Statistical Properties of Microstructure Noise

Jacod, Jean; Li, Yingying; Zheng, Xinghua

doi:10.3982/ecta13085

Cited by 93 publications

(13 citation statements)

References 38 publications

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“…There are several possible extensions for future work. Besides the additional presence of price jumps as discussed in Section 5.3, serial dependence of random noise is also documented in, eg, the works of Da and Xiu and Jacod et al, among others. Further research should take these stylized empirical facts into consideration as well.…”

Section: Resultsmentioning

confidence: 88%

A combined filtering approach to high‐frequency volatility estimation with mixed‐type microstructure noises

Tang

Zhang

2018

Appl Stoch Models Bus & Ind

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This paper introduces a solution that combines the Kalman and particle filters to the challenging problem of estimating integrated volatility using high-frequency data where the underlying prices are perturbed by a mixture of random noise and price discreteness. An explanation is presented of how the proposed combined filtering approach is able to correct for bias due to this mixed-type microstructure effect. Simulation and empirical studies on the tick-by-tick trade price data for four US stocks in the year 2009 show that our method has clear advantages over existing high-frequency volatility estimation methods. KEYWORDScombined filters, high-frequency data, integrated volatility, market microstructure noise, price discreteness INTRODUCTIONThe last 15 years have seen growing interest in volatility estimation using high-frequency data. One challenge when making inferences using high-frequency data is the presence of a market microstructure effect that causes the traditional realized volatility (RV) method to fail. 1 The market microstructure effect may be attributable to, among other causes, bid-ask bounce, adverse selection due to asymmetry of information for different traders, dealer's inventory control, and price discreteness. In contrast to those random effects that can be deemed measurement errors, the effect that stems from price discreteness is of a nonlinear nature. Although the work described in the existing literature has usually treated the two kinds of effect somewhat separately, they are both present in real data and pose a great challenge to volatility estimation using high-frequency data. Subsampling (eg, at an adhoc 5-minute frequency as suggested by Andersen et al 2 ) may mitigate the microstructure effect to a certain degree; however, it is one of the first principles of statistics that one should not throw away a large amount of data. In this paper, we address the problem by proposing an approach that combines the Kalman and particle filters.The study of price discreteness can be dated back to the 1980s. If one takes price discreteness as rounding errors, then explicitly characterizing the effect of rounding on the latent "true" asset returns becomes surprisingly difficult, except under specific parametric Brownian/geometric Brownian models (cf the work of Campbell et al 3 ). In particular, under the parametric Brownian/geometric Brownian setup for the latent "true" price, Ball, 4 Gottlieb and Kalay, 5 and Harris, 6 among others, studied the effect of price discreteness on estimation of the volatility of the latent true price process. For models other than those that take price discreteness as rounding errors and are related to volatility estimation, see, eg, the ordered probit model in the work of Hausman et al 7 and the barrier models in the works of Marsh and Rosenfeld 8 and Cho and Frees. 9Appl Stochastic Models Bus Ind. 2019;35:603-623.wileyonlinelibrary.com/journal/asmb

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Section: Resultsmentioning

confidence: 88%

A combined filtering approach to high‐frequency volatility estimation with mixed‐type microstructure noises

Tang

Zhang

2018

Appl Stoch Models Bus & Ind

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“…It is also worth mentioning that the alternative approach allows for rather general dependence structures in the noise process, both cross-sectional and temporal, and even dependence between the noise and price process. The temporal dependence between microstructure noise has been documented in recent studies; see, e.g., Hansen and Lunde (2006), Ubukata and Oya (2009) and Jacod et al (2017).…”

Section: Approach IImentioning

confidence: 90%

“…We actually do not put any restrictions on the cross-sectional dependence, and even dependence between the noise and price process is allowed. Note also that Jacod et al (2017) provides an approach to estimate the decay rate of the ρ-mixing coefficients. Assumption (D.ii) concerns the dependence between the covolatility process and the Brownian motion that drives the price processes.…”

Section: Approach IImentioning

confidence: 99%

On the Inference About the Spectral Distribution of High-Dimensional Covariance Matrix Based on High-Frequency Noisy Observations

Xia

Zheng

2016

SSRN Journal

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In practice, observations are often contaminated by noise, making the resulting sample covariance matrix a signal-plus-noise sample covariance matrix. Aiming to make inferences about the spectral distribution of the population covariance matrix under such a situation, we establish an asymptotic relationship that describes how the limiting spectral distribution of (signal) sample covariance matrices depends on that of signalplus-noise-type sample covariance matrices. As an application, we consider inferences about the spectral distribution of integrated covolatility (ICV) matrices of high-dimensional diffusion processes based on high-frequency data with microstructure noise. The (slightly modified) pre-averaging estimator is a signal-plus-noise sample covariance matrix, and the aforementioned result, together with a (generalized) connection between the spectral distribution of signal sample covariance matrices and that of the population covariance matrix, enables us to propose a two-step procedure to consistently estimate the spectral distribution of ICV for a class of diffusion processes. An alternative approach is further proposed, which possesses several desirable properties: it is more robust, it eliminates the effects of microstructure noise, and the asymptotic relationship that enables consistent estimation of the spectral distribution of ICV is the standard Marčenko-Pastur equation. The performance of the two approaches is examined via simulation studies under both synchronous and asynchronous observation settings.

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“…For example, in Liesenfeld, Nolte, and Pohlmeier (2006), the proportion of flat trades for two stocks traded in NYSE is over 60%. Jacod, Li, and Zheng (2017) reports an over 70% of flat trades in the transaction data from Citigroup. For the mid-quote data the proportion of flat price changes will be even larger, as the best quotes can remain constant even when the transaction price moves.…”

Section: Simulation Designmentioning

confidence: 99%

Asymptotic Theory for Renewal Based High-Frequency Volatility Estimation

Nolte

2018

SSRN Journal

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Statistical Properties of Microstructure Noise

Cited by 93 publications

References 38 publications

A combined filtering approach to high‐frequency volatility estimation with mixed‐type microstructure noises

A combined filtering approach to high‐frequency volatility estimation with mixed‐type microstructure noises

On the Inference About the Spectral Distribution of High-Dimensional Covariance Matrix Based on High-Frequency Noisy Observations

Asymptotic Theory for Renewal Based High-Frequency Volatility Estimation

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