Bitcoin Volatility Forecasting: GARCH, XGBoost, LSTM & GRU

Project overview

This project builds a leakage-aware Bitcoin volatility forecasting pipeline using 4,239 daily BTC-USD returns from 2 January 2015 to 10 August 2026. The primary target is next-day squared return, with Parkinson variance used as a secondary robustness proxy.

The study compares historical variance, a 30-day rolling estimator, EWMA, sGARCH, XGBoost, LSTM, GRU and two GARCH-neural combinations. Model choice is made on the chronological validation period; the final test period is reserved for one unbiased performance assessment.

Why a volatility model was required

Bitcoin prices were nonstationary, while daily returns were stationary under both ADF and KPSS evidence. Returns were heavy-tailed and negatively skewed: excess kurtosis was 12.16, the largest daily loss was −46.47%, and the Jarque-Bera test strongly rejected normality.

Raw returns showed limited serial dependence, while absolute and squared returns were strongly autocorrelated. The ARCH-LM test was also highly significant. Together, these results identify volatility clustering and justify modelling conditional variance rather than treating risk as constant through time.

• Training: 2,967 observations ending 15 February 2023.
• Validation: 635 observations from 16 February 2023 to 11 November 2024.
• Test: 637 observations from 12 November 2024 to 10 August 2026.
• All predictors were lagged or rolling features available before the forecast target.

Econometric foundation

ARMA(0,1) was selected for the conditional mean using the training-sample BIC. Its residual Ljung-Box p-values at lags 7, 14 and 30 were above 0.12, indicating that the short mean equation removed the remaining linear serial dependence adequately.

Among ARCH, sGARCH, GJR-GARCH, EGARCH and APARCH candidates, sGARCH(1,1) with skewed Student-t innovations achieved the lowest validation QLIKE at 1.95326. The Student-t alternative was virtually tied, and the skew parameter was not statistically significant, so the distributional distinction should not be overstated.

The selected variance model removed the remaining ARCH pattern: squared standardised-residual Ljung-Box p-values exceeded 0.86 and the 30-lag ARCH-LM p-value was 0.997. Some serial dependence remained in standardised residuals, while the Q-Q plot still showed extreme tails.

Machine learning and robustness checks

XGBoost, LSTM and GRU used lagged returns, absolute and squared returns, rolling moments, range-based volatility estimators, volume and cyclical calendar features. Standalone machine-learning models achieved lower MAE than GARCH, yet their QLIKE values were much worse. This distinction matters: MAE rewards smaller point errors, while QLIKE is more appropriate for noisy variance targets and penalises severely underestimated risk.

Repeated runs across five random seeds produced mean test QLIKE values of 3.300 for GRU and 3.313 for LSTM. Three rolling validation windows were less favourable: mean QLIKE was 1.953 for GARCH, compared with 4.372 for GRU, 4.667 for XGBoost and 4.766 for LSTM. The neural learning curves also showed widening training-validation gaps, making early stopping essential.

Selected model and untouched-test result

Validation weight searches selected an 82% GARCH / 18% LSTM combination with QLIKE 1.94252, narrowly ahead of the 85% GARCH / 15% GRU combination at 1.94592 and standalone GARCH at 1.95326. The modest neural weight is the substantive finding: machine learning added a small correction to a strong econometric core rather than replacing it.

On the untouched test period, the preselected GARCH-LSTM model achieved QLIKE 1.73043, RMSE 13.5836 and MAE 6.4778. GARCH-GRU posted a slightly lower test QLIKE of 1.72974, yet it was not selected after seeing the test data and the difference was not statistically significant (Diebold-Mariano p = 0.870).

Relative to GARCH-LSTM, QLIKE loss was significantly higher for standalone GARCH (p = 0.0026), LSTM, GRU, XGBoost, the 30-day rolling estimator and historical variance. The difference from EWMA was not significant (p = 0.195). A Mincer-Zarnowitz joint test did not reject ideal calibration for GARCH-LSTM (p = 0.178), although that result should not be read as proof of perfect calibration.

Thirty-day risk outlook and limitations

After refitting the selected sGARCH specification to the full sample, the model projected annualised volatility rising from 32.4% on 11 August 2026 to 54.1% on 9 September 2026. This is a conditional risk path rather than a Bitcoin price forecast.

The fitted GARCH coefficients sum to approximately one, indicating near-unit volatility persistence. That feature explains the slow decay of shocks and makes the long-horizon path highly sensitive to specification and recent observations. The reported long-run variance and half-life are therefore not economically stable, so the 30-day curve should be treated as a scenario generated by the fitted model, not a trading signal.