A time-varying distance based interval-valued functional principal component analysis method – A case study of consumer price index

Abstract

Functional principal component analysis (FPCA) is an extension of conventional principal component analysis (PCA) that allows the processing of functional data. Besides the reduction in dimensionality that is inherent to PCA, FPCA relies on fewer assumptions and offers a greater ability to visualize the functional data. Thus, FPCA can be used in, for example, social, economic, and medical research. However, the existing FPCA methods are sensitive to outliers, and underperform when extracting features from interval-valued functional data. At the same time, the existing PCA methods for interval-valued functional data suffer from inconsistency in the interpretation of the principal components, and substantial information loss. Therefore, this paper proposes an interval-valued functional principal component analysis (IFPCA) method based on the time-varying distance function. The time-varying distance function containing information on the midpoint and radius is constructed to mitigate information loss. The novel IFPCA method is also able to solve the problem of the inconsistent interpretation of the principal components. The effectiveness of the method is verified by considering the case of the consumer price index.