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Abstract

A method is provided that comprises collecting financial data points and normalizing the data points into a time series. The time series is merged into aggregates according to sliding windows that comprise different time periods and a sliding step increment. A periodic change in an increasing and convex transformation is computed for each aggregate, and multi-dimensional time-delayed coordinate embedding is applied to each aggregate. The sliding windows are applied to the time-delayed aggregates, and time series of variances and point clouds are derived within each sliding window. Persistence homologies and time series norms are computed for the point clouds, and the time series norms are correlated with the time series of variances. A warning of an impending financial crisis is output if the correlation of the time series norms with the time series of variances exceeds a predefined threshold.

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