Cyclic Nonlinear Correlation Analysis for Time Series

Abstract

Principal component analysis (PCA) and kernel PCA allow the decorrelation of data with respect to a basis that is found via variance maximization. However, these techniques are based on pointwise correlations. Especially in the context of time series analysis this is not optimal. We present a novel generalization of PCA that allows to imprint any desired correlation pattern. Thus the proposed method can be used to incorporate previously known statistical dependencies between input variables into the model which is increasing the overall performance. This is achieved by generalizing the projection onto the direction of maximum variance—as known from PCA—to a projection onto a multi-dimensional subspace. We focus on the use of cyclic correlation patterns, which is especially of interest in the domain of time series analysis. Beneath introducing the presented variation of PCA, we discuss the role of this method with respect to other well-known time series analysis techniques.

Keywords

• PCA
• discrete Fourier transform
• filter
• correlation
• time series
• kernel PCA