Time series models for realized covariance matrices based on the matrix-F distribution

Covariance Matrix Estimation for Stationary Time Series

We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix estimator that can better characterize sparsity if the true covariance matrix is sparse. As our main tool, we implement Toeplitz [Math. Ann. 70 (1911) 351–376...

Covariance Matrix Estimation in Time Series

Covariances play a fundamental role in the theory of time series and they are critical quantities that are needed in both spectral and time domain analysis. Estimation of covariance matrices is needed in the construction of confidence regions for unknown parameters, hypothesis testing, principal component analysis, prediction, discriminant analysis among others. In this paper we consider both l...

DYNAMIC CONDITIONAL CORRELATION MODELS FOR REALIZED COVARIANCE MATRICES (Preliminary and incomplete version)

New dynamic models for realized covariance matrices are proposed. The expected value of the realized covariance matrix is specified in two steps: a model for each realized variance, and a model for the realized correlation matrix. The realized correlation model is a dynamic conditional correlation model. Estimation can be done in two steps as well, and a QML interpretation is given to each step...

Supplement to “ Covariance Matrix Estimation for Stationary Time Series ”

Econometric analysis of vast covariance matrices using composite realized kernels∗

We propose a composite realized kernel to estimate the ex-post covariation of asset prices. Composite realized kernels are a data efficient method where the covariance estimate is composed of univariate realized kernels to estimate variances and bivariate realized kernels to estimate correlations. We analyze the merits of our composite realized kernels in an ultra high dimensional environment, ...