoustime observat ..."
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Cited by 10 (3 self)
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An efficient estimator is constructed for the quadratic covariation or integrated covolatility matrix of a multivariate continuous martingale based on noisy and nonsynchronous observations under highfrequency asymptotics. Our approach relies on an asymptotically equivalent continuoustime observation model where a local generalised method of moments in the spectral domain turns out to be optimal. Asymptotic semiparametric efficiency is established in the CramérRao sense. Main findings are that nonsynchronicity of observation times has no impact on the asymptotics and that major efficiency gains are possible under correlation. Simulations illustrate the finitesample behaviour. 1. Introduction. The
ASYMPTOTIC EQUIVALENCE FOR INHOMOGENEOUS JUMP DIFFUSION PROCESSES AND WHITE NOISE.
"... Abstract. We prove the global asymptotic equivalence between the experiments generated by the discrete (high frequency) or continuous observation of a path of a time inhomogeneous jumpdiffusion process and a Gaussian white noise experiment. Here, the considered parameter is the drift function, and ..."
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Cited by 1 (1 self)
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Abstract. We prove the global asymptotic equivalence between the experiments generated by the discrete (high frequency) or continuous observation of a path of a time inhomogeneous jumpdiffusion process and a Gaussian white noise experiment. Here, the considered parameter is the drift function, and we suppose that the observation time T tends to ∞. The approximation is given in the sense of the Le Cam ∆distance, under smoothness conditions on the unknown drift function. These asymptotic equivalences are established by constructing explicit Markov kernels that can be used to reproduce one experiment from the other. 1.
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"... SFB 649 Discussion Paper 2014005 Functional stable limit theorems for efficient spectral covolatility estimators Randolf Altmeyer* ..."
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SFB 649 Discussion Paper 2014005 Functional stable limit theorems for efficient spectral covolatility estimators Randolf Altmeyer*
Adaptive wavelet estimation of the diffusion coefficient under additive error measurements
, 2012
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Common price and volatility jumps in noisy highfrequency data
"... We introduce a statistical test for simultaneous jumps in the price of a financial asset and its volatility process. The proposed test is based on highfrequency tickdata and is robust to market microstructure frictions. To localize volatility jumps, we design and analyze a nonparametric spectral e ..."
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We introduce a statistical test for simultaneous jumps in the price of a financial asset and its volatility process. The proposed test is based on highfrequency tickdata and is robust to market microstructure frictions. To localize volatility jumps, we design and analyze a nonparametric spectral estimator of the spot volatility process. A simulation study and an empirical example with NASDAQ order book data demonstrate the practicability of the proposed methods and highlight the important role played by price volatility cojumps.