6:00 PM Seminar Begins
7:30 PM Reception
Hybrid Event:
Fordham University
McNally Amphitheater
140 West 62nd Street
New York, NY 10023
Free Registration!
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Abstract:
Topological Data Analysis (TDA) has emerged as a powerful methodology in time-series analysis and signal processing. TDA is able to provide detailed descriptions of complex data which complements statistical methods. Recent applications include detection of critical transitions in financial time series, particularly of financial bubbles. The methodology relies on time-delay coordinate embedding, which is used to construct, from the time-series, a point-cloud in some space. The dynamics on the point-cloud unveils patterns in the time-series. Most of the evidence so far on the adeptness of TDA to detect financial bubbles has been empirical. We present, for the first time, a heuristic argument for why TDA can detect financial bubbles. We use models from economics that assert that the time series exhibit certain oscillatory patterns when approaching a tipping point. These oscillations determine holes in the point-clouds, which can be quantified by TDA. When approaching the tipping point of a bubble, there are significant changes in the nature of the oscillations, and consequently in the TDA output. These changes can be captured via persistence homology and yield early warning signals. As an application, we illustrate this approach on a sample of positive and negative bubbles in the Bitcoin price.
Bio:
Marian Gidea is a professor of mathematics at Yeshiva University in New York City. He held previous appointments at the Mathematical Sciences Research Institute in Berkeley, the Institute for Advanced Study in Princeton, Centre de Recerca Matemàtica in Barcelona, Northeastern Illinois University, Northwestern University, and Loyola University Chicago. He also served at the National Science Foundation as a program director in the Mathematical Sciences Division. His research interests include Dynamical Systems, Topological Data Analysis, and Financial Mathematics.
