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
Copyright Status
Unknown
Socpus ID
85027489613 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/85027489613
STARS Citation
Chen, Xiaohui; Xu, Mengyu; and Wu, Wei Biao, "Regularized Estimation Of Linear Functionals Of Precision Matrices For High-Dimensional Time Series" (2016). Scopus Export 2015-2019. 3472.
https://stars.library.ucf.edu/scopus2015/3472