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Principal Components Analysis Of Nonstationary Time Series Data

机译：非平稳时间序列数据的主成分分析

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The effect of nonstationarity in time series columns of input data in principal components analysis is examined. Nonstationarity are very common among economic indicators collected over time. They are subsequently summarized into fewer indices for purposes of monitoring. Due to the simultaneous drifting of the nonstationary time series usually caused by the trend, the first component averages all the variables without necessarily reducing dimensionality. Sparse principal components analysis can be used, but attainment of sparsity among the loadings (hence, dimension-reduction is achieved) is influenced by the choice of parameter(s) (λ_(l,i)). Simulated data with more variables than the number of observations and with different patterns of cross-correlations and autocorrelations were used to illustrate the advantages of sparse principal components analysis over ordinary principal components analysis. Sparse component loadings for nonstationary time series data can be achieved provided that appropriate values of λ_(l,i) are used. We provide the range of values of λ_(l,i) that will ensure convergence of the sparse principal components algorithm and consequently achieve sparsity of component loadings.
机译：在主成分分析中检查了输入数据的时间序列列中的非平稳性的影响。在一段时间内收集的经济指标中，非平稳性非常普遍。随后出于监控目的将它们汇总为更少的索引。由于通常由趋势引起的非平稳时间序列的同时漂移，因此第一部分对所有变量取平均值，而不必降低维数。可以使用稀疏主成分分析，但是载荷之间稀疏性的获得（因此，实现了降维）受参数（λ_（l，i））的选择影响。具有比观察次数更多的变量和互相关和自相关的不同模式的模拟数据被用来说明稀疏主成分分析相对于普通主成分分析的优势。只要使用适当的λ_（l，i）值，就可以实现非平稳时间序列数据的稀疏分量加载。我们提供了λ_（l，i）的值范围，该范围将确保稀疏主成分算法的收敛性，从而实现稀疏的成分加载。

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