Extreme point bias compensation: A similarity method of functional clustering and its application to the stock market

Abstract

Functional clustering is based on functional similarity measures that are adapted to functional data. However, the existing functional similarity measures account either for the position (value) or temporal deviation (bias) of extreme points of the functional curves. This may lead to erroneous conclusions on the similarities of the curves. In this case, most functional clustering measures underperform in (for example) the analysis of stock market data. To address this methodological limitation, a new similarity measure that is based on extreme point bias compensation is proposed in this paper. By penalizing the curves with the temporal deviation of extreme points and rewarding the curves that are close to each other, the new similarity measure better reflects the shape of the curve. In addition, the proposed method overcomes the difficulty of unifying the dimensions of the horizontal and vertical axes (i.e., time and function value) when calculating the distance between two adjacent extreme points. Finally, an empirical example of stock return analysis verifies the validity of this new measure.