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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