Regularized Estimation of Linear Functionals of Precision Matrices for High-Dimensional Time Series

Xiaohui Chen, Mengyu Xu, Wei Biao Wu

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)6459-6470
Number of pages12
JournalIEEE Transactions on Signal Processing
Issue number24
StatePublished - Dec 15 2016


  • High-dimension
  • regularization
  • sparsity
  • time series

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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