Abstract
This paper provides a statistical methodology for quantifying causality in complex dynamical systems, based on analysis of multidimensional time series data of the state variables. The methodology integrates Granger’s causality analysis based on the log-likelihood function expansion (Partial pair-wise causality), and Akaike’s power contribution approach over the whole frequency domain (Total causality). The proposed methodology addresses a major drawback of existing methodologies namely, their inability to use time series observation of state variables to quantify causality in complex systems. We first perform a simulation study to verify the efficacy of the methodology using data generated by several multivariate autoregressive processes, and its sensitivity to data sample size. We demonstrate application of the methodology to real data by deriving inter-species relationships that define key food web drivers of the Barents Sea ecosystem. Our results show that the proposed methodology is a useful tool in early stage causality analysis of complex feedback systems.
Highlights
The first attempt at deriving causal inference between variables goes back to a study on feedback systems by Wiener [1], where by his definition, a given time series is causal to another if knowledge of the first series reduces the mean square prediction error of the second
We have provided a statistical methodology that integrates the pairwise causality methodology by Granger and Geweke, with the total causality approach defined by the Akaike’s power contribution
We have investigated the sensitivity of the method through simulation studies, using data generated by Multivariate Autoregressive (MAR) models
Summary
The first attempt at deriving causal inference between variables goes back to a study on feedback systems by Wiener [1], where by his definition, a given time series is causal to another if knowledge of the first series reduces the mean square prediction error of the second. Granger [2] followed this notion of causality, and applied it to the analysis of economic time series data. Granger applied bivariate time series models within the time domain, and based on this, defined the prediction error as a metric for assessing model results. A parallel development to Granger’s approach is by Akaike [4], who provided a feedback system analysis based on a multivariate auto-regressive model. We define feedback as being present when given bivariate time series, each of them is mutually causal to the other [5].
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