Forecasting Explosive Bubble Regimes in Bitcoin Time Series with Multi-Step Ensemble Learning.

Abstract

Bitcoin bubbles exhibit locally explosive dynamics, but identifying past episodes does not establish their predictability. We combine the generalized supremum augmented Dickey-Fuller test with nine probabilistic learners and three probability-output ensembles to forecast bubble states over one-, three-, and seven-day horizons. Using daily data from January 2016 to April 2026, we identify 30 maximal uninterrupted episodes comprising 455 bubble days. Development-period validation selects the lookback window and oversampling ratios before final-test evaluation; ensemble weights are estimated from development-period rolling forecasts. No model family dominates across horizons. The constrained least-squares ensemble has the lowest final-test mean squared error at one day, whereas logistic regression has the lowest error at three and seven days. The inverse-error-weighted ensemble has the highest average precision at seven days. Moving-block bootstrap intervals overlap substantially, and the 90% Model Confidence Set retains several models at every horizon. A cross-source robustness check yields 99.58% agreement in daily bubble-state classifications. These findings support horizon-dependent probabilistic risk monitoring, while the limited number of independent episodes and low recall at longer horizons constrain the practical interpretation of the forecasts.