Related papers: Why Topological Data Analysis Detects Financial Bu…
We exploit a recent computational framework to model and detect financial crises in stock markets, as well as shock events in cryptocurrency markets, which are characterized by a sudden or severe drop in prices. Our method manages to detect…
Much research has been conducted arguing that tipping points at which complex systems experience phase transitions are difficult to identify. To test the existence of tipping points in financial markets, based on the alternating offer…
Topological Data Analysis (TDA) is a powerful mathematical theory, largely unexplored in theoretical chemistry. In this work we demonstrate how TDA provides new insights into topological features of electron densities and reduced density…
In this paper we introduce a new data-driven run-time monitoring system for analysing the behaviour of time evolving complex systems. The monitor controls the evolution of the whole system but it is mined from the data produced by its…
This paper addresses the statistical properties of time series driven by rational bubbles a la Blanchard and Watson (1982), corresponding to multiplicative maps, whose study has recently be revived recently in physics as a mechanism of…
Analyzing flight trajectory data sets poses challenges due to the intricate interconnections among various factors and the high dimensionality of the data. Topological Data Analysis (TDA) is a way of analyzing big data sets focusing on the…
Using a recently introduced rational expectation model of bubbles, based on the interplay between stochasticity and positive feedbacks of prices on returns and volatility, we develop a new methodology to test how this model classifies 9…
Exploring the shape of point configurations has been a key driver in the evolution of TDA (short for topological data analysis) since its infancy. This survey illustrates the recent efforts to broaden these ideas to model spatial…
Accurately assessing financial risk requires capturing both individual asset volatility and the complex, asymmetric dependence structures that emerge during extreme market events. While modern diffusion-based models have advanced…
Topological Data Analysis (TDA) is a discipline that applies algebraic topology techniques to analyze complex, multi-dimensional data. Although it is a relatively new field, TDA has been widely and successfully applied across various…
Topological Data Analysis (TDA) can broadly be described as a collection of data analysis methods that find structure in data. This includes: clustering, manifold estimation, nonlinear dimension reduction, mode estimation, ridge estimation…
Investors in stock market are usually greedy during bull markets and scared during bear markets. The greed or fear spreads across investors quickly. This is known as the herding effect, and often leads to a fast movement of stock prices.…
This application paper presents a comprehensive experimental evaluation of the suitability of Topological Data Analysis (TDA) for the quantitative comparison of turbulent flows. Specifically, our study documents the usage of the persistence…
Understanding temporal patterns in online search behavior is crucial for real-time marketing and trend forecasting. Google Trends offers a rich proxy for public interest, yet the high dimensionality and noise of its time-series data present…
Improvements in experimental and computational technologies have led to significant increases in data available for analysis. Topological data analysis (TDA) is an emerging area of mathematical research that can identify structures in these…
A broad range of natural and social systems from human microbiome to financial markets can go through critical transitions, where the system suddenly collapses to another stable configuration. Critical transitions can be unexpected, with…
We propose that imitation between traders and their herding behaviour not only lead to speculative bubbles with accelerating over-valuations of financial markets possibly followed by crashes, but also to ``anti-bubbles'' with decelerating…
Since August 2000, the stock market in the USA as well as most other western markets have depreciated almost in synchrony according to complex patterns of drops and local rebounds. In \cite{SZ02QF}, we have proposed to describe this…
In the context of rapid urbanization, understanding the patterns of urban residents' activities and mobility is crucial for optimizing transportation systems and enhancing urban management efficiency. This study addresses the limitations of…
Topological Data Analysis (TDA) is a rigorous framework that borrows techniques from geometric and algebraic topology, category theory, and combinatorics in order to study the "shape" of such complex high-dimensional data. Research in this…