Related papers: Why Topological Data Analysis Detects Financial Bu…
We show that infinite divisibility of a trading commodity leads to a self-sustained price bubble when traders use adaptive investment strategies. The adaptive strategy can be viewed as a psychological response of a trader to the situation…
A hypothesis that the financial log-periodicity, cascading self-similarity through various time scales, carries signatures of a law is pursued. It is shown that the most significant historical financial events can be classified amazingly…
The study of topology is strictly speaking, a topic in pure mathematics. However in only a few years, Topological Data Analysis (TDA), which refers to methods of utilizing topological features in data (such as connected components, tunnels,…
Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…
There are many research papers yielding the financial data models, where returns are tied either to the fundamental analysis or to the individual, often irrational, behaviour of investors. In the second case the bubble followed by the…
This paper introduces advanced techniques of Topological Data Analysis (TDA) for unsupervised anomaly detection and customer segmentation in banking data. Using the Mapper algorithm and persistent homology, we develop unsupervised…
We present a dynamical theory of asset price bubbles that exhibits the appearance of bubbles and their subsequent crashes. We show that when speculative trends dominate over fundamental beliefs, bubbles form, leading to the growth of asset…
Topological Data Analysis (TDA) is a recent and growing branch of statistics devoted to the study of the shape of the data. In this work we investigate the predictive power of TDA in the context of supervised learning. Since topological…
Portfolio management is essential for any investment decision. Yet, traditional methods in the literature are ill-suited for the characteristics and dynamics of cryptocurrencies. This work presents a method to build an investment portfolio…
We construct a statistical indicator for the detection of short-term asset price bubbles based on the information content of bid and ask market quotes for plain vanilla put and call options. Our construction makes use of the martingale…
Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustness to deformation and…
Recurrence Plot (RP) and Recurrence Quantification Analysis (RQA) are signal numerical analysis methodologies able to work with non linear dynamical systems and non stationarity. Moreover they well evidence changes in the states of a…
Flow in porous media is difficult to address using standard analytical or numerical methods due to its complexity. However, since synthetic representations of porous media are easy to produce and data from physical experiments are becoming…
The log-periodic power law (LPPL) is a model of asset prices during endogenous bubbles. A major open issue is to verify the presence of LPPL in price sequences and to estimate the LPPL parameters. Estimation is complicated by the fact that…
Based on the Log-Periodic Power Law (LPPL) methodology, with the universal preferred scaling factor $\lambda \approx 2$, the negative bubble on the oil market in 2014-2016 has been detected. Over the same period a positive bubble on the so…
Topological data analysis (TDA) is a tool from data science and mathematics that is beginning to make waves in environmental science. In this work, we seek to provide an intuitive and understandable introduction to a tool from TDA that is…
Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…
We introduce a new diffusion process Xt to describe asset prices within an economic bubble cycle. The main feature of the process, which differs from existing models, is the drift term where a mean-reversion is taken based on an exponential…
A financial system contains many elements networked by their relationships. Extensive works show that topological structure of the network stores rich information on evolutionary behaviors of the system such as early warning signals of…
Topological Data Analysis (TDA) gives practioners the ability to analyse the global structure of cybersecurity data. We use TDA for anomaly detection in host-based logs collected with the open-source Logging Made Easy (LME) project. We…