Longitudinal Cross-Temporal Dynamics in Foreign Exchange via Bayesian Multifractal Analysis

Multifractal temporal dynamics in asset price time series are well documented stylized facts, that however remained univariate when multivariate (basket) properties are critical in financial applications, and for long enough samples only. This is due to a lack of theoretical and practical tools for multivariate multifractal analysis, and tools that can be used on short sample sizes. Recently, multivariate wavelet-leader multifractal analysis has been grounded theoretically and the corresponding Bayesian estimation framework developed. Elaborating on preliminary attempts, the Bayesian multivariate multifractal formalism is used to perform a short-term sliding window analysis of the cross-temporal dynamics for 17 years of exchange rates. Results suggest solid and reproducible organized bursts of co-volatilities with temporal dynamics mainly driven by the same clock worldwide.