Sparse principal component analysis for high-dimensional stationary time series

TL;DR

This paper develops a sparse principal component analysis method tailored for high-dimensional stationary time series, providing theoretical guarantees, tuning guidelines, and demonstrating its effectiveness through simulations and real data application.

Contribution

It introduces penalized estimators for sparse PCA in high-dimensional time series, with proven convergence rates and practical tuning strategies, including for heavy-tailed data.

Findings

Establishes oracle inequalities for penalized PCA estimators.

Provides convergence rates for estimators in high-dimensional settings.

Demonstrates effectiveness through simulations and temperature data analysis.

Abstract

We consider the sparse principal component analysis for high-dimensional stationary processes. The standard principal component analysis performs poorly when the dimension of the process is large. We establish the oracle inequalities for penalized principal component estimators for the processes including heavy-tailed time series. The rate of convergence of the estimators is established. We also elucidate the theoretical rate for choosing the tuning parameter in penalized estimators. The performance of the sparse principal component analysis is demonstrated by numerical simulations. The utility of the sparse principal component analysis for time series data is exemplified by the application to average temperature data.