Causality in Continuous Wavelet Transform Without Spectral Matrix Factorization: Theory and Application

Abstract

This paper proposes a continuous wavelet transform causality method that dispenses with minimum-phase spectral density matrix factorization. Extant methods based on minimum-phase function are computationally intensive and those utilizing discrete wavelet transform also fail to unfold causal effects over time and frequency. The proposed method circumvents the need for minimum-phase transfer functions and is able to localize causality in time and frequency suitably. We study the ability of the proposed method using simulated data and find that it performs excellently in identifying the causal islands. We then use the method to analyze the time---frequency causal effects in the relationship between the US financial stress and economic activity and find that financial stress has been causing economic activity particularly during the unwinding financial and economic distress and not the other way around.