Principal Components Analysis of Nonstationary Time Series Data

by Joseph Ryan G. Lansangan and Erniel B. Barrios .

Abstract: The effect of nonstationarity in time series columns of input data in principal components analysis is examined. This usually happens when indexing economic indicators for monitoring purposes. The first component averages all the variables without reducing dimensionality. As an alternative, sparse principal components analysis can be used but attainment of sparsity among the loadings is influenced by the choice of a parameter (?). Varying cross-correlation and autocorrelation structures were simulated with number of observations exceeding the number of variables. Sparse component loadings even for nonstationary time series columns of the input data can be achieved provided that appropriate value of ? is used. We provide the possible range of values of ? that will ensure convergence of the sparse principal components algorithm and sparsity of component loadings.

Key Words: principal components analysis, sparse principal components analysis, time series, non-stationarity, singular value decomposition

Authors:
Joseph Ryan G. Lansangan, jrlansangan@yahoo.com
Erniel B. Barrios ernielb@yahoo.com

Editor: Ravi Khattree , khattree@oakland.edu

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