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

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.