Paper: arXiv 2306.13371

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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper contains dense theoretical derivations using fractional Brownian motion, the Lamperti transform, and entropy definitions, indicating high mathematical complexity, while its empirical application to real financial data (Bitcoin, indices, FX) and multiscale methods demonstrates solid backtest-ready implementation.

Research Flowchart

  flowchart TD
  A["Research Goal: Link between Hurst Exponent<br>and Entropy-based Market Information"] --> B["Key Methodology: Theoretical Framework"]
  
  B --> C{"Data & Inputs"}
  C --> D["Bitcoin, CAC 40, Nikkei 225, EUR/USD"]
  C --> E["Daily & Intraday Log-Prices"]
  
  D & E --> F["Computational Processes"]
  F --> G["Multiscale Analysis<br>Estimate Hurst Exponent H"]
  F --> H["Calculate Market Information<br>Entropy-based Metric"]
  
  G & H --> I["Key Findings & Outcomes"]
  I --> J["Stationary Extension (Lamperti)<br>High Informativeness near H=0.5"]
  I --> K["Validation of Multiscale Method<br>for Interpreting EMH"]