Uncertainty Quantification for Cryptocurrency Price Forecasting

Applied UQ to obtain robust confidence intervals for short-term cryptocurrency price forecasts by comparing the prediction and confidence interval (CI) of AutoRegressive Integrated Moving Average (ARIMA) with Bayesian Neural Networks (BNN), calibrated using conformal prediction.

Introduction

• UQ helps quantify and manage inherent uncertainties in financial models and data
• Cryptocurrency markets are highly volatile
• Predicting price movements and managing risk is particularly challenging for short-term cryptocurrency data
• Many ML/UQ studies on stock markets, but few studies on cryptocurrency markets
• Goal: Apply UQ to highly volatile cryptocurrency price forecasts to obtain robust confidence intervals
• Idea: Compare the prediction and CI of ARIMA with BNN after calibrating CI using conformal prediction

Methods

• Dataset: Bitcoin tether order book data (millisecond bid/ask prices and volumes) collected from June to September 2021
• Compute open, close, low, and high prices for ten-minute intervals
• Train-test split: 70% train, 30% test
• Predictive models used to predict next time step open price
• Traditional statistical method: ARIMA (AutoRegressive Integrated Moving Average)
• Newer ML based method: Bayesian Neural Networks (BNNs)
• Conformal Prediction using α = 0.1
• Calibrate using first 1000 points of the test set
• Allows for comparison of model CI

Evaluation

• Comparison of CI for both models after CP using various metrics
• BNN
  • Architecture
    • 14 neurons, two hidden layers (20 neurons), 1 neuron output layers
  • AutoDiagonalNormal guide
  • Adam optimizer with learning rate of 1e-3
  • Coverage
    • Before CP: 0.998
    • After CP: 0.847
• ARIMA
  • Best model found with auto ARIMA
  • ARIMA(0, 1, 0) (random walk), where ŷt = μ + yt - 1
  • Coverage
    • Before CP: 0.935
    • After CP: 0.896

Conclusion/Future Directions

• After CP, ARIMA model gives better confidence interval compared to BNN model under evaluation metrics
• Future directions
  • Investigate different ML models for price prediction
  • Incorporate price variance as one of the calibration parameters of the confidence interval