Bayesian framework for characterizing cryptocurrency market dynamics, structural dependency, and volatility using potential field

ArXiv ID: 2308.01013 “View on arXiv”

Authors: Unknown

Abstract

Identifying the structural dependence between the cryptocurrencies and predicting market trend are fundamental for effective portfolio management in cryptocurrency trading. In this paper, we present a unified Bayesian framework based on potential field theory and Gaussian Process to characterize the structural dependency of various cryptocurrencies, using historic price information. The following are our significant contributions: (i) Proposed a novel model for cryptocurrency price movements as a trajectory of a dynamical system governed by a time-varying non-linear potential field. (ii) Validated the existence of the non-linear potential function in cryptocurrency market through Lyapunov stability analysis. (iii) Developed a Bayesian framework for inferring the non-linear potential function from observed cryptocurrency prices. (iv) Proposed that attractors and repellers inferred from the potential field are reliable cryptocurrency market indicators, surpassing existing attributes, such as, mean, open price or close price of an observation window, in the literature. (v) Analysis of cryptocurrency market during various Bitcoin crash durations from April 2017 to November 2021, shows that attractors captured the market trend, volatility, and correlation. In addition, attractors aids explainability and visualization. (vi) The structural dependence inferred by the proposed approach was found to be consistent with results obtained using the popular wavelet coherence approach. (vii) The proposed market indicators (attractors and repellers) can be used to improve the prediction performance of state-of-art deep learning price prediction models. As, an example, we show improvement in Litecoin price prediction up to a horizon of 12 days.

Keywords: Gaussian Process, Potential Field Theory, Dynamical Systems, Bayesian Inference, Lyapunov Stability, Cryptocurrencies

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical concepts including dynamical systems, Lyapunov stability analysis, Bayesian inference with Gaussian Processes, and potential field theory, indicating high mathematical density. Empirically, it validates its model using historical cryptocurrency data across multiple crash periods, compares results with established wavelet coherence methods, and demonstrates practical improvements in prediction tasks, showcasing significant implementation and backtest-ready analysis.

  flowchart TD
    A["Research Goal:<br>Characterize Crypto Market Dynamics &<br>Structural Dependency for Portfolio Management"] --> B["Data Input:<br>Historic Cryptocurrency Price Data<br>e.g., Bitcoin, Litecoin"]
    B --> C["Methodology: Bayesian Framework<br>• Potential Field Theory<br>• Gaussian Process<br>• Dynamical Systems"]
    C --> D{"Computational Process"}
    D --> D1["Lyapunov Stability Analysis<br>Validate Non-linear Potential Function"]
    D --> D2["Bayesian Inference<br>Inferring Potential Function from Prices"]
    D --> D3["Identify Market Indicators<br>Attractors & Repellers"]
    D1 & D2 & D3 --> E["Key Findings & Outcomes<br>1. Structural Dependency Consistent with Wavelet Coherence<br>2. Attractors/Repellers Surpass Traditional Metrics<br>3. Captured Market Trend, Volatility, & Correlation<br>4. Improved Prediction (e.g., Litecoin up to 12 days)"]