Noisy High Frequency Data Research Articles

Estimation of the quadratic variation of log prices based on the Itô semi-martingale

<abstract><p>As the availability of high-frequency data becomes more widespread, it has become very popular to model random fluctuations of some econometric variables over time using Itô semi-martingale. An emblematic problem is to estimate the quadratic variation, i.e., the integrated volatility of log prices, using noisy high frequency data with endogenous time and jumps. We propose a methodology that combines the multiple sub-grids and thresholds. First, the sub-sample is used to reduce the effect of the noise. Then, the threshold method is used to get rid of the effect of jumps. Finally, the multiple sub-grids method is used to increase the convergence rate. The asymptotic properties, such as consistency and asymptotic normality, are investigated. Simulation is also included to illustrate the performance of the proposed procedure.</p></abstract>

Principal Component Analysis based on Correlation Matrix with Asynchronous and Noisy High Frequency Data

Principal Component Analysis based on Correlation Matrix with Asynchronous and Noisy High Frequency Data

Volatility of volatility: Estimation and tests based on noisy high frequency data with jumps

We establish a feasible central limit theorem with convergence rate n1/8 for the estimation of the integrated volatility of volatility (VoV) based on noisy high-frequency data with jumps. This is the first inference theory ever built for VoV estimation under such a general setup. The central limit theorem is applied to provide interval estimates of the VoV and conduct hypothesis tests. Furthermore, when one is interested in the null hypothesis that the VoV is zero, we show that a more powerful test can be established based on a VoV estimator with a convergence rate n1/5 under the null. Empirical results on the S&P 500 and individual stocks show strong evidence of non-zero VoV.

A Factor-Based Estimation of Integrated Covariance Matrix With Noisy High-Frequency Data

This article studies a high-dimensional factor model with sparse idiosyncratic covariance matrix in continuous time, using asynchronous high-frequency financial data contaminated by microstructure noise. We focus on consistent estimations of the number of common factors, the integrated covariance matrix and its inverse, based on the flat-top realized kernels introduced by Varneskov. Simulation results illustrate the satisfactory performance of our estimators in finite samples. We apply our methodology to the high-frequency price data on a large number of stocks traded in Shanghai and Shenzhen stock exchanges, and demonstrate its value for capturing time-varying covariations and portfolio allocation.

On truncated multi-power estimator of integrated volatility with noisy high frequency data

This paper develops the asymptotic theory of the threshold pre-averaged multi-power variation estimation in the simultaneous presence of jumps and market microstructure noise and then proposes an improved estimator for integrated volatility of an Ito semi-martingale based on the obtained theory. This new class of estimation is based on the joint use of pre-averaging multi-power variation estimation in a noisy diffusion setting and the threshold technique, which serve to remove microstructure noise and jumps, respectively. Asymptotic properties of the proposed integrated volatility estimator, such as consistency and associated central limit theorems are also provided. Monte Carlo simulations show that the estimator is robust to both Levy jumps and microstructure noise and it provides less biased estimation, compared to existing estimators, of the continuous variation in finite samples. We also apply our estimator to some real high frequency financial data-sets.

Testing for jumps based on high-frequency data: a method exploiting microstructure noise

This paper tests for jumps of the price process based on noisy high-frequency data. Under the null hypothesis that the price process is continuous, the test statistic converges to a normal distribution, and under the alternative hypothesis that the price has jumps, the statistic converges to infinity. Compared with the test of Aït-Sahalia et al. [Testing for jumps in noisy high frequency data. J. Econom., 2012, 168(2), 207–222], our proposed statistic uses information on the microstructure noise, tends to infinity more rapidly under the alternative hypothesis and has a better power. A simulation confirms the theoretical results and an empirical study illustrates the practical application of the method.

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.

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 fairly 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 spot covariance matrix is developed based on the Smoothed TSRV (Mykland et al. (2017)). 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 by freeing several strong assumptions in classical PCA. As an application, we show that our first principal component (PC) potentially outperforms the S&P 100 market index, while three of the next four PCs are cointegrated with two of the Fama-French non-market factors.

Measuring the Intraday Jump Tail Risk of Financial Asset Price with Noisy High Frequency Data

This paper proposes a simple two-step nonparametric procedure to estimate the intraday jump tail and measure the jump tail risk in asset price with noisy high frequency data. We first propose the pre-averaging threshold approach to estimate the intraday jumps occurred, and then use the peaks-over-threshold (POT) method and generalized Pareto distribution (GPD) to model the intraday jump tail and further measure the jump tail risk. Finally, an empirical example further demonstrates the power of the proposed method to measure the jump tail risk under the effect of microstructure noise.

Testing for Heteroscedasticity in Jumpy and Noisy High-frequency Data: A Resampling Approach

In this paper, we propose a nonparametric way to test the hypothesis that time-variation in intraday volatility is caused solely by a deterministic and recurrent diurnal pattern. We assume that noisy high-frequency data from a discretely sampled jump-diffusion process are available. The test is then based on asset returns, which are deflated by the seasonal component and therefore homoskedastic under the null. To construct our test statistic, we extend the concept of pre-averaged bipower variation to a general Ito semimartingale setting via a truncation device. We prove a central limit theorem for this statistic and construct a positive semi-definite estimator of the asymptotic covariance matrix. The t-statistic (after pre-averaging and jump-truncation) diverges in the presence of stochastic volatility and has a standard normal distribution otherwise. We show that replacing the true diurnal factor with a model-free jump- and noise-robust estimator does not affect the asymptotic theory. A Monte Carlo simulation also shows this substitution has no discernable impact in finite samples. The test is, however, distorted by small infinite-activity price jumps. To improve inference, we propose a new bootstrap approach, which leads to almost correctly sized tests of the null hypothesis. We apply the developed framework to a large cross-section of equity high-frequency data and find that the diurnal pattern accounts for a rather significant fraction of intraday variation in volatility, but important sources of heteroskedasticity remain present in the data.

On Estimating the Integrated Co-Volatility Using Noisy High-Frequency Data with Jumps

In this article, we consider the estimation of covariation of two asset prices which contain jumps and microstructure noise, based on high-frequency data. We propose a realized covariance estimator, which combines pre-averaging method to remove the microstructure noise and the threshold method to reduce the jumps effect. The asymptotic properties, such as consistency and asymptotic normality, are investigated. The estimator allows very general structure of jumps, for example, infinity activity or even infinity variation. Simulation is also included to illustrate the performance of the proposed procedure.

Robust Estimation and Inference for Jumps in Noisy High Frequency Data: A Local-to-Continuity Theory for the Pre-Averaging Method

We develop an asymptotic theory for the pre-averaging estimator when asset price jumps are weakly identified, here modeled as local to zero. The theory unifies the conventional asymptotic theory for continuous and discontinuous semimartingales as two polar cases with a continuum of local asymptotics, and explains the breakdown of the conventional procedures under weak identification. We propose simple bias-corrected estimators for jump power variations, and construct robust confidence sets with valid asymptotic size in a uniform sense. The method is also robust to certain forms of microstructure noise.

Testing for jumps in noisy high frequency data

This paper proposes a robustification of the test statistic of Aït-Sahalia and Jacod (2009b) for the presence of market microstructure noise in high frequency data, based on the pre-averaging method of Jacod et al. (2010). We show that the robustified statistic restores the test’s discriminating power between jumps and no jumps despite the presence of market microstructure noise in the data.