Empirical Assessment of Normalized Information Flow for Quantifying Causal Contributions
Abstract. To understand the plethora of important processes that are characterized by their complexity, such as global climate change, it is important to quantify causal contributions between time series variables. Here, we examine the hypothesis that the normalized causal sensitivity (nCS) can be measured by the (modified) normalized information flow, nIF (or mdnIF). The instantaneous causal sensitivity is defined by absolute causal contributions to the effect variable over the change in cause variable. The nCS needs to be comparable among i) causes, ii) at different times and iii) from various locations. Therefore, if our hypothesis holds, the nIF must also fulfil these three requirements. We verify, empirically, that the causal contributions between variables can be reasonably estimated by the product of a constant “maximal causal sensitivity” and a modified nIF. Between opposite causal directions, causal sensitivity can be further normalized by the larger “maximal causal sensitivity”. Our method is useful when there are: i) strong but hard-to-quantify noise contributions to the effect variable, ii) significant causal time-lags with a need to estimate the lag, iii) many causes from various locations to an overall mean effect with a need to differentiate their causal contributions, or iv) causal contributions at higher order.
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