Earthquakes, stock market crashes, and brain spikes all share an identical mathematical heartbeat that causes big events to cluster together in time.
April 25, 2026
Original Paper
THE MAGNITUDE-DIRECTION SEPARATION THEOREM Magnitude Clusters, Direction Does Not: A Universal Property of Self-Exciting Point Processes
SSRN · 6616338
The Takeaway
A universal property has been discovered in self-exciting systems where the size of one event directly influences the size of the next. The math shows that while the magnitude of these events tends to group up, the direction they move in does not follow the same pattern. This explains why one large earthquake is often followed by several more, regardless of the specific fault line involved. This Magnitude-Direction Separation Theorem provides a single rule that governs seemingly unrelated parts of our world. It gives us a better way to predict the timing of catastrophic failures in everything from global finance to human health.
From the abstract
We establish a general property of marked self-exciting point processes: the magnitude of consecutive events exhibits positive autocorrelation (AC1 > 0) while the direction of consecutive changes exhibits non-positive autocorrelation (AC1 ≤ 0). We prove this separation theorem for the Hawkes process class and verify it empirically across four domains: foreign exchange markets (264,000 H1 bars and 41,000 D1 bars across six currency pairs, 2000-2026), seismology (37,650 earthquakes in Southern Cal