Realized Covariance Estimator Research Articles

High-dimensional realized covariance estimation: a parametric approach

We introduce a parametric dynamic factor specification for high-frequency financial data that simplifies considerably the estimation of the realized covariance matrix in high dimensions. The estimation method is tested in an empirical setting that emphasizes the effect of the curse of dimensionality. Compared to standard parametric approaches, our factor specification is computationally less demanding and provides statistically indistinguishable performances in standard risk management applications. The method is also assessed on Monte-Carlo simulations under several forms of misspecification.

Efficient and positive semidefinite pre-averaging realized covariance estimator

Efficient and positive semidefinite pre-averaging realized covariance estimator

A closed-form formula characterization of the Epps effect

In this study we provide an analytical characterization of the impact of zero returns on the popular realized covariance estimator of Barndorff-Nielsen and Shephard [Econometric analysis of realized covariation: High frequency based covariance, regression, and correlation in financial economics. Econometrica, 2004, 72(3), 885–925]. In our framework, efficient price processes evolve as a semimartingale with some likelihood of repeated prices. We show that the standard realized covariance estimator is asymptotically affected by a downward bias, and the size of the bias depends on these likelihoods. We demonstrate that this result can be used to construct a consistent estimator of the integrated covariance of a vector semimartingale. The advantages with respect to other estimators are discussed with data.

Sparse Kalman filtering approaches to realized covariance estimation from high frequency financial data

Estimation of the covariance matrix of asset returns from high frequency data is complicated by asynchronous returns, market mi- crostructure noise and jumps. One technique for addressing both asynchronous returns and market microstructure is the Kalman-EM (KEM) algorithm. However the KEM approach assumes log-normal prices and does not address jumps in the return process which can corrupt estimation of the covariance matrix. In this paper we extend the KEM algorithm to price models that include jumps. We propose two sparse Kalman filtering approaches to this problem. In the first approach we develop a Kalman Expectation Conditional Maximization (KECM) algorithm to determine the un- known covariance as well as detecting the jumps. For this algorithm we consider Laplace and the spike and slab jump models, both of which promote sparse estimates of the jumps. In the second method we take a Bayesian approach and use Gibbs sampling to sample from the posterior distribution of the covariance matrix under the spike and slab jump model. Numerical results using simulated data show that each of these approaches provide for improved covariance estima- tion relative to the KEM method in a variety of settings where jumps occur.

Quadratic covariation estimation of an irregularly observed semimartingale with jumps and noise

This paper presents a central limit theorem for a pre-averaged version of the realized covariance estimator for the quadratic covariation of a discretely observed semimartingale with noise. The semimartingale possibly has jumps, while the observation times show irregularity, non-synchronicity, and some dependence on the observed process. It is shown that the observation times' effect on the asymptotic distribution of the estimator is only through two characteristics: the observation frequency and the covariance structure of the noise. This is completely different from the case of the realized covariance in a pure semimartingale setting.

Economic benefits of using realized covariance forecasts in risk-based portfolios

ABSTRACTThis article examines the economic benefit of using the realized covariance matrix forecasts, for constructing the risk-based portfolios. We use the two-scale realized covariance estimator (TSC), the jump robust two-scale realized covariance estimator (RTSC) and the realized bipower covariance estimator (BPC), to forecast the daily realized covariance matrix. Using these covariance matrix forecasts, we implement three risk-based portfolios: the global minimum variance portfolio, the equal risk contribution portfolio and the most diversified portfolio. There is evidence that the portfolio performance improves by using TSC or RTSC estimators as compared to the daily-returns-based estimator. The performance gains are robust to the choice of risk-based portfolio strategy, the degree of investor’s relative risk-aversion, the market conditions and the choice of time intervals.

Missing in Asynchronicity: A Kalman‐em Approach for Multivariate Realized Covariance Estimation

SummaryMotivated by the need for a positive‐semidefinite estimator of multivariate realized covariance matrices, we model noisy and asynchronous ultra‐high‐frequency asset prices in a state‐space framework with missing data. We then estimate the covariance matrix of the latent states through a Kalman smoother and expectation maximization (KEM) algorithm. Iterating between the two EM steps, we obtain a covariance matrix estimate which is robust to both asynchronicity and microstructure noise, and positive‐semidefinite by construction. We show the performance of the KEM estimator using extensive Monte Carlo simulations that mimic the liquidity and market microstructure characteristics of the S&P 500 universe as well as in a high‐dimensional application on US stocks. KEM provides very accurate covariance matrix estimates and significantly outperforms alternative approaches recently introduced in the literature. Copyright © 2014 John Wiley & Sons, Ltd.

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.

Dynamic stock market covariances in the Eurozone

This paper examines the short-term dynamics, macroeconomic sensitivities, and longer-term trends in the variances and covariances of national equity market index daily returns for eleven countries in the Euro currency zone. We modify Colacito, Engle and Ghysel's Mixed Data Sampling Dynamic Conditional Correlation Garch model to include a new scalar measure for the degree of correlatedness in time-varying correlation matrices. We also explore the robustness of the findings with a less model-dependent realized covariance estimator. We find a secular trend toward higher correlation during our sample period, and significant linkages between macroeconomic and market-wide variables and dynamic correlation. One notable finding is that average correlation between these markets is lower when their average GDP growth rate is lower or when more of them have negative GDP growth.

Dynamic Stock Market Covariances in the Eurozone

This paper examines the short-term dynamics, macroeconomic sensitivities, and longer-term trends in the variances and covariances of national equity market index daily returns for eleven countries in the Euro currency zone. We modify Colacito, Engle and Ghysel's Mixed Data Sampling Dynamic Conditional Correlation Garch model to include a new scalar measure for the degree of correlatedness in time-varying correlation matrices. We also explore the robustness of the findings with a less model-dependent realized covariance estimator. We find a secular trend toward higher correlation during our sample period, and significant linkages between macroeconomic and market-wide variables and dynamic correlation. One notable finding is that average correlation between these markets is lower when their average GDP growth rate is lower or when more of them have negative GDP growth.

Missing in Asynchronicity: A Kalman-EM Approach for Multivariate Realized Covariance Estimation

Motivated by the need of an unbiased and positive-semidefinite estimator of multivariate realized covariance matrices, we model noisy and asynchronous ultra-high-frequency asset prices in a state-space framework with missing data. We then estimate the covariance matrix of the latent states through a Kalman smoother and Expectation Maximization (KEM) algorithm. Iterating between the two EM steps, we obtain a covariance matrix estimate which is robust to both asynchronicity and microstructure noise, and positive-semidefinite by construction. We show the performance of the KEM estimator using extensive Monte Carlo simulations mimicking the liquidity and market microstructure characteristics of the S&P 500 universe as well as in an high-dimensional application on US stocks: KEM provides very accurate covariance matrix estimates and significantly outperforms alternative approaches recently introduced in the literature.

A blocking and regularization approach to high‐dimensional realized covariance estimation

SUMMARYWe introduce a blocking and regularization approach to estimate high‐dimensional covariances using high‐frequency data. Assets are first grouped according to liquidity. Using the multivariate realized kernel estimator of Barndorff‐Nielsen et al. (2010), the covariance matrix is estimated block‐wise and then regularized. The performance of the resulting blocking and regularization (‘RnB’) estimator is analyzed in an extensive simulation study mimicking the liquidity and market microstructure features of the S&P 1500 universe. The RnB estimator yields efficiency gains for varying liquidity settings, noise‐to‐signal ratios and dimensions. An empirical application of estimating daily covariances of the S&P 500 index confirms the simulation results. Copyright © 2010 John Wiley & Sons, Ltd.

Covariance Estimation in Dynamic Portfolio Optimization: A Realized Single Factor Model

Realized covariance estimation for large dimension problems is little explored and poses challenges in terms of computational burden and estimation error. In a global minimum volatility setting, we investigate the performance of covariance conditioning techniques applied to the realized covariance matrices of the 30 DJIA stocks. We find that not only is matrix conditioning necessary to deliver the benefits of high frequency data, but a single factor model, with a smoothed covariance estimate, outperforms the fully estimated realized covariance in one-step ahead forecasts. Furthermore, a mixed-frequency single-factor model - with factor coefficients estimated using low-frequency data and variances estimated using high-frequency data performs better than the realized single-factor estimator. The mixed-frequency model is not only parsimonious but it also avoids estimation of high-frequency covariances, an attractive feature for less frequently traded assets. Volatility dimension curves reveal that it is difficult to distinguish among estimators at low portfolio dimensions, but for well-conditioned estimators the performance gain relative to the benchmark 1/N portfolio increases with N.

Realized Covariance Estimation in Dynamic Portfolio Optimization

Mean-variance portfolio optimization requires both invertible and well-conditioned covariance matrices. This paper compares the performance of covariance conditioning techniques applied to the realized covariance matrices of the portfolio of constituents of the Dow Jones Industrial Average. We use the volatility of portfolio returns derived from volatility-timing investment strategies employing dierent conditioning techniques as the criterion of assessment. As portfolio dimensions increase there is increasing need for matrix conditioning to maintain the precision improvement oered by intraday data. We nd that the relative performance of the single factor model provides a computationally tractable alternative to fully estimated realized covariance matrices in a global minimum variance dynamic portfolio setting.

Realized Correlation Tick-By-Tick

In this paper we extend the approach of directly using all the available tick-by-tick data to the realized correlation estimation. As for the realized volatility, the presence of market microstructure can induce signiflcant bias in standard realized covariance measure computed with artiflcially regularly spaced returns. Contrary to these standard approaches we analyse a very simple and unbiased realized covariance estimator which does not resort on the construction of a regular grid, but directly and e‐ciently employs the raw tick-by-tick returns of the two series. Montecarlo simulations calibrated on realistic market microstructure conditions show that this simple tick-by-tick covariance posses no bias and the smallest dispersion, among the covariance estimators considered in the study. Combining this ralized covariance measure together with tickby-tick volatility estimator we obtain a realized correlation measure where both the volatilities and the covariances are computed from tick-by-tick data. In the empirical analysis performed on S&P 500 and US bond data we apply the HAR model to the tick-by-tick realized correlation obtaining remarkably good out of sample forecasting performance.

On covariance estimation of non-synchronously observed diffusion processes

We consider the problem of estimating the covariance of two diffusion processes when they are observed only at discrete times in a non-synchronous manner. The modern, popular approach in the literature, the realized covariance estimator, which is based on (regularly spaced) synchronous data, is problematic because the choice of regular interval size and data interpolation scheme may lead to unreliable estimation. We propose a new estimator which is free of any `synchronization' processing of the original data, hence free of bias or other problems caused by it.