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Title: Regularized estimation of high dimensional auto- and cross-covariance matrices Authors:  Tommaso Proietti - University of Roma Tor Vergata (Italy) [presenting]
Abstract: The estimation of the (auto- and) cross-covariance matrices of a stationary random process plays a central role in prediction theory and time series analysis. When the dimension of the matrix is of the same order of magnitude as the number of observations and/or the number of time series, the sample cross-covariance matrix provides an inconsistent estimator. In the univariate framework, we proposed an estimator based on regularizing the sample partial autocorrelation function, via a modified Durbin-Levinson algorithm that receives as an input the banded and tapered sample partial autocorrelations and returns a consistent and positive definite estimator of the autocovariance matrix; also, we established the convergence rate of the regularized autocovariance matrix estimator and characterised the properties of the corresponding optimal linear predictor. The multivariate generalization is based on a regularized Whittle algorithm, shrinking the lag structure towards a finite order vector autoregressive system (by penalizing the partial canonical correlations), on the one hand, and shrinking the cross-sectional covariance towards a diagonal target, on the other.