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Statistical inference of causal interactions and synchronization between dynamical phenomena evolving on different temporal scales is of vital importance for better understanding and prediction of natural complex systems such as the Earth's climate. This article introduces and applies information theory diagnostics to phase and amplitude time series of different oscillatory components of observed data that characterizes El Niño/Southern Oscillation. A suite of significant interactions betweendoi:10.1038/s41612-018-0043-7 fatcat:2lwv2qjg7vd6dmlygkfy5rk5x4