Foreign Exchange Multivariate Multifractal Analysis

Patrice Abry (), Yannick Malevergne, Herwig Wendt (), Stéphane Jaffard (), Marc Senneret () and Laurent Jaffrès ()
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Patrice Abry: Phys-ENS - Laboratoire de Physique de l'ENS Lyon - ENS de Lyon - École normale supérieure de Lyon - Université de Lyon - Université de Lyon - CNRS - Centre National de la Recherche Scientifique
Herwig Wendt: Phys-ENS - Laboratoire de Physique de l'ENS Lyon - ENS de Lyon - École normale supérieure de Lyon - Université de Lyon - Université de Lyon - CNRS - Centre National de la Recherche Scientifique
Stéphane Jaffard: LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées - UPEM - Université Paris-Est Marne-la-Vallée - BEZOUT - Fédération de Recherche Bézout - CNRS - Centre National de la Recherche Scientifique - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12 - CNRS - Centre National de la Recherche Scientifique

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Abstract: 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.

Keywords: multivariate multifractal analysis; wavelet leaders; Financial times series; Foreign exchange; basket properties (search for similar items in EconPapers)
Date: 2022-08-29
New Economics Papers: this item is included in nep-ets
Note: View the original document on HAL open archive server: https://hal.science/hal-03735497v2
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Published in European Signal Processing Conference (EUSIPCO), European Association for Signal Processing (EURASIP), Aug 2022, Belgrade, Serbia. ⟨10.23919/EUSIPCO55093.2022.9909911⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03735497

DOI: 10.23919/EUSIPCO55093.2022.9909911

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