Segmented inner composition alignment to detect coupling of different subsystems

Inner composition alignment (IOTA) is a recently proposed, permutation-based asymmetric association measure to identify coupling (interrelations) between different subsystems, together with the associated directionality, which is especially designed for very short time series. In this paper, we extended IOTA to investigate the coupling between subsystems for long time series, which is called segmented IOTA (SIOTA). Both global and local degree of couplings can be detected by varying the segment length. SIOTA is then applied to investigate interactions between stock market indices of America and different countries, and obtain many interesting results. Compared to SIOTA, cross-sample entropy is introduced to obtain consistent results. Besides, time-delay SIOTA, modified from SIOTA, is employed to find the best delay time for two time series with missing values.