Statistical Properties of Microstructure Noise

Jacod, Jean; Li, Yingying; Zheng, Xinghua

doi:10.2139/ssrn.2212119

Cited by 25 publications

(87 citation statements)

References 39 publications

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“…is indeed possible, it further requires the evaluation of the correlation structure of the noise process which can be quite burdensome (e.g. see, Jacod et al (2016)). 4 As of today, the general consensus in the literature is to simply use one of the estimators presented in Equation 15and Equation 16.…”

Section: Feasible Noise Reduction By Virtue Of Futuresmentioning

confidence: 99%

“…Following Jacod et al (2016) the autocorrelated noise processes are generated as MA series which approximate fractionally differenced processes. This allows the simulation design to replicate the slow autocorrelation decay empirically evidenced in the aforementioned paper.…”

Section: Simulation Studymentioning

confidence: 99%

“…A detailed discussion on the argument can be found, among others, inZhang et al (2005),Aït-Sahalia and Yu (2009).4 The methodology proposed inJacod et al (2016) have been investigated and no superior performance has been registered. Additionally, as the estimation of the noise covariance matrix heavily relies on an heuristic approach to tailor some key parameter to the series of interest and can be quite convoluted we decided to disregard this procedure in favour of other, more convenient, estimators.…”

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confidence: 99%

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Cross-Sectional Noise Reduction and More Efficient Estimation of Integrated Variance

Mirone¹

2018

SSRN Journal

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In this paper we propose a straightforward approach to obtain a more efficient estimate of the integrated variance of an asset through a cross-sectional combination with a futures contract written on it. Our method constructs a variance-preserving series with reduced noise size as a linear combination of the underlying asset and the futures and base measurement of the integrated variance on this new series. We first illustrate how a theoretically but infeasible optimal series can be obtained and then suggest a feasible procedure to attain noise reduction. In a simulation study we verify how prevalent estimators of integrated variance applied to such noise-reduced series outperform estimators applied directly to the asset price. Finally, we apply the method to an empirical data set and, through the stabilized signature plot, we show how the noise reduced series provides consistent integrated variance estimates using naive realized measures at very high frequencies.

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Section: Feasible Noise Reduction By Virtue Of Futuresmentioning

confidence: 99%

Section: Simulation Studymentioning

confidence: 99%

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confidence: 99%

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Cross-Sectional Noise Reduction and More Efficient Estimation of Integrated Variance

Mirone¹

2018

SSRN Journal

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“…We present some simulation studies comparing the ReMeDI approach with the method of Jacod et al (2017). We find that the ReMeDI approach is relatively robust to: the data frequency, the sample size, the tuning parameter, and to model specification.…”

Section: Introductionmentioning

confidence: 98%

“…The estimation method is based on the differencing paradigm, which is widely used in microeconometrics to eliminate nuisance parameters, see, e.g., Athey and Imbens (2006). We build on the general setup introduced in the seminal work of Jacod et al (2017). Specifically, we assume that the underlying efficient price follows a semimartingale, which may accommodate stochastic volatility, jumps, etc.…”

Section: Introductionmentioning

confidence: 99%

A ReMeDI for Microstructure Noise

Li,

Linton

2020

SSRN Journal

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We introduce the Realized moMents of Disjoint Increments (ReMeDI) paradigm to measure microstructure noise (the deviation of the observed asset prices from the fundamental values caused by market imperfections). We propose consistent estimators of arbitrary moments of the microstructure noise process based on highfrequency data, where the noise process could be serially dependent, endogenous, and nonstationary. We characterize the limit distributions of the proposed estimators and construct confidence intervals under infill asymptotics. Our simulation and empirical studies show that the ReMeDI approach is very effective to measure the scale and the serial dependence of microstructure noise. Moreover, the estimators are quite robust to model specifications, sample sizes and data frequencies.

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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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Statistical Properties of Microstructure Noise

Cited by 25 publications

References 39 publications

Cross-Sectional Noise Reduction and More Efficient Estimation of Integrated Variance

Cross-Sectional Noise Reduction and More Efficient Estimation of Integrated Variance

A ReMeDI for Microstructure Noise

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

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