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When Will the Next Shock Happen? A Dynamic Framework for Event Probability Estimation
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DOI：10.3390/fintech5010013.png)
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Abstract
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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.
Keywords:
event detection
Hawkes process
probability estimation
logistic regression
C22
C58
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