Generalized principal component analysis for moderately non-stationary vector time series

This paper extends the principal component analysis (PCA) to moderately non-stationary vector time series. We propose a method that searches for a linear transformation of the original series such that the transformed series is segmented into uncorrelated subseries with lower dimensions. A columns’ rearrangement method is proposed to regroup transformed series based on their relationships. We discuss the theoretical properties of the proposed method for fixed and large dimensional cases. Many simulation studies show our approach is suitable for moderately non-stationary data. Illustrations on real data are provided.