Fractal properties, information theory, and market efficiency
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
Cite
@article{arxiv.2306.13371,
title = {Fractal properties, information theory, and market efficiency},
author = {Xavier Brouty and Matthieu Garcin},
journal= {arXiv preprint arXiv:2306.13371},
year = {2023}
}