Causal wavelet analysis of the Bitcoin price dynamics

Abstract

This study employed wavelet analysis to investigate Bitcoin price dynamics from 2014 to 2024. Unlike existing research, which relies on bidirectional wavelet functions, our approach utilized causal wavelet analysis. This method ensures that wavelet basis functions only account for past values, reflecting the impact of past prices on present prices while maintaining causality. The complex Morlet wavelet revealed that market complexity varies over time and scale. Our results showed that regions of high wavelet power coincide with bearish market phases leading to historical price maxima. The phase scalogram indicated that price return dynamics are primarily dominated by even components, reflecting fluctuation patterns across a wide range of oscillation frequencies. In a secondary analysis, we modified the wavelet analysis by decoupling the oscillation scale and the modulation (memory) function scale. This allowed us to estimate the decaying memory characteristic time scale. The resulting scalograms exhibited sharper magnitude and phase patterns, suggesting that Bitcoin price return dynamics are influenced by long-run memory. Our findings conclude that incorporating causality and long-run memory into wavelet analysis provides a more accurate characterization of cryptocurrency price dynamics.