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Per A Mykland - One of the best experts on this subject based on the ideXlab platform.

  • in sample asymptotics and across sample efficiency gains for high frequency Data statistics
    Econometric Theory, 2021
    Co-Authors: Eric Ghysels, Per A Mykland, Eric Renault
    Abstract:

    We revisit in-sample asymptotic analysis extensively used in the realized volatility literature. We show that there are gains to be made in estimating current realized volatility from considering realizations in prior periods. Our analysis is reminiscent of local-to-unity asymptotics. The weighting schemes also relate to Kalman-Bucy filters, although our approach is non-Gaussian and model-free. We derive theoretical results for a broad class of processes pertaining to volatility, higher moments and leverage. The paper also contains a Monte Carlo simulation study showing the benefits of across-sample combinations.

  • local parametric estimation in high frequency Data
    Journal of Business & Economic Statistics, 2020
    Co-Authors: Yoann Potiron, Per A Mykland
    Abstract:

    We give a general time-varying parameter model, where the multidimensional parameter possibly includes jumps. The quantity of interest is defined as the integrated value over time of the parameter ...

  • the five trolls under the bridge principal component analysis with asynchronous and noisy high frequency Data
    Journal of the American Statistical Association, 2020
    Co-Authors: Dachuan Chen, Per A Mykland, Lan Zhang
    Abstract:

    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 nois...

  • the five trolls under the bridge principal component analysis with asynchronous and noisy high frequency Data
    2018
    Co-Authors: Dachuan Chen, Per A Mykland, Lan Zhang
    Abstract:

    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.

  • discerning non stationary market microstructure noise and time varying liquidity in high frequency Data
    Social Science Research Network, 2016
    Co-Authors: Richard Y Chen, Per A Mykland
    Abstract:

    In this paper, we investigate the implication of non-stationary market microstructure noise to integrated volatility estimation, provide statistical tools to test stationarity and non-stationarity in market microstructure noise, and discuss how to measure liquidity risk using high frequency financial Data. In particular, we discuss the impact of non-stationary microstructure noise on TSRV (Two-Scale Realized Variance) estimator, and design three test statistics by exploiting the edge effects and asymptotic approximation. The asymptotic distributions of these test statistics are provided under both stationary and non-stationary noise assumptions respectively, and we empirically measure aggregate liquidity risks by these test statistics from 2006 to 2013. As byproducts, functional dependence and endogenous market microstructure noise are briefly discussed. Simulation studies corroborate our theoretical results. Our empirical study indicates the prevalence of non-stationary market microstructure noise in the New York Stock Exchange.

Yacine Aitsahalia - One of the best experts on this subject based on the ideXlab platform.

  • a hausman test for the presence of market microstructure noise in high frequency Data
    Journal of Econometrics, 2019
    Co-Authors: Yacine Aitsahalia, Dacheng Xiu
    Abstract:

    Abstract We develop tests that help assess whether a high frequency Data sample can be treated as reasonably free of market microstructure noise at a given sampling frequency for the purpose of implementing high frequency volatility and other estimators. The tests are based on the Hausman principle of comparing two estimators, one that is efficient but not robust to the deviation being tested, and one that is robust but not as efficient. We investigate the asymptotic properties of the test statistic in a general nonparametric setting, and compare it with several alternatives that are also developed in the paper. Empirically, we find that improvements in stock market liquidity over the past decade have increased the frequency at which simple, uncorrected, volatility estimators can be safely employed.

  • principal component analysis of high frequency Data
    Journal of the American Statistical Association, 2019
    Co-Authors: Yacine Aitsahalia, Dacheng Xiu
    Abstract:

    We develop the necessary methodology to conduct principal component analysis at high frequency. We construct estimators of realized eigenvalues, eigenvectors, and principal components, and provide ...

  • using principal component analysis to estimate a high dimensional factor model with high frequency Data
    Journal of Econometrics, 2017
    Co-Authors: Yacine Aitsahalia, Dacheng Xiu
    Abstract:

    This paper constructs an estimator for the number of common factors in a setting where both the sampling frequency and the number of variables increase. Empirically, we document that the covariance matrix of a large portfolio of US equities is well represented by a low rank common structure with sparse residual matrix. When employed for out-of-sample portfolio allocation, the proposed estimator largely outperforms the sample covariance estimator.

  • principal component analysis of high frequency Data
    National Bureau of Economic Research, 2015
    Co-Authors: Yacine Aitsahalia, Dacheng Xiu
    Abstract:

    We develop the necessary methodology to conduct principal component analysis at high frequency. We construct estimators of realized eigenvalues, eigenvectors, and principal components and provide the asymptotic distribution of these estimators. Empirically, we study the high frequency covariance structure of the constituents of the S&P 100 Index using as little as one week of high frequency Data at a time. The explanatory power of the high frequency principal components varies over time. During the recent financial crisis, the first principal component becomes increasingly dominant, explaining up to 60% of the variation on its own, while the second principal component drives the common variation of financial sector stocks.

  • analyzing the spectrum of asset returns jump and volatility components in high frequency Data
    Journal of Economic Literature, 2012
    Co-Authors: Yacine Aitsahalia, Jean Jacod
    Abstract:

    This paper describes a simple yet powerful methodology to decompose asset returns sampled at high frequency into their base components (continuous, small jumps, large jumps), determine the relative magnitude of the components, and analyze the finer characteristics of these components such as the degree of activity of the jumps. We extend the existing theory to incorporate to effect of market microstructure noise on the test statistics, apply the methodology to high frequency individual stock returns, transactions and quotes, stock index returns and compare the qualitative features of the estimated process for these different Data and discuss the economic implications of the results.

Jianqing Fan - One of the best experts on this subject based on the ideXlab platform.

  • factor garch ito models for high frequency Data with application to large volatility matrix prediction
    Social Science Research Network, 2017
    Co-Authors: Donggyu Kim, Jianqing Fan
    Abstract:

    Several novel large volatility matrix estimation methods have been developed based on the High-Frequency financial Data. They often employ the approximate factor model that leads to a low-rank plus sparse structure for the integrated volatility matrix and facilitates estimation of large volatility matrices. However, for predicting future volatility matrices, these nonparametric estimators do not have a dynamic structure to implement. In this paper, we introduce a novel Ito diffusion process based on the approximate factor models and call it a factor GARCH-Ito model. We then investigate its properties and propose a quasi-maximum likelihood estimation method for the parameter of the factor GARCH-Ito model. We also apply it to estimating conditional expected large volatility matrices and establish their asymptotic properties. Simulation studies are conducted to validate the finite sample performance of the proposed estimation methods. The proposed method is also illustrated by using Data from the constituents of the S&P 500 index and an application to constructing the minimum variance portfolio with gross exposure constraints.

  • vast volatility matrix estimation using high frequency Data for portfolio selection
    Journal of the American Statistical Association, 2012
    Co-Authors: Jianqing Fan
    Abstract:

    Portfolio allocation with gross-exposure constraint is an effective method to increase the efficiency and stability of portfolios selection among a vast pool of assets, as demonstrated by Fan, Zhang, and Yu. The required high-dimensional volatility matrix can be estimated by using High-Frequency financial Data. This enables us to better adapt to the local volatilities and local correlations among a vast number of assets and to increase significantly the sample size for estimating the volatility matrix. This article studies the volatility matrix estimation using high-dimensional, High-Frequency Data from the perspective of portfolio selection. Specifically, we propose the use of “pairwise-refresh time” and “all-refresh time” methods based on the concept of “refresh time” proposed by Barndorff-Nielsen, Hansen, Lunde, and Shephard for the estimation of vast covariance matrix and compare their merits in the portfolio selection. We establish the concentration inequalities of the estimates, which guarantee desi...

  • vast volatility matrix estimation using high frequency Data for portfolio selection
    Research Papers in Economics, 2010
    Co-Authors: Jianqing Fan
    Abstract:

    Portfolio allocation with gross-exposure constraint is an effective method to increase the efficiency and stability of selected portfolios among a vast pool of assets, as demonstrated in Fan et al (2008). The required high-dimensional volatility matrix can be estimated by using high frequency financial Data. This enables us to better adapt to the local volatilities and local correlations among vast number of assets and to increase significantly the sample size for estimating the volatility matrix. This paper studies the volatility matrix estimation using high-dimensional High-Frequency Data from the perspective of portfolio selection. Specifically, we propose the use of "pairwise-refresh time" and "all-refresh time" methods proposed by Barndorff-Nielsen et al (2008) for estimation of vast covariance matrix and compare their merits in the portfolio selection. We also establish the concentration inequalities of the estimates, which guarantee desirable properties of the estimated volatility matrix in vast asset allocation with gross exposure constraints. Extensive numerical studies are made via carefully designed simulations. Comparing with the methods based on low frequency daily Data, our methods can capture the most recent trend of the time varying volatility and correlation, hence provide more accurate guidance for the portfolio allocation in the next time period. The advantage of using High-Frequency Data is significant in our simulation and empirical studies, which consist of 50 simulated assets and 30 constituent stocks of Dow Jones Industrial Average index.

Yoann Potiron - One of the best experts on this subject based on the ideXlab platform.

  • Estimation for High-Frequency Data under parametric market microstructure noise
    Annals of the Institute of Statistical Mathematics, 2020
    Co-Authors: Simon Clinet, Yoann Potiron
    Abstract:

    We develop a general class of noise-robust estimators based on the existing estimators in the non-noisy High-Frequency Data literature. The microstructure noise is a parametric function of the limit order book. The noise-robust estimators are constructed as plug-in versions of their counterparts, where we replace the efficient price, which is non-observable, by an estimator based on the raw price and limit order book Data. We show that the technology can be applied to five leading examples where, depending on the problem, price possibly includes infinite jump activity and sampling times encompass asynchronicity and endogeneity.

  • local parametric estimation in high frequency Data
    Journal of Business & Economic Statistics, 2020
    Co-Authors: Yoann Potiron, Per A Mykland
    Abstract:

    We give a general time-varying parameter model, where the multidimensional parameter possibly includes jumps. The quantity of interest is defined as the integrated value over time of the parameter ...

  • efficient asymptotic variance reduction when estimating volatility in high frequency Data
    Journal of Econometrics, 2018
    Co-Authors: Simon Clinet, Yoann Potiron
    Abstract:

    This paper shows how to carry out efficient asymptotic variance reduction when estimating volatility in the presence of stochastic volatility and microstructure noise with the realized kernels (RK) from [Barndorff-Nielsen et al., 2008] and the quasi-maximum likelihood estimator (QMLE) studied in [Xiu, 2010]. To obtain such a reduction, we chop the Data into B blocks, compute the RK (or QMLE) on each block, and aggregate the block estimates. The ratio of asymptotic variance over the bound of asymptotic efficiency converges as B increases to the ratio in the parametric version of the problem, i.e. 1.0025 in the case of the fastest RK Tukey-Hanning 16 and 1 for the QMLE. The estimators are shown to be robust to jumps in price process and stochastic sampling times. The finite sample performance of both estimators is investigated in simulations, while empirical work illustrates the gain in practice.

  • estimation for high frequency Data under parametric market microstructure noise
    Research Papers in Economics, 2017
    Co-Authors: Simon Clinet, Yoann Potiron
    Abstract:

    In this paper, we propose a general class of noise-robust estimators based on the existing estimators in the non-noisy High-Frequency Data literature. The market microstructure noise is a known parametric function of the limit order book. The noise-robust estimators are constructed as a plug-in version of their counterparts, where we replace the efficient price, which is non-observable in our framework, by an estimator based on the raw price and the limit order book Data. We show that the technology can be directly applied to estimate volatility, High-Frequency covariance, functionals of volatility and volatility of volatility in a general nonparametric framework where, depending on the problem at hand, price possibly includes infinite jump activity and sampling times encompass asynchronicity and endogeneity.

  • efficient asymptotic variance reduction when estimating volatility in high frequency Data
    arXiv: Statistical Finance, 2017
    Co-Authors: Simon Clinet, Yoann Potiron
    Abstract:

    This paper shows how to carry out efficient asymptotic variance reduction when estimating volatility in the presence of stochastic volatility and microstructure noise with the realized kernels (RK) from [Barndorff-Nielsen et al., 2008] and the quasi-maximum likelihood estimator (QMLE) studied in [Xiu, 2010]. To obtain such a reduction, we chop the Data into B blocks, compute the RK (or QMLE) on each block, and aggregate the block estimates. The ratio of asymptotic variance over the bound of asymptotic efficiency converges as B increases to the ratio in the parametric version of the problem, i.e. 1.0025 in the case of the fastest RK Tukey-Hanning 16 and 1 for the QMLE. The impact of stochastic sampling times and jump in the price process is examined carefully. The finite sample performance of both estimators is investigated in simulations, while empirical work illustrates the gain in practice.

Lan Zhang - One of the best experts on this subject based on the ideXlab platform.

  • the five trolls under the bridge principal component analysis with asynchronous and noisy high frequency Data
    Journal of the American Statistical Association, 2020
    Co-Authors: Dachuan Chen, Per A Mykland, Lan Zhang
    Abstract:

    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 nois...

  • the five trolls under the bridge principal component analysis with asynchronous and noisy high frequency Data
    2018
    Co-Authors: Dachuan Chen, Per A Mykland, Lan Zhang
    Abstract:

    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.

  • assessment of uncertainty in high frequency Data the observed asymptotic variance
    Econometrica, 2017
    Co-Authors: Per Aslak Mykland, Lan Zhang
    Abstract:

    The availability of high frequency financial Data has generated a series of estimators based on intra‐day Data, improving the quality of large areas of financial econometrics. However, estimating the standard error of these estimators is often challenging. The root of the problem is that traditionally, standard errors rely on estimating a theoretically derived asymptotic variance, and often this asymptotic variance involves substantially more complex quantities than the original parameter to be estimated. Standard errors are important: they are used to assess the precision of estimators in the form of confidence intervals, to create “feasible statistics” for testing, to build forecasting models based on, say, daily estimates, and also to optimize the tuning parameters. The contribution of this paper is to provide an alternative and general solution to this problem, which we call Observed Asymptotic Variance. It is a general nonparametric method for assessing asymptotic variance (AVAR). It provides consistent estimators of AVAR for a broad class of integrated parameters Θ = ∫ θ t dt, where the spot parameter process θ can be a general semimartingale, with continuous and jump components. The observed AVAR is implemented with the help of a two‐scales method. Its construction works well in the presence of microstructure noise, and when the observation times are irregular or asynchronous in the multivariate case. The methodology is valid for a wide variety of estimators, including the standard ones for variance and covariance, and also for more complex estimators, such as, of leverage effects, high frequency betas, and semivariance.

  • a tale of two time scales determining integrated volatility with noisy high frequency Data
    Journal of the American Statistical Association, 2005
    Co-Authors: Lan Zhang, Per A Mykland, Yacine Aitsahalia
    Abstract:

    It is a common nancial practice to estimate volatility from the sum of frequently-sampled squared returns. However market microstructure poses challenge to this estimation approach, as evidenced by recent empirical studies in nance. This work attempts to lay out theoretical grounds that reconcile continuous-time modeling and discrete-time samples. We propose an estimation approach that takes advantage of the rich sources in tick-by-tick Data while preserving the continuous-time assumption on the underlying returns. Under our framework, it becomes clear why and where the \usual" volatility estimator fails when the returns are sampled at the highest frequency.

  • a tale of two time scales determining integrated volatility with noisy high frequency Data
    National Bureau of Economic Research, 2003
    Co-Authors: Lan Zhang, Per A Mykland, Yacine Aitsahalia
    Abstract:

    It is a common practice in finance to estimate volatility from the sum of frequently-sampled squared returns. However market microstructure poses challenges to this estimation approach, as evidenced by recent empirical studies in finance. This work attempts to lay out theoretical grounds that reconcile continuous-time modeling and discrete-time samples. We propose an estimation approach that takes advantage of the rich sources in tick-by-tick Data while preserving the continuous-time assumption on the underlying returns. Under our framework, it becomes clear why and where the usual' volatility estimator fails when the returns are sampled at the highest frequency.