Sparse principal component analysis for high dimensional multivariate time series

Zhaoran Wang, Fang Han, Han Liu

Research output: Contribution to journalConference article

4 Scopus citations

Abstract

We study sparse principal component analy- sis (sparse PCA) for high dimensional multi- variate vector autoregressive (VAR) time se- ries. By treating the transition matrix as a nuisance parameter, we show that sparse PCA can be directly applied on analyzing multivariate time series as if the data are i.i.d. generated. Under a double asymp- totic framework in which both the length of the sample period T and dimensionality d of the time series can increase (with possi- bly d ≥ T), we provide explicit rates of con- vergence of the angle between the estimated and population leading eigenvectors of the time series covariance matrix. Our results suggest that the spectral norm of the tran- sition matrix plays a pivotal role in deter- mining the final rates of convergence. Im- plications of such a general result is further illustrated using concrete examples. The re- sults of this paper have impacts on different applications, including financial time series, biomedical imaging, and social media, etc.

Original languageEnglish (US)
Pages (from-to)48-56
Number of pages9
JournalJournal of Machine Learning Research
Volume31
StatePublished - Jan 1 2013
Event16th International Conference on Artificial Intelligence and Statistics, AISTATS 2013 - Scottsdale, United States
Duration: Apr 29 2013May 1 2013

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence

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