Bayesian Potential Fields for Cryptocurrency Trends and Dependencies
Summary
This paper models cryptocurrency prices as trajectories in a changing nonlinear potential field. It combines Bayesian inference with Gaussian Processes to estimate the field from historical prices, then uses inferred attractors and repellers as indicators of market conditions and structural relationships among cryptocurrencies. Lyapunov stability analysis is used to support the existence of the proposed potential function.
The authors analyze Bitcoin crash periods from April 2017 to November 2021. They report that attractors reflect market trend, volatility, and correlation, and that inferred dependencies agree with wavelet coherence results. Adding the proposed indicators to deep-learning price models improves Litecoin forecasts, with reported gains extending to a 12-day horizon. The document presents these as empirical findings, but the supplied description gives no detailed sample design, benchmark results, or evidence of performance beyond the studied data and models. It does not establish that the indicators will remain reliable in other periods or support profitable trading after costs.
Key ideas
- The framework represents cryptocurrency price movement as a trajectory shaped by a time-varying nonlinear potential field.
- Bayesian inference with Gaussian Processes estimates the potential field from historical prices.
- Inferred attractors and repellers are proposed as indicators of market trends and structural dependencies.
- The reported dependency patterns align with wavelet coherence analysis.
- The authors report improved Litecoin forecast performance when their indicators augment deep-learning models.
Tags
Full text
# 2308.01013 # Bayesian framework for characterizing cryptocurrency market dynamics, structural dependency, and volatility using potential field 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.
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