Mild explocivity, persistent homology and cryptocurrencies' bubbles: An empirical exercise

Stelios Arvanitis; Michalis Detsis; Stelios Arvanitis; Michalis Detsis

doi:10.3934/math.2024045

AIMS Mathematics

2024, Volume 9, Issue 1: 896-917. doi: 10.3934/math.2024045

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Mild explocivity, persistent homology and cryptocurrencies' bubbles: An empirical exercise

Stelios Arvanitis ^,,
Michalis Detsis

Department of Economics of Athens University of Economics and Business, Athens, Greece

Received: 19 September 2023 Revised: 22 November 2023 Accepted: 24 November 2023 Published: 04 December 2023
MSC : 55, 62, 91

An empirical investigation was held regarding whether topological properties associated with point clouds formed by cryptocurrencies' prices could contain information on (locally) explosive dynamics of the processes involved. Those dynamics are associated with financial bubbles. The Phillips, Shi and Yu ^[33,34] (PSY) timestamping method as well as notions associated with the Topological Data Analysis (TDA) like persistent simplicial homology and landscapes were employed on a dataset consisting of the time series of daily closing prices of the Bitcoin, Ethereum, Ripple and Litecoin. The note provides some empirical evidence that TDA could be useful in detecting and timestamping financial bubbles. If robust, such an empirical conclusion opens some interesting paths of further research.
- financial bubbles,
- mild explocivity,
- PSY,
- bubble detection and timestamping,
- topological data analysis,
- persistent simplicial homology,
- persistent landscapes,
- EGARCH,
- cryptocurrencies
Citation: Stelios Arvanitis, Michalis Detsis. Mild explocivity, persistent homology and cryptocurrencies' bubbles: An empirical exercise[J]. AIMS Mathematics, 2024, 9(1): 896-917. doi: 10.3934/math.2024045

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Abstract

An empirical investigation was held regarding whether topological properties associated with point clouds formed by cryptocurrencies' prices could contain information on (locally) explosive dynamics of the processes involved. Those dynamics are associated with financial bubbles. The Phillips, Shi and Yu ^[33,34] (PSY) timestamping method as well as notions associated with the Topological Data Analysis (TDA) like persistent simplicial homology and landscapes were employed on a dataset consisting of the time series of daily closing prices of the Bitcoin, Ethereum, Ripple and Litecoin. The note provides some empirical evidence that TDA could be useful in detecting and timestamping financial bubbles. If robust, such an empirical conclusion opens some interesting paths of further research.

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