Efficient Covariance Estimation for Asynchronous Noisy High‐Frequency Data

Bibinger, Markus

doi:10.1111/j.1467-9469.2010.00712.x

Cited by 44 publications

(68 citation statements)

References 24 publications

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“…The local weighted sums (5a) and (5b) on each block thus constitute the corresponding Karhunen-Loève expansion. We refer to Bibinger (2011) and Curci & Corsi (2012) as well as Gloter & Jacod (2001) for the one-dimensional case and for the explicit computation of the eigenvalues.…”

Section: Asymptotic Equivalence Of the Discrete Regression-type And Tmentioning

confidence: 99%

Spectral Estimation of Covolatility from Noisy Observations Using Local Weights

Bibinger

Reiß

2013

Scandinavian J Statistics

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ABSTRACT. We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes which are observed discretely with additive observation noise. The eligibility of this approach to lead to an appropriate estimation for time-varying volatilities stems from an asymptotic equivalence of the underlying statistical model to a white noise model with correlation and volatility processes being constant over small intervals. The asymptotic equivalence of the continuous-time and the discrete-time experiments are proved by a construction with linear interpolation in one direction and local means for the other. The new estimator outperforms earlier nonparametric approaches in the considered model. We investigate its finite sample size characteristics in simulations and draw a comparison between the various proposed methods.

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Section: Asymptotic Equivalence Of the Discrete Regression-type And Tmentioning

confidence: 99%

Spectral Estimation of Covolatility from Noisy Observations Using Local Weights

Bibinger

Reiß

2013

Scandinavian J Statistics

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“…[6] or [11]. We remark that the covariance matrix Ψ of the noise process ε always appears in the representation of …”

Section: Remark 32 (Univariate Case)mentioning

confidence: 99%

“…Also, for any b = 1, 2, 3 and as long as the conditions for the corresponding theorem above are satisfied, we have the standard central limit theorem 6) where…”

Section: Corollary 44 Under the Assumptions Of Theorem 34 We Obtainmentioning

confidence: 99%

“…In a second step, a noise robust estimator is constructed from this new data set. Similar in spirit is the extension of the multi-scale estimator due to [6], where synchronous observations are obtained using the pseudo-aggregation algorithm of [19] first. The resulting covariance estimator then becomes a multi-scale version of the Hayashi-Yoshida estimator from [12], which originally has been introduced to deal with non-synchronicity in semimartingale models without noise.…”

Section: Introductionmentioning

confidence: 99%

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On Covariation Estimation for Multivariate Continuous Itô Semimartingales with Noise in Non-Synchronous Observation Schemes

2011

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This paper presents a Hayashi-Yoshida type estimator for the covariation matrix of continuous Itô semimartingales observed with noise. The coordinates of the multivariate process are assumed to be observed at highly frequent nonsynchronous points. The estimator of the covariation matrix is designed via a certain combination of the local averages and the Hayashi-Yoshida estimator. Our method does not require any synchronization of the observation scheme (as e.g. previous tick method or refreshing time method) and it is robust to some dependence structure of the noise process.We show the associated central limit theorem for the proposed estimator and provide a feasible asymptotic result. Our proofs are based on a blocking technique and a stable convergence theorem for semimartingales. Finally, we show simulation results for the proposed estimator to illustrate its finite sample properties.

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“…They suggest to synchronize the high frequency prices using a Refresh Time Scheme combined with a multivariate realized kernel to provide a consistent and positive semi-definite estimator of 1 In the literature, there are several proposed corrections to HY that make it robust to this noise. For example, Voev and Lunde (2007), Bibinger (2011), based on a multiscale subsampling correction of HY that improves the convergence properties of the estimator proposed by Palandri (2006) and the Two-Scales Realized Covariance (TSRC) estimator of Zhang (2011). the covariance matrix.…”

Section: Introductionmentioning

confidence: 99%

A Bayesian High-Frequency Estimator of the Multivariate Covariance of Noisy and Asynchronous Returns

Peluso

Corsi

Mira

2014

JOURNAL OF FINANCIAL ECONOMETRICS

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A multivariate positive definite estimator of the covariance matrix of noisy and asynchronously observed asset returns is proposed. We adopt a Bayesian Dynamic Linear Model which allows us to interprete microstructure noise as measurement errors, and the asynchronous trading as missing observations in an otherwise synchronous series. These missing observations are treated as any other parameter of the problem as typically done in a Bayesian framework. We use an augmented Gibbs algorithm and thus sample the covariance matrix, the observational error variance matrix, the latent process and the missing observations of the noisy process from their full conditional distributions. Convergence issues and robustness of the Gibbs sampler are discussed. A simulation study compares our Bayesian estimator with recently proposed pair-wise QMLE-type and Multivariate Realized Kernel estimators, under different liquidity and microstructure noise conditions. The results suggest that our estimator is superior in terms of RMSE in both a two-and ten-dimensional settings, especially with dispersed and high missing percentages and with high noise. This suggests that our Bayesian estimator is more robust in severe conditions, such as portfolios of assets with heterogeneous liquidity profiles, or particularly illiquid, or when there is a high level of microstructure noise in the market.

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Efficient Covariance Estimation for Asynchronous Noisy High‐Frequency Data

Cited by 44 publications

References 24 publications

Spectral Estimation of Covolatility from Noisy Observations Using Local Weights

Spectral Estimation of Covolatility from Noisy Observations Using Local Weights

On Covariation Estimation for Multivariate Continuous Itô Semimartingales with Noise in Non-Synchronous Observation Schemes

A Bayesian High-Frequency Estimator of the Multivariate Covariance of Noisy and Asynchronous Returns

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