Source-linked AI summary
Bayesian regression and Bitcoin
Devavrat Shah, Kang Zhang
TL;DR
The paper applies Bayesian regression under a latent source model to predict Bitcoin price changes, extending its prior use beyond binary classification. It then uses those predictions in a trading strategy that achieved an 89% return in 50 days on real data.
Problem
Prior latent-source Bayesian regression work focused primarily on binary classification, leaving its use for estimating real-valued variables such as Bitcoin price changes to be examined.
Method
The paper uses historical Bitcoin price-variation time series at 30-, 60-, and 120-minute lengths, together with order-book volume imbalance, to estimate future average price changes through Bayesian regression.
Results
89% return in 50 days, with 3,362 yuan total profit, 2,872 trades, 3,781 yuan average investment, and a 4.10 Sharpe ratio.
Takeaways & Limitations
The resulting strategy remained profitable during a decreasing-price period and performed better during the testing period's high-volatility middle section.
Takeaways & Limitations
The strategy uses positions of at most ±1 Bitcoin, and scaling to larger investment volumes requires further research because finite order-book depth prevents expected linear scaling.
Abstract
from arXiv · showhide
In this paper, we discuss the method of Bayesian regression and its efficacy for predicting price variation of Bitcoin, a recently popularized virtual, cryptographic currency. Bayesian regression refers to utilizing empirical data as proxy to perform Bayesian inference. We utilize Bayesian regression for the so-called "latent source model". The Bayesian regression for "latent source model" was introduced and discussed by Chen, Nikolov and Shah (2013) and Bresler, Chen and Shah (2014) for the purpose of binary classification. They established theoretical as well as empirical efficacy of the method for the setting of binary classification. In this paper, instead we utilize it for predicting real-valued quantity, the price of Bitcoin. Based on this price prediction method, we devise a simple strategy for trading Bitcoin. The strategy is able to nearly double the investment in less than 60 day period when run against real data trace.
I. Bayesian Regression
The paper presents Bayesian regression under a latent source model as an alternative to choosing a difficult parametric function space for high-dimensional data. It estimates conditional outcomes from empirical observations and extends prior mainly binary-classification uses to real-valued prediction.
- Our approach: High-dimensional applications can make choosing a useful parametric function space difficult, motivating the latent source model.The paper describes time-series data as potentially too complicated or meaningless for straightforward parametric modeling.
- Our approach: Each observation is generated by selecting a latent source, adding Gaussian noise to its source vector, and sampling the response from that source’s distribution.The model uses K source vectors, source probabilities, and source-specific distributions over real-valued responses.
- Our approach: Under the latent source model, regression becomes Bayesian inference, but the latent sources, source probabilities, and response distributions are unknown.The unknown quantities include K, the source vectors, the probabilities, and the distributions P1,...,PK.
- Empirical Bayesian regression: The proposed algorithm uses empirical data to estimate the conditional distribution of y given x and then the conditional expectation for prediction.The empirical conditional probability is constructed from observed data and used as a linear estimator of the conditional expectation.
- Contribution: Prior latent-source Bayesian regression work primarily addressed binary classification, whereas this paper applies it to real-valued variables.The paper positions Bitcoin price variation as the real-valued prediction setting for this extension.
II. Trading Bitcoin
The paper applies Bayesian regression inspired by a latent source model to predict Bitcoin price changes and drive a simple trading strategy. Using historical price and order-book data, the strategy nearly doubles investment over the testing period, with performance varying by threshold and market conditions.
- The study asks whether historical Bitcoin and order-book data contain information useful for predicting future price variation and developing a profitable quantitative strategy.
- Bayesian regression for the latent source model is used here to estimate a real-valued variable rather than primarily perform binary classification.
- The trading strategy holds +1, 0, or −1 Bitcoin, buying when predicted movement exceeds threshold t and selling when it falls below −t.
- The strategy predicts average Bitcoin price movement over 10-second intervals using Bayesian regression on historical windows of 30, 60, and 120 minutes.It also incorporates the current order book through the relative bid–ask volume measure r.
- As the threshold increases, the number of trades decreases, average holding time increases, and average profit per trade increases.
- The best reported strategy peaked at 3362 yuan total profit across 2872 trades, representing an 89% return in 50 days with a Sharpe ratio of 4.10.It performed better during high market volatility and remained profitable while Bitcoin’s price decreased late in the testing period.
III. Discussion
The discussion identifies clustered price patterns resembling triangle and head-and-shoulder formations, while highlighting practical limits on scaling both the strategy and computation.
- The prediction patterns were clustered with standard k-means, and high-price-variation, high-confidence clusters were inspected.
- The cluster centers include triangle and head-and-shoulder patterns also reported in technical-analysis literature.
- These observed patterns provide evidence for the latent source model and an explanation for the trading strategy’s success.
- The strategy nearly doubles investment in 50 days while holding at most ±1 Bitcoin, but linear scaling is not expected because order books are finite.
- The method uses representative prior time series for computational feasibility, although using all possible series might improve prediction power and strategy efficacy.
- Equation (7) is trivially parallelizable and mapreducable, but the role of computation in improving prediction quality remains open.