Foreign Exchange Multivariate Multifractal Analysis

After Mandelbrot's seminal work, scale-free and multifractal temporal dynamics have been recognized as classical stylized facts for financial time series and massively documented. Multifractal analysis in finance has however mainly remained univariate (one time series at a time) when multivariate (or basket) properties are critical for financial applications. This is mostly due to a lack of theoretical foundations and practical tools for multivariate multifractal analysis. Expanding on a theoretically-grounded recently proposed multivariate multifractal formalism, the present work performs an original multivariate analysis for a basket of six Foreign Exchange rate time series. Beyond confirming multifractality for each component independently, the definition of cross-multifractalities amongst components is introduced, assessing cross-dependencies in temporal dynamics not already accounted for by cross-correlations. The key practical outcome is to show that, essentially, one same multifractal time governs jointly the temporal dynamics of all the Foreign Exchange time series studied here.