Covariance Matrix Estimation in Time Series

Robust Inverse Covariance Estimation under Noisy Measurements

This paper proposes a robust method to estimate the inverse covariance under noisy measurements. The method is based on the estimation of each column in the inverse covariance matrix independently via robust regression, which enables parallelization. Different from previous linear programming based methods that cannot guarantee a positive semi-definite covariance matrix, our method adjusts the ...

Nonparametric estimation of large covariance matrices of longitudinal data

Estimation of an unstructured covariance matrix is difficult because of its positivedefiniteness constraint. This obstacle is removed by regressing each variable on its predecessors, so that estimation of a covariance matrix is shown to be equivalent to that of estimating a sequence of varying-coefficient and varying-order regression models. Our framework is similar to the use of increasing-ord...

Dynamic covariance estimation via positive semidefinite dictionary learning

Time series are among the most prevalent forms of data we encounter in the real world, whether it be a sequence of audio, biomedical, demographic, climate, or financial measurements. Covariance estimation, where we try to estimate the covariance matrix of a time series, is a classic and important problem that can provide us predictive power in many applications. The vast majority of covariance ...

A subspace estimator for fixed rank perturbations of large random matrices

This paper deals with the problem of parameter estimation based on certain eigenspaces of the empirical covariance matrix of an observed multidimensional time series, in the case where the time series dimension and the observation window grow to infinity at the same pace. In the area of large random matrix theory, recent contributions studied the behavior of the extreme eigenvalues of a random ...

Supplement to “ Covariance Matrix Estimation for Stationary Time Series ”