Regularized Estimation Of Linear Functionals Of Precision Matrices For High-Dimensional Time Series

Keywords

High-dimension; regularization; sparsity; time series

Abstract

This paper studies a Dantzig-selector type regularized estimator for linear functionals of high-dimensional linear processes. Explicit rates of convergence of the proposed estimator are obtained and they cover the broad regime from independent identically distributed samples to long-range dependent time series and from sub-Gaussian innovations to those with mild polynomial moments. It is shown that the convergence rates depend on the degree of temporal dependence and the moment conditions of the underlying linear processes. The Dantzig-selector estimator is applied to the sparse Markowitz portfolio allocation and the optimal linear prediction for time series, in which the ratio consistency when compared with an oracle estimator is established. The effect of dependence and innovation moment conditions is further illustrated in the simulation study. Finally, the regularized estimator is applied to classify the cognitive states on a real functional magnetic resonance imaging dataset and to portfolio optimization on a financial dataset.

Publication Date

12-15-2016

Publication Title

IEEE Transactions on Signal Processing

Volume

64

Issue

24

Number of Pages

6459-6470

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1109/TSP.2016.2605079

Socpus ID

85027489613 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85027489613

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