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Sparse principal component analysis for high‐dimensional stationary time series

Author

Listed:
  • Kou Fujimori
  • Yuichi Goto
  • Yan Liu
  • Masanobu Taniguchi

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 oracle inequalities for penalized principal component estimators for the large class of 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.

Suggested Citation

  • Kou Fujimori & Yuichi Goto & Yan Liu & Masanobu Taniguchi, 2023. "Sparse principal component analysis for high‐dimensional stationary time series," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(4), pages 1953-1983, December.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:4:p:1953-1983
    DOI: 10.1111/sjos.12664
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    References listed on IDEAS

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