Realized Covariance Matrices Research Articles

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.

Forecasting Realized (Co)Variances with a Block Structure Wishart Autoregressive Model

The increased availability of high-frequency data provides new tools for forecasting of variances and covariances between assets. However, recent realized (co)variance models may suffer from a 'curse of dimensionality' problem similar to that of multivariate GARCH specifications. As a result, they need strong parameter restrictions, in order to avoid non-interpretability of model coefficients, as in the matrix and log exponential representations. Among the proposed models, the Wishart autoregressive model introduced by Gourieroux et al. (2005) analyzes the realized covariance matrices without any restriction on the parameters while maintaining coefficient interpretability. Indeed, the model, under mild stationarity conditions, provides positive definite forecasts for the realized covariance matrices. Unfortunately, it is still not feasible for large asset cross-section dimensions. In this paper we propose a restricted parametrization of the Wishart Autoregressive model which is feasible even with a large cross-section of assets. In particular, we assume that the asset variances-covariances have no or limited spillover and that their dynamic is sector-specific. In addition, we propose a Wishart-based generalization of the HAR model of Corsi (2004). We present an empirical application based on variance forecasting and risk evaluation of a portfolio of two US treasury bills and two exchange rates. We compare our restricted specifications with the traditional WAR parameterizations. Our results show that the restrictions may be supported by the data and that the risk evaluations of the models are extremely close. This confirms that our model can be safely used in a large cross-sectional dimension given that it provides results similar to fully parametrized specifications.

Federated Kalman Filtering Via Formation of Relation Equations in Augmented State Space

A new approach to the synthesis of federated e lters used in the solution of multisensor system state estimation problems is considered. The method is based on two principles. The principle of state vector augmentation makes it possible to substitute a solution of an optimal estimation problem using a centralized Kalman e lter for bias error measurement processing for an optimal estimation problem solution in the augmented state space. The equivalence of estimation results is achieved by a certain adjustment of local e lters and formation of additional error-free pseudomeasurements. The principle of rejection of part of the information contained in the relation equations makes it possible to establish a relation between federated e ltering and e ltering in the augmented state space, between weighting of local estimates and processing of pseudomeasurements, and, as a result, to reveal the reasons for the loss of optimality of federated e lters. It is emphasized that at a certain adjustment, the covariance matrix calculated in the master e lter is an upper bound for a real covariance matrix of a global estimate, and it can be used as an accuracy characteristic of the parameters estimated. The results of a simulation are given to illustrate the approach.

Optimization of imaging configuration

In a bundle adjustment, the imaging configuration is an important factor in computing the accuracy of the object points. The theory of optimizing network configuration is applied to photogrammetry. For application to imaging, camera stations are shifted in order to improve the precision of object-point determination by improved intersections of rays. A criterion matrix is used as a target function in the optimization process. This matrix is constructed as an ideal covariance matrix that demands homogeneous and isotropic errors. The optimization process approximates the real covariance matrix of the network to the ideal criterion matrix by means of small shifts of the camera stations. The approximation is performed by a least-squares process which minimizes the discrepancies between the real covariance matrix of a given starting configuration, and an ideal, constructed criterion matrix.