By David DeFusco
Katz School mathematics researchers have developed a model that anticipates market crashes and financial bubbles in the Bitcoin industry.
In the paper, “,” Dr. Marian Gidea, associate dean for STEM education and research, and Samuel Akingbade, a Ph.D. student in mathematics, discuss how Topological Data Analysis (TDA), which identifies patterns and features in data not apparent through traditional statistical methods, can be used to detect early-warning signals of financial bubbles.
Dr. Gidea and Akingbade were joined in the research by Matteo Manzi, lead quant researcher at CrunchDAO, and Vahid Nateghi of the Max Planck Institute for Dynamics of Complex Technical Systems in Magdeburg, Germany.
The main idea of the TDA approach, according to Dr. Gidea, who is also director of the graduate programs in mathematical sciences, is to represent a dataset as a point cloud, which in mathematical theory is a discrete set of data points in space that may represent a 3D shape or object, and to describe it in terms of its shape expressed via topological invariants.
Topology is sometimes called “rubber-sheet geometry” because objects can be stretched and contracted but cannot be broken. For example, a square can be deformed into a circle without breaking it, but a figure 8 cannot. In the Katz School paper, changes of shape reflect subtle shifts in the patterns of the underlying data.
Their argument is built upon a model called the Log-Periodic Power Law Singularity (LPPLS), which can track the rapid, unsustainable growth or the precipitous decline of an asset price, be it stocks, bonds or commodities, while capturing wild swings in assets prices in the period before a crash.
“When the LPPLS model applies to a dataset, we show that the TDA method yields early-warning signals,” said Dr. Gidea. “The upshot is that TDA can detect early-warning signals even when LPPLS fits the data poorly.”
The researchers apply this approach to historical price data of Bitcoin, identifying and analyzing financial bubbles in that industry. The goal, they argue in the paper, is to compare TDA with the LPPLS as tools for detecting early-warning signals related to critical transitions in financial markets.
Analyzing financial time series, which is the variation of a financial instrument’s value over time, is a critical component of various financial disciplines. Traders, investors and financial analysts use historical price and volume data to identify trends, patterns and potential turning points in the market, helping to inform investment decisions and risk-management strategies.
“The combination of the TDA and the LPPLS models offers a hands-on approach for gaining insights into the dynamics of financial bubbles and potentially predicting critical transitions in asset prices,” said Dr. Gidea. “The application to Bitcoin serves as a practical demonstration of the proposed methodology.”
