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<jats:title>Abstract</jats:title> <jats:p> <jats:italic>Objective.</jats:italic> Noise-assisted multivariate empirical mode decomposition (NA-MEMD) based causal decomposition depicts a cause and effect relationship that is not based on the term of prediction, but rather on the phase dependence of time series. Here, we present the NA-MEMD based causal decomposition approach according to the covariation and power views traced to Hume and Kant: <jats:italic>a priori</jats:italic> cause-effect interaction is first acquired, and the presence of a candidate cause and of the effect is then computed from the sensory input somehow. <jats:italic>Approach.</jats:italic> Based on the definition of NA-MEMD based causal decomposition, we show such causal relation is a phase relation where the candidate causes are not merely followed by effects, but rather produce effects. <jats:italic>Main results.</jats:italic> The predominant methods used in neuroscience (Granger causality, empirical mode decomposition-based causal decomposition) are validated, showing the applicability of NA-MEMD based causal decomposition, particular to brain physiological processes in bivariate and multiscale time series. <jats:italic>Significance.</jats:italic> We point to the potential use in the causality inference analysis in a complex dynamic process.</jats:p>