Topological Recognition of Critical Transitions in Time Series of Cryptocurrencies

  title={Topological Recognition of Critical Transitions in Time Series of Cryptocurrencies},
  author={Marian Gidea and Daniel Goldsmith and Yuri A. Katz and Pablo Rold{\'a}n and Yonah Shmalo},
  journal={Capital Markets: Asset Pricing \& Valuation eJournal},
We analyze the time series of four major cryptocurrencies (Bitcoin, Ethereum, Litecoin, and Ripple) before the digital market crash at the end of 2017 - beginning 2018. We introduce a methodology that combines topological data analysis with a machine learning technique -- $k$-means clustering -- in order to automatically recognize the emerging chaotic regime in a complex system approaching a critical transition. We first test our methodology on the complex system dynamics of a Lorenz-type… Expand
Topological Data Analysis for Identifying Critical Transitions in Cryptocurrency Time Series
Good early warning signals before the financial crashes are demonstrated and it is shown that the L1-norm and C1 – norm of persistent landscapes peak before the crashes occur. Expand
Detecting Early Warning Signals of Major Financial Crashes in Bitcoin Using Persistent Homology
This study explores persistent homology to detect early warning signals of the 2017 and 2019 major financial crashes in Bitcoin using sliding window to quantify transient loops that appear in multiscale topological spaces, which associated on each point cloud dataset and encode the quantified information in a persistence landscape. Expand
A look into chaos detection through topological data analysis
Abstract Traditionally, computation of Lyapunov exponents has been the marque method for identifying chaos in a time series. Recently, new methods have emerged for systems with both known and unknownExpand
Topological Data Analysis for Portfolio Management of Cryptocurrencies
Research shows that the proposed system enables analysts to outperform a classic method from the literature without requiring any feature engineering or domain knowledge in TDA, and introduces TDA-based portfolio management of cryptocurrencies as a viable tool for the practitioner. Expand
Dissecting Ethereum Blockchain Analytics: What We Learn from Topology and Geometry of Ethereum Graph
Ethereum network can provide critical insights on price strikes of crypto-tokens that are otherwise largely inaccessible with conventional data sources and traditional analytic methods by introducing novel tools based on topological data analysis and functional data depth into Blockchain Data Analytics. Expand
The Better Turbulence Index? Forecasting Adverse Financial Markets Regimes with Persistent Homology
Persistent homology is the workhorse of modern topological data analysis, which in recent years becomes increasingly powerful due to methodological and computing power advances. In this paper, afterExpand
The better turbulence index? Forecasting adverse financial markets regimes with persistent homology
Persistent homology is the workhorse of modern topological data analysis, which in recent years becomes increasingly powerful due to methodological and computing power advances. In this paper, afterExpand
Topological Features of Multivariate Distributions: Dependency on the Covariance Matrix
The dependency of mean values of functional p-norms of ’persistence landscapes’ on a uniform scaling of the underlying multivariate distribution is established and it is demonstrated that average values of p- norms are decreasing, when the covariance in a system is increasing. Expand
Topological Attention for Time Series Forecasting
This work proposes topological attention, which allows attending to local topological features within a time horizon of historical data, and easily integrates into existing end-to-end trainable forecasting models, such as N-BEATS, and in combination with the latter exhibits state-of-the-art performance on the large-scale M4 benchmark dataset. Expand
A T ] 2 7 N ov 2 01 9 Topological Machine Learning for Multivariate Time Series
We develop a framework for analyzing multivariate time series using topological data analysis (TDA) methods. The proposed methodology involves converting the multivariate time series to point cloudExpand


Forecasting Cryptocurrencies Financial Time Series
This paper studies the predictability of cryptocurrencies time series. We compare several alternative univariate and multivariate models in point and density forecasting of four of the mostExpand
A Statistical Analysis of Cryptocurrencies
We analyze statistical properties of the largest cryptocurrencies (determined by market capitalization), of which Bitcoin is the most prominent example. We characterize their exchange rates versusExpand
Modelling Crypto-Currencies Financial Time-Series
This paper studies the behaviour of crypto{currencies financial time{series of which Bitcoin is the most prominent example. The dynamic of those series is quite complex displaying extremeExpand
Dissection of Bitcoin’s multiscale bubble history from January 2012 to February 2018
A robust automatic peak detection method is introduced that classifies price time series into periods of uninterrupted market growth (drawups) and regimes of uninterrupted Market decrease (drawdowns) and a predictive scheme provides useful information to warn of an imminent crash risk. Expand
Topological Data Analysis of Financial Time Series: Landscapes of Crashes
The study suggests that TDA provides a new type of econometric analysis, which goes beyond the standard statistical measures, and can be used to detect early warning signals of imminent market crashes. Expand
The Economics of Cryptocurrencies – Bitcoin and Beyond
How well can a cryptocurrency serve as a means of payment? We study the optimal design of cryptocurrencies and assess quantitatively how well such currencies can support bilateral trade. TheExpand
A modified method for detecting incipient bifurcations in a dynamical system
[1] We assess the proximity of a system to a bifurcation point using a degenerate fingerprinting method that estimates the declining decay rate of fluctuations in a time series as an indicator ofExpand
Chatter detection in turning using persistent homology
Abstract This paper describes a new approach for ascertaining the stability of stochastic dynamical systems in their parameter space by examining their time series using topological data analysisExpand
Three-Dimensional HÉnon-like Maps and Wild Lorenz-like attractors
There is evidence that there are different types of Lorenz-like attractor domains in the parameter space of the 3D Henon map and in all cases the maximal Lyapunov exponent, Λ1, is positive. Expand
Topology Data Analysis of Critical Transitions in Financial Networks
We develop a topology data analysis-based method to detect early signs for critical transitions in financial data. From the time-series of multiple stock prices, we build time-dependent correlationExpand