Advanced Permutation Entropy Metrics for Bitcoin: Towards Robust Early Warning Indicators of Market Instability

Abstract

The article explores the potential of advanced permutation entropy (PEn) techniques as early-warning indicators for detecting instability in cryptocurrency markets, specifically focusing on Bitcoin. While classical permutation entropy is a popular method for assessing time series complexity due to its simplicity and computational efficiency, it has limitations - especially in its inability to account for amplitude variations and identical values.

To address these shortcomings, the authors present a comparative analysis of the classical PEn and three of its extended versions: Weighted Permutation Entropy (WPEn); Amplitude-Aware Permutation Entropy (AAPEn); Uniform Quantization-Based Permutation Entropy (UPEn).

These methods are applied to the 2017–2018 Bitcoin market crash. The study reveals that advanced metrics, particularly AAPEn, are more sensitive to subtle changes in market dynamics that precede price collapses. AAPEn is highlighted for its ability to incorporate both the order and amplitude of data points, allowing it to detect significant fluctuations that may signal panic or uncertainty in the market.

The results suggest that variations in advanced entropy metrics can serve as valuable indicators of market efficiency shifts and irregular patterns, making them promising tools for forecasting financial turbulence. The article concludes that incorporating such methods into financial risk management systems could significantly enhance the predictive capabilities of early-warning mechanisms in the volatile digital asset ecosystem.