Topological Recognition of Critical Transitions in Time Series of Cryptocurrencies

Abstract

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 attractor, and then we apply it to the four major cryptocurrencies. We find early warning signals for critical transitions in the cryptocurrency markets, even though the relevant time series exhibit a highly erratic behavior.

A look into chaos detection through topological data analysis

“…The ability to quantify the topology of a data structure has led to many breakthroughs in various fields. Specifically, TDA has already made meaningful contributions in time series analysis [13,14,15], economics [16], machining dynamics [17,18,19,20], biochemistry [21], and plant morphology [22]. In this section, we extend the application of this powerful computational tool to chaos detection.…”

Topological Data Analysis for Portfolio Management of Cryptocurrencies

“…The field of cryptocurrencies is relatively new. However, the work of [5] is important to highlight. They also propose a pipeline using TDA for cryptocurrencies to identify major changes in the price of a currency.…”

“…Other works have sought to develop analytics for the Blockchain such as [8]. With the exception of [5], this work is not familiar with further literature developoing methods to evaluate cryptocurrencies using Machine Learning methods or TDA.…”

“…with p ≥ 1. [17] suggests to work with the L 2 -norm, whereas [5] proposes the L 1 -norm. In this work, the L 2 -norm is used.…”

Dissecting Ethereum Blockchain Analytics: What We Learn from Topology and Geometry of the Ethereum Graph?

“…The important methodological distinction of our new approach is that while TDA has been applied before to financial time series, including time series of cryptocurrencies [20], TDA has never been yet applied to complex networks of financial transactions on accountbased blockchains such as Ethereum. Moreover, to the best of our knowledge, the only other paper discussing utility of TDA on financial networks, including both traditional finance and blockchain, is our earlier study of Bitcoin graph [1] which belongs to the unspent transaction output (UTXO) based blockchains.…”