When Will the Next Shock Happen? A Dynamic Framework for Event Probability Estimation

Extreme movements in financial time series pose challenges for risk management and forecasting, particularly when their timing is irregular and difficult to anticipate. This study aims to develop a probabilistic framework for detecting and predicting such events using daily Bitcoin returns as a case study. We first identify extreme positive and negative return events using the Isolation Forest algorithm and estimate their empirical recurrence patterns using a dynamic frequency table to derive baseline parametric probabilities. A 7-day Hawkes excitation kernel is then applied to capture short-run self-exciting dynamics, and both components are integrated using logistic regression to produce real-time probability forecasts. The results show that positive events occur more frequently than negative ones and that prediction accuracy improves over time: Brier scores, which measure the accuracy of probabilistic predictions, decrease as additional event data accumulate, and log loss values exhibit a consistent downward trend. Overall, by combining anomaly detection, empirical inter-arrival estimation, and excitation dynamics into a unified structure, the proposed framework offers a transparent and adaptable tool for forecasting extreme events in the financial market.