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.