Fractal properties, information theory, and market efficiency

Xavier Brouty () and Matthieu Garcin ()
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Xavier Brouty: ESILV - École Supérieure d'Ingénierie Léonard de Vinci
Matthieu Garcin: DVRC - De Vinci Research Center - DVHE - De Vinci Higher Education

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Abstract: Considering that both the entropy-based market information and the Hurst exponent are useful tools for determining whether the efficient market hypothesis holds for a given asset, we study the link between the two approaches. We thus provide a theoretical expression for the market information when log-prices follow either a fractional Brownian motion or its stationary extension using the Lamperti transform. In the latter model, we show that a Hurst exponent close to 1/2 can lead to a very high informativeness of the time series, because of the stationarity mechanism. In addition, we introduce a multiscale method to get a deeper interpretation of the entropy and of the market information, depending on the size of the information set. Applications to Bitcoin, CAC 40 index, Nikkei 225 index, and EUR/USD FX rate, using daily or intraday data, illustrate the methodological content.

Keywords: fractional Brownian motion; Hurst exponent; market information; multiscale entropy; Shannon entropy; stationary process (search for similar items in EconPapers)
Date: 2023-06-21
Note: View the original document on HAL open archive server: https://hal.science/hal-04138656v1
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