Microstructure Noise Research Articles

The distribution of index futures realised volatility under seasonality and microstructure noise

Previous research documents that the distribution of realised volatility appears approximately log-normal. However, formal tests reject normality fairly convincingly, which may indicate intrinsic features in the intraday data series, namely, the presence of seasonal intraday patterns and microstructure noise. Because many models are based on a normality assumption, this must be verified in order to validate the results. We find departures from normality due to the seasonal and noise components of intraday data, such that, after controlling for both features, the volatility estimates follow a log-normal distribution. Our results reveal that failing to account for these market imperfections can have important implications for analyses of volatility transmission and for investment and hedging decisions.

Jumps at ultra-high frequency: Evidence from the Chinese stock market

This paper investigates the magnitude of the jump component to total price variance in the Chinese stock market based on the highest resolution data. We apply the newly proposed jump test for semi-martingale contaminated by microstructure noise based on the truncated pre-averaging bi-power estimation. Theoretically, we prove that such test achieves satisfactory asymptotic size and power. The universal threshold technique can also be adopted to avoid spurious detections and the Monte Carlo simulations show reasonable performance of the test in noisy setting. The empirical results imply that jump variation is an order of magnitude smaller than typical estimates found in the existing literature from different angles, and the further empirical results also support these findings.

Evaluating the Underlying Components of High Frequency Financial Data: Finite Sample Performance and Microstructure Noise Effects

This paper examines the finite sample properties of novel theoretical tests that evaluate the presence of: a) Brownian motion, b) jumps; c) finite vs. infinite activity jumps. In allowing for Gaussian, t-distributed, and Gaussian-T mixture noise, our Monte Carlo experiment guides a search for optimal performance across sampling frequencies. Using 100 stocks and SPY, we find that: i) a Brownian and a jump component characterize 1-min stock data; ii) Jumps should allow for both finite and infinite activity; iii) Rejection rates are time-varying, such that more jump days are usually associated with an increase of infinite jumps vis-a-vis finite jumps.

Nothing but noise? Price discovery across cryptocurrency exchanges

We examine the price discovery contributions of cryptocurrency exchanges in the presence of market microstructure noise. Cryptocurrency markets exhibit a decisively higher level of microstructure noise compared with the NYSE or NASDAQ. Therefore, traditional measures of price discovery could be biased. To overcome this concern, we draw on the information leadership share proposed by Putniņš (2013); by leveraging this information, we find that Bitfinex is the leader in the price discovery process. These results highlight the importance of accounting for different levels of noise when evaluating price discovery contributions.

High-dimensional integrated volatility matrix estimation forhigh-frequency financial data with jumps

The joint volatility matrix of assets is an important statistic for resource allocation and risk management. Accurate estimation of the joint volatility matrix is one of the hot issues in financial statistics and risk measurement. In this paper, we study theintegral volatility matrix estimation of logarithmic price data with jumps under microstructure noise including market information. When the prices are not synchronized, and the number of assets and sample size tend to infinity, four estimation methods of high-dimensional integral volatility matrices are proposed by using the non-overlapping interval method and sparse characteristics. The convergence rate can reach the optimal convergence rate of the existing high-dimensional integral volatility matrix estimation. At the same time, the proposed adjusted estimators are consistent and semi-positive definite. The advantages and disadvantages of these estimators are compared in the simulation study. Finally the proposed methods are applied to the empirical study of Shanghai Securities Index data.

A Data Paradigm to Operationalise Expanded Filtration: Realized Volatilities and Kernels from Non-Synchronous NASDAQ Quotes and Trades

Ultra High Frequency (UHF) quotes and trades are examined in high resolution. Patterns which do not correspond to plausible market activity as in Brownlees and Gallo (2006) are observed. Noise other than microstructure noise is identified and diagnostic methods are evaluated. Extending Barndorff-Nielsen et al. (2009), a paradigm of data handling that synthesizes statistical technique and limit order book modeling is developed. The data paradigm operationalises the use of expanded filtration in empirical research. Empirical evidence from the NASDAQ 100 demonstrates that removal of non microstructure noise from the limit order book robustifies estimation across techniques and levels of market depth.

Investigation of Welded Joints Made of Construction Steel by the Barkhausen Noise Method

Steel weld seams are characterized by heterogeneity of their microstructure. Microstructure affects the nature of the distribution, sign and magnitude of residual stresses. In combination with unfavorable factors (low temperature, metal hypoductility and an unsuccessful joint form) residual stresses lead to a decrease of load carrying capacity of a whole structure. In a weld seam residual stresses are distributed in a complex way and can affect the build quality of heavy section welded structures. Monitoring of residual stresses remains a big problem. Residual stresses in welds are often evaluated only by modeling. Unfortunately, all mathematical models describe the stress state of the welded material with low accuracy. Simple quality control, the results of which can be easy interpreted, is necessary. Welded joints made by manual arc welding and by automatic submerged arc welding were investigated. Butt seams of steel sheets of different thickness have been welded. Steel was low-carbon and low-alloyed. It is often used in welded structures for various purposes, including construction, and for pipelines manufacture. The temperature range of welded structures operation is very large – from-70 to 450С. The authors studied the structure of butt weld seams by the Barkhausen noise method, which is interesting as it represents an alternative to the known methods, which characterizes the structure and stress state of material. The relationship between the weld microstructure and magnetic noise is shown. Studies have allowed us to establish the relationship between the structure and magnetic properties and to evaluate the feasibility of applying the Barkhausen noise method to welded structures.

Nonparametric estimation of volatility function in the jump-diffusion model with noisy data

In this article, we propose a two-step approach to estimate the volatility function of a jump-diffusion model in noisy data setting. The preaveraging method and threshold technique is used to remove microstructure noise and jumps, respectively. The newly proposed estimator is shown to be consistent and asymptotically normal. A simulation study and a real data application are undertaken to assess the finite sample performance of the proposed method.

Nothing but Noise? Price Discovery between Cryptocurrency Exchanges

We examine the price discovery contributions of cryptocurrency exchanges in the presence of market microstructure noise. Cryptocurrency markets exhibit a decisively higher level of microstructure noise compared to the New York Stock Exchange or NASDAQ. Therefore, traditional measures of price discovery are potentially biased. To overcome this concern, we draw on the information leadership share (ILS) proposed by Putnins [2013, J.Emp.Fin]. Based on the ILS, we find that Bitfinex is the leader in the price discovery process. Our results highlight the importance of accounting for different levels of noise when evaluating price discovery contributions

High-frequency jump tests: Which test should we use?

We conduct an extensive evaluation of price jump tests based on high-frequency financial data. After providing a concise review of multiple alternative tests, we document the size and power of all tests in a range of empirically relevant scenarios. Particular focus is given to the robustness of test performance to the presence of jumps in volatility and microstructure noise, and to the impact of sampling frequency. The paper concludes by providing guidelines for empirical researchers about which test to choose in any given setting.

A Score-Driven Conditional Correlation Model for Noisy and Asynchronous Data: An Application to High-Frequency Covariance Dynamics

The analysis of the intraday dynamics of covariances among high-frequency returns is challenging due to asynchronous trading and market microstructure noise. Both effects lead to significant data reduction and may severely affect the estimation of the covariances if traditional methods for low-frequency data are employed. We propose to model intraday log-prices through a multivariate local-level model with score-driven covariance matrices and to treat asynchronicity as a missing value problem. The main advantages of this approach are: (i) all available data are used when filtering the covariances, (ii) market microstructure noise is taken into account, (iii) estimation is performed by standard maximum likelihood. Our empirical analysis, performed on 1-sec NYSE data, shows that opening hours are dominated by idiosyncratic risk and that a market factor progressively emerges in the second part of the day. The method can be used as a nowcasting tool for high-frequency data, allowing to study the real-time response of covariances to macro-news announcements and to build intraday portfolios with very short optimization horizons.

Parametric Estimation of Large Realized Covariance Matrices: Revisiting the Method of Corsi et al. (2015)

The estimation of the covariances of high-frequency asset prices is problematic because of asynchronous trading and market microstructure noise. In the last years, both parametric and non-parametric methods have been proposed in order to handle these effects. Little attention has instead been devoted to the curse of dimensionality problem, which makes the use of standard methodologies prohibitive when the cross-section dimension increases. In this paper, we introduce a parametric factor structure which allows for dimensionality reduction and simplifies considerably the inference problem. We test our method in an empirical setting that emphasizes the effect of the curse of dimensionality. Compared to standard parametric approaches, our factor specification is computationally simpler and provides statistically indistinguishable performances in standard risk management applications.

On the estimation of integrated volatility in the presence of jumps and microstructure noise

This paper is concerned with the problem of the estimation of the integrated volatility of log-prices based on high frequency data when both price jumps and market microstructure noise are present. We begin by providing a survey of the leading estimators introduced in the literature to tackle volatility estimation in this setting. We then introduce novel integrated volatility estimators based on a truncation technique and establish their properties. Finally, we carry out a simulation study to compare the performance of the different estimation techniques.

Semiparametric estimation and inference on the fractal index of Gaussian and conditionally Gaussian time series data

This paper studies the properties of a particular estimator of the fractal index of a time series with a view to applications in financial econometrics and mathematical finance. We show how measurement noise (e.g., microstructure noise) in the observations will bias the estimator, potentially resulting in the econometrician erroneously finding evidence of fractal characteristics in a time series. We propose a new estimator which is robust to such noise and construct a formal hypothesis test for the presence of noise in the observations. A number of simulation exercises are carried out, providing guidance for implementation of the theory. Finally, the methods are illustrated on two empirical data sets; one of turbulent velocity flows and one of financial prices.

Are Corn Futures Prices Getting “Jumpy”?

The article sheds light on price jump risk in corn futures prices in the era of electronic trading and after the shift to real‐time announcement of USDA reports. Using intraday prices from 2008 to 2015, we employ a nonparametric test to detect jumps and variance analysis to assess the relative importance of jump risk. Real‐time trading of major USDA reports has substantially increased the frequency and clustering of price jumps, and results in higher market liquidity costs. In contrast, although the presence of jumps on non‐announcement days has doubled recently, their magnitude has declined as have transactions costs during their occurrence. The largest jump risk or execution risk is experienced by high frequency traders due to heightened microstructure noise during price jumps. However, traders holding long‐term market positions are only minimally affected by increased jump risk.

The Five Trolls Under the Bridge: Principal Component Analysis With Asynchronous and Noisy High Frequency Data

We develop a principal component analysis (PCA) for high frequency data. As in Northern fairy tales, there are trolls waiting for the explorer. The first three trolls are market microstructure noise, asynchronous sampling times, and edge effects in estimators. To get around these, a robust estimator of the spot covariance matrix is developed based on the smoothed two-scale realized variance (S-TSRV). The fourth troll is how to pass from estimated time-varying covariance matrix to PCA. Under finite dimensionality, we develop this methodology through the estimation of realized spectral functions. Rates of convergence and central limit theory, as well as an estimator of standard error, are established. The fifth troll is high dimension on top of high frequency, where we also develop PCA. With the help of a new identity concerning the spot principal orthogonal complement, the high-dimensional rates of convergence have been studied after eliminating several strong assumptions in classical PCA. As an application, we show that our first principal component (PC) closely matches but potentially outperforms the S&P 100 market index. From a statistical standpoint, the close match between the first PC and the market index also corroborates this PCA procedure and the underlying S-TSRV matrix, in the sense of Karl Popper. Supplementary materials for this article are available online.

Comparing robustness of realised measures under round-off errors, price adjustments and serial correlations: a simulation study

We compare the accuracy of realised measures using a number of computer simulations. Realised measures are the methods used to estimate the integrated volatility from high-frequency data. We consider a simple realised volatility (RV), a five-minute RV, a subsampled five-minute RV, a two-scale (TS) estimator, a realised kernel (RK), a pre-averaging (PA) estimator and a separating information maximum likelihood (SIML) estimator. We use seven market microstructure models, which includes round-off errors, price adjustments and serial correlation. The SIML is not irrationally biased in any case; this implies that the SIML is sufficiently robust to the market microstructure noise in any form. We have also found that the SIML is the only realised measure for maintaining consistency in all our simulations. We conclude that SIML is suitable for practical applications.

Оценщики квадратичной вариации основанные на высокочастотных данных – эмпирический обзор

Recently, advances in computer technology and data recording and storage have made high-frequency financial data readily available to researchers. As a result, the volatility literature has steadily progressed toward the use of higher-frequency data. However, the move towards the use of higher-frequency financial data in the estimation of volatility of financial returns has resulted in the development of many realised volatility measures of asset return variability based on a variety of different assumptions and functional forms and thus making theoretical comparison and selection of the estimators for empirical applications very difficult if not impossible. This article provides an empirical review on the performance of estimators of quadratic variation/integrated variance based on high-frequency data to aid their application in empirical analysis. The result of the review shows that no single estimator works best in all situations; however, the more sophisticated realised measures, in particular the TSRV and KRV, are superior to the other estimators in terms of their estimation accuracy in the presence of market microstructure noise.

Supplementary Material for 'A ReMeDI for Microstructure Noise''

Supplementary Material for 'A ReMeDI for Microstructure Noise''

Robust Estimation of Integrated Volatility

We introduce a new method to estimate the integrated volatility (IV) based on noisy high-frequency data. Our method employs the ReMeDI approach introduced by Li and Linton (2021a) to estimate the moments of the microstructure noise and thereby eliminate their influence, and the pre-averaging method to target the volatility parameter. The method is robust: it can be applied when the efficient price exhibits stochastic volatility and jumps, the observation times are random and endogenous, and the noise process is nonstationary, autocorrelated and dependent on the efficient price. We derive the limit distribution for the proposed estimators under infill asymptotics in a general setting. Our simulation and empirical studies demonstrate the robustness, accuracy and computational efficiency of our estimators compared to several alternatives recently proposed in the literature.