Time endogeneity and an optimal weight function in pre-averaging covariance estimation
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We establish a central limit theorem for a class of pre-averaging covariance estimators in a general endogenous time setting. In particular, we show that the time endogeneity has no impact on the asymptotic distribution if certain functionals of observation times are asymptotically well-defined. This contrasts with the case of the realized volatility in a pure diffusion setting. We also discuss an optimal choice of the weight function in the pre-averaging.
KeywordsCentral limit theorem Jumps Market microstructure noise Non-synchronous observations Pre-averaging Time endogeneity
The author thanks the Editors and an anonymous referee for their careful reading and helpful comments. In particular, the author strongly appreciates the referee for having pointed out errors in the statement of Proposition 5.1 and the proof of Proposition 6.1 contained in earlier versions of the paper. The author is also grateful to Teppei Ogihara who pointed out a problem on the mathematical construction of the noise process in a previous version of this paper. This work was partly supported by Grant-in-Aid for JSPS Fellows, the Program for Leading Graduate Schools, MEXT, Japan and CREST JST.
- Bibinger M, Mykland PA (2014) Inference for multi-dimensional high-frequency data: equivalence of methods, central limit theorems, and an application to conditional independence testing, preprint. arXiv: http://arxiv.org/abs/1301.2074
- Koike Y (2013) Central limit theorems for pre-averaging covariance estimators under endogenous sampling times, unpublished paper. arXiv: http://arxiv.org/abs/1305.1229
- Koike Y (2015a) Estimation of integrated covariances in the simultaneous presence of nonsynchronicity, microstructure noise and jumps. Econom. Theory (forthcoming). doi: 10.1017/S0266466614000954
- Koike Y (2015b) Quadratic covariation estimation of an irregularly observed semimartingale with jumps and noise. Bernoulli (forthcoming). arXiv: http://arxiv.org/abs/1408.0938v2
- Li J, Todorov V, Tauchen G (2014a) Jump regressions, working paperGoogle Scholar
- Mancini C (2001) Disentangling the jumps of the diffusion in a geometric jumping Brownian motion. G dell’Istituto Ital degli Attuari 64:19–47Google Scholar
- Mykland PA, Zhang L (2012) The econometrics of high-frequency data. In: Kessler M, Lindner A, Sørensen M (eds) Statistical methods for stochastic differential equations, chap 3. CRC Press, Boca RatonGoogle Scholar
- Ogihara T (2014) Parametric inference for nonsynchronously observed diffusion processes in the presence of market microstructure noise. arXiv: http://arxiv.org/abs/1412.8173
- Potiron Y, Mykland PA (2015) Estimation of integrated quadratic covariation between two assets with endogenous sampling times, working paper. arXiv: http://arxiv.org/abs/1507.01033