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.

中文翻译：

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高维平稳时间序列的稀疏主成分分析

我们考虑高维平稳过程的稀疏主成分分析。当过程维数较大时，标准主成分分析效果较差。我们为包括重尾时间序列在内的大类过程建立了惩罚主成分估计量的预言不等式。确定了估计器的收敛速度。我们还阐明了在惩罚估计器中选择调整参数的理论速率。通过数值模拟证明了稀疏主成分分析的性能。时间序列数据的稀疏主成分分析的实用性通过对平均温度数据的应用来例证。