Akaike’s relative power contribution: a revisit

Abstract Statistical analysis of inter-variable relationships in multivariate time series plays a central role in econometrics and engineering. Existing approaches based on vector autoregressive models and spectral decompositions often rely on assumptions that limit their interpretability when innovation variables are correlated. This paper highlights these limitations and proposes a decomposition of the predictive spectral density matrix under a finite prediction horizon. Based on this framework, we introduce the Predictive Relative Power Contribution (PRPC), which generalizes relative power contribution measures to the predictive setting. The practical utility of the proposed approach is illustrated and discussed.