Integrated Covariance Matrix Research Articles

Limiting Spectral Distribution of High-dimensional Hayashi-Yoshida Estimator of Integrated Covariance Matrix

Limiting Spectral Distribution of High-dimensional Hayashi-Yoshida Estimator of Integrated Covariance Matrix

An adaptive biogeography-based optimization with integrated covariance matrix learning for robust visual object tracking

An adaptive biogeography-based optimization with integrated covariance matrix learning for robust visual object tracking

Forecasting High-Dimensional Covariance Matrices Using High-Dimensional Principal Component Analysis

We modify the recently proposed forecasting model of high-dimensional covariance matrices (HDCM) of asset returns using high-dimensional principal component analysis (PCA). It is well-known that when the sample size is smaller than the dimension, eigenvalues estimated by classical PCA have a bias. In particular, a very small number of eigenvalues are extremely large and they are called spiked eigenvalues. High-dimensional PCA gives eigenvalues which correct the biases of the spiked eigenvalues. This situation also happens in the financial field, especially in situations where high-frequency and high-dimensional data are handled. The research aims to estimate the HDCM of asset returns using high-dimensional PCA for the realized covariance matrix using the Nikkei 225 data, it estimates 5- and 10-min intraday asset-returns intervals. We construct time-series models for eigenvalues which are estimated by each PCA, and forecast HDCM. Our simulation analysis shows that the high-dimensional PCA has better estimation performance than classical PCA for the estimating integrated covariance matrix. In our empirical analysis, we show that we will be able to improve the forecasting performance using the high-dimensional PCA and make a portfolio with smaller variance.

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.

Estimation of high-dimensional integrated covariance matrix based on noisy high-frequency data with multiple observations

In this paper, we study the estimation of integrated covariance matrix based on noisy high-frequency data with multiple transactions using random matrix theory. We further prove that the proposed estimator is also asymptotically optimal for portfolio selection.

Factor state–space models for high-dimensional realized covariance matrices of asset returns

Abstract We propose a dynamic factor state–space model for high-dimensional covariance matrices of asset returns. It makes use of observed risk factors and assumes that the latent integrated joint covariance matrix of the assets and the factors is observed through their realized covariance matrix with a Wishart measurement density. For the latent integrated covariance matrix of the assets we impose a strict factor structure allowing for dynamic variation in the covariance matrices of the factors and the residual components as well as in the factor loadings. This factor structure translates into a factorization of the Wishart measurement density which facilitates statistical inference based on simple Bayesian MCMC procedures making the approach scalable w.r.t. the number of assets. An empirical application to realized covariance matrices for 60 NYSE traded stocks using the Fama–French factors and sector-specific factors represented by Exchange Traded Funds (ETFs) shows that the model performs very well in- and out of sample.

A nonparametric eigenvalue-regularized integrated covariance matrix estimator for asset return data

In high-frequency data analysis, the extreme eigenvalues of a realized covariance matrix are biased when its dimension p is large relative to the sample size n. Furthermore, with non-synchronous trading and contamination of microstructure noise, we propose a nonparametrically eigenvalue-regularized integrated covariance matrix estimator (NERIVE) which does not assume specific structures for the underlying integrated covariance matrix. We show that NERIVE is positive definite in probability, with extreme eigenvalues shrunk nonlinearly under the high dimensional framework p∕n→c>0. We also prove that in portfolio allocation, the minimum variance optimal weight vector constructed using NERIVE has maximum exposure and actual risk upper bounds of order p−1∕2. Incidentally, the same maximum exposure bound is also satisfied by the theoretical minimum variance portfolio weights. All these results hold true also under a jump–diffusion model for the log-price processes with jumps removed using the wavelet method proposed in Fan and Wang (2007). They are further extended to accommodate the existence of pervasive factors such as a market factor under the setting p3∕2∕n→c>0. The practical performance of NERIVE is illustrated by comparing to the usual two-scale realized covariance matrix as well as some other nonparametric alternatives using different simulation settings and a real data set.

Pre-averaging estimate of high dimensional integrated covariance matrix with noisy and asynchronous high-frequency data

With rapid development of the global market, the number of financial securities has significantly grown, which greatly challenges the measuring of financial quantities. Among others, the estimation of covariance matrix which plays an important role in risk management becomes no longer accurate. In this paper, we consider the estimation of integrated covariance matrix of semi-martingales under framework of high dimension by using high frequency data. We assume that the multivariate asset prices are observed asynchronously and all the observed prices are contaminated by microstructure noise. We employ the pre-averaging method to remove the microstructure noise and the generalized synchronization method to deal with the non-synchronicity. Moreover, to avoid the inconsistency in the high-dimensional covariance matrix estimation, we propose a regularized estimate. The consistency under matrix [Formula: see text]-norm is established. Compared to existing results, our estimator improves the accuracy of the estimation. Finally, we assess the theoretical results via some simulation studies.

Nonlinear shrinkage estimation of large integrated covariance matrices

Integrated covariance matrices arise in intraday models of asset returns, which allow volatility to change over the trading day. When the number of assets is large, the natural estimator of such a matrix suffers from bias due to extreme eigenvalues. We introduce a novel nonlinear shrinkage estimator for the integrated covariance matrix which shrinks the extreme eigenvalues of a realized covariance matrix back to an acceptable level, and enjoys a certain asymptotic efficiency when the number of assets is of the same order as the number of data points. Novel maximum exposure and actual risk bounds are derived when our estimator is used in constructing the minimum variance portfolio. In simulations and a real-data analysis, our estimator performs favourably in comparison with other methods.

Bootstrapping integrated covariance matrix estimators in noisy jump–diffusion models with non-synchronous trading

We propose a bootstrap method for estimating the distribution (and functionals of it such as the variance) of various integrated covariance matrix estimators. In particular, we first adapt the wild blocks of blocks bootstrap method suggested for the pre-averaged realized volatility estimator to a general class of estimators of integrated covolatility. We then show the first-order asymptotic validity of this method in the multivariate context with a potential presence of jumps, dependent microstructure noise, irregularly spaced and non-synchronous data. Our results justify using the bootstrap to estimate the covariance matrix of a broad class of covolatility estimators. The bootstrap variance estimator is positive semi-definite by construction, an appealing feature that is not always shared by existing variance estimators of the integrated covariance estimator. As an application of our results, we also consider the bootstrap for regression coefficients. We show that the wild blocks of blocks bootstrap, appropriately centered, is able to mimic both the dependence and heterogeneity of the scores. We provide a proof of construction of bootstrap percentile and percentile-t intervals as well as variance estimates in this context. This contrasts the traditional pairs bootstrap which is not able to mimic the score heterogeneity even in the simple case where no microstructure noise is present. Our Monte Carlo simulations show that the wild blocks of blocks bootstrap improve the finite sample properties of the alternative approach based on the Gaussian approximation. We illustrate its practical use on high-frequency equity data.

Robust estimation of a high-dimensional integrated covariance matrix

ABSTRACTIn this article, we consider a robust method of estimating a realized covariance matrix calculated as the sum of cross products of intraday high-frequency returns. According to recent articles in financial econometrics, the realized covariance matrix is essentially contaminated with market microstructure noise. Although techniques for removing noise from the matrix have been studied since the early 2000s, they have primarily investigated a low-dimensional covariance matrix with statistically significant sample sizes. We focus on noise-robust covariance estimation under converse circumstances, that is, a high-dimensional covariance matrix possibly with a small sample size. For the estimation, we utilize a statistical hypothesis test based on the characteristic that the largest eigenvalue of the covariance matrix asymptotically follows a Tracy–Widom distribution. The null hypothesis assumes that log returns are not pure noises. If a sample eigenvalue is larger than the relevant critical value, then we fail to reject the null hypothesis. The simulation results show that the estimator studied here performs better than others as measured by mean squared error. The empirical analysis shows that our proposed estimator can be adopted to forecast future covariance matrices using real data.

Smoothing it Out: Empirical and Simulation Results for Disentangled Realized Covariances

We study the class of disentangled realized estimators for the integrated covariance matrix of Brownian semimartingales with finite activity jumps. These estimators separate correlations and volatilities. We analyze different combinations of quantile- and median- based realized volatilities, and four estimators of realized correlations with three synchronization schemes. Their finite sample properties are studied under five data generating processes, in presence, or not, of microstructure noise, and under synchronous and asynchronous trading. The main finding is that synchronizing with previous tick interpolation combined with the pre- averaged version of disentangled estimators based on Gaussian ranks (for the correlations) and median deviations (for the volatilities) provide a precise, computationally efficient, and easy alternative to measure integrated covariances. A minimum variance portfolio application shows the superiority of this disentangled realized estimator in terms of numerous performance metrics.

A Bayesian High-Frequency Estimator of the Multivariate Covariance of Noisy and Asynchronous Returns

A multivariate positive definite estimator of the integrated covariance matrix of noisy and asynchronously observed asset returns is proposed. We adopt a Bayesian Dynamic Linear Model where microstructure noise is interpreted as measurement error, and asynchronous trading as missing observations in an otherwise synchronous series. Missing observations are treated as any other parameter, as typical in a Bayesian framework. An augmented Gibbs algorithm is used since all full conditionals are available and its convergence and robustness are discussed. A realistic simulation study compares our estimator with existing alternatives, under different liquidity and microstructure noise conditions. The results suggest that our estimator is superior in terms of RMSE particularly under severe conditions, such as portfolios of assets with heterogeneous liquidity and high level of microstructure noise. The application to the empirical dataset of ten tick-by-tick stock price series confirms the simulation results.

A quasi-maximum likelihood approach for integrated covariance matrix estimation with high frequency data

Estimating the integrated covariance matrix (ICM) from high frequency financial trading data is crucial to reflect the volatilities and covariations of the underlying trading instruments. Such an objective is difficult due to contaminated data with microstructure noises, asynchronous trading records, and increasing data dimensionality. In this paper, we study a quasi-maximum likelihood (QML) approach for estimating an ICM from high frequency financial data. We explore a novel multivariate moving average time series device that is convenient for evaluating the estimator both theoretically for its asymptotic properties and numerically for its practical implementations. We demonstrate that the QML estimator is consistent to the ICM, and is asymptotically normally distributed. Efficiency gain of the QML approach is theoretically quantified, and numerically demonstrated via extensive simulation studies. An application of the QML approach is illustrated through analyzing a high frequency financial trading data set.

Disentangled Jump-Robust Realized Covariances and Correlations with Non-Synchronous Prices

We study the class of disentangled realized estimators for the integrated covariance matrix of Brownian semimartingales with finite activity jumps. These estimators separate correlations and volatilities. We analyze different combinations of quantile- and median-based realized volatilities, and four estimators of realized correlations with three synchronization schemes. Their finite sample properties are studied under four data generating processes, in presence, or not, of microstructure noise, and under synchronous and asynchronous trading. The main finding is that the pre-averaged version of disentangled estimators based on Gaussian ranks (for the correlations) and median deviations (for the volatilities) provide a precise, computationally efficient, and easy alternative to measure integrated covariances on basis of noisy and asynchronous prices. A minimum variance portfolio application shows the superiority of this disentangled realized estimator in terms of numerous performance metrics.

Robust Estimation of a High-Dimensional Integrated Covariance Matrix

In this paper, we consider a robust method of estimating a realized covariance matrix calculated as the sum of cross products of intraday high-frequency returns. According to recent papers in financial econometrics, the realized covariance matrix is essentially contaminated with market microstructure noise. Although techniques for removing noise from the matrix have been studied since the early 2000s, they have primarily investigated a low-dimensional covariance matrix with statistically significant sample sizes. We focus on noise-robust covariance estimation under converse circumstances; that is, a high-dimensional covariance matrix possibly with a small sample size. For the estimation, we utilize a statistical hypothesis test based on the characteristic that the largest eigenvalue of the covariance matrix asymptotically follows a Tracy-Widom distribution. The null hypothesis assumes that log returns are not pure noises. If a sample eigenvalue is larger than the relevant critical value, then we fail to reject the null hypothesis. The simulation results show that the estimator studied here performs better than others as measured by mean squared error. The empirical analysis shows that our proposed estimator can be adopted to forecast future covariance matrices using real data.

A Bayesian High-Frequency Estimator of the Multivariate Covariance of Noisy and Asynchronous Returns

A multivariate positive definite estimator of the integrated covariance matrix of noisy and asynchronously observed asset returns is proposed. We adopt a Bayesian Dynamic Linear Model where microstructure noise is interpreted as measurement error, and asynchronous trading as missing observations in an otherwise synchronous series. Missing observations are treated as any other parameter, as typical in a Bayesian framework. An augmented Gibbs algorithm is used since all full conditionals are available and its convergence and robustness are discussed. A realistic simulation study compares our estimator with existing alternatives, under different liquidity and microstructure noise conditions. The results suggest that our estimator is superior in terms of RMSE particularly under severe conditions, such as portfolios of assets with heterogeneous liquidity and high level of microstructure noise. The application to the empirical dataset of ten tick-by-tick stock price series confirms the simulation results.

Proper orthogonal decomposition of building wind pressure specified at non-uniformly distributed pressure taps

The paper discusses the proper orthogonal decomposition of wind pressure specified at non-uniformly spaced locations. The developed methodology is illustrated by considering pressure on the roof of a low-rise building. The results are presented for both non-uniformly and uniformly distributed pressure taps. The case of the non-uniformly distributed taps was obtained by discarding some of the uniformly distributed taps. In the analysis, the pressure space covariance was computed and employed to solve an eigenvalue problem. The eigenvalues and eigenvectors for the non-uniformly distributed pressure taps were computed using a symmetric matrix resulting from transformation of the non-symmetric, integrated covariance matrix. The results were compared with those for the uniformly distributed pressure taps. The best agreement was obtained when the rectangular rule of integration was applied to the non-uniformly distributed pressure taps.

A state space model approach to integrated covariance matrix estimation with high frequency data

A state space model approach to integrated covariance matrix estimation with high frequency data