**1. Introduction**

The cryptocurrency market has become an attractive target for many financial investors in recent years due to its potential for rapid gains. One research topic being explored in this market is the correlation between different cryptocurrencies. Understanding how different assets interact with each other can help in portfolio optimization [1], predicting the future volatility or downturn [2] and also in observing the risk spillover that benefits portfolio diversification [3], to mention only a few.

Thanks to a network-based methodology, cryptocurrencies' cross-relationships can be learned and observed visually [4]. The idea of this method is that it builds up a network of different objects such that the distance between two objects depends on how similar they are: the shorter the distance, the more similar the two objects are. Eventually, we can see the interaction between objects by looking at their network's structure and analyzing characteristics of the network. Different network construction approaches have been explored in the literature, from Minimum Spanning Tree (MST) [5], k-Nearest neighbors (kNN) [6], planar maximally filtered graph (PMFG) [2] to Threshold Weighted-Minimum Dominating Set (TW-MDS) [7], to name but a few. In financial markets, normally, the similarity between two assets is measured by comparing the evolution of two corresponding price time series, one typical method to do this is Pearson correlation metric [8]. The study on correlation of traditional asset classes such as stocks, bonds, national fiat currencies and commodities has been developed a long time ago, with varying approaches invented to learn the correlation

**Citation:** Nguyen, A.P.N.; Mai, T.T.; Bezbradica, M.; Crane, M. The Cryptocurrency Market in Transition before and after COVID-19: An Opportunity for Investors? *Entropy* **2022**, *24*, 1317. https://doi.org/ 10.3390/e24091317

Academic Editors: Stanisław Drozd˙ z,˙ Jarosław Kwapie ´n and Marcin W ˛atorek

Received: 19 August 2022 Accepted: 14 September 2022 Published: 19 September 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

<sup>1</sup> School of Computing, Dublin City University, Collins Ave Ext, Whitehall, D09 Y074 Dublin, Ireland

between different entities in the same market but also between different asset classes, ranging from statistical [9,10] to AI-based methods [11].

Generally, there are two common shortcomings with correlation-related studies. Firstly, one mainly uses a low-frequency dataset such as daily or monthly, and this might cause a loss of important information from each time series, hence failing to reflect their true nature [12]. This appears to be a major concern in the cryptocurrency market, since it is well-known for its high fluctuations in terms of price movement. For example, in [13], the authors show that the losses of cryptocurrencies can reach 70% within one day. Recently, in 2020, by comparing the volatility in the returns between cryptocurrency and stock markets, the authors of [14] revealed that major cryptocurrencies such as BTC and ETH have volatilities of 5.68 and 7.10, respectively, which is two-fold higher than that of *S*&*P*500 and Euro Stoxx 50 indices. Notably, Dirk et al. calculated the daily price volatility of Bitcoin from 2001 until 2021 and found that there are extremely volatile days when the volatility can hit 120% [15]. Thus, using a high frequency means that we are ignoring valuable information (e.g., the intraday fluctuations of a time series) on purpose. As a result, this can adversely affect the correlation extracted from the dataset, potentially leading to inaccurate correlation-using experiments (e.g., portfolio optimization). Secondly, researchers tend to analyze the inter-relation between different time series by using trading price values reported on a website (e.g., Coinmarket (https://coinmarketcap.com/), Yahoo Finance (https://finance.yahoo.com/)). However, this practice deliberately ignores the effects of noise and trends in financial time series, which we will describe clearly in Section 4.

Another important factor to consider is the recent *COVID-19* pandemic which forced all countries to close off borders and restrict movements for residents as well as businesses [16]. This had a strong effect on the global downturn which occurred in March 2020 as a response to governments' efforts to control the disease spreading [17]. These historical events have been shown to disturb and devalue different financial asset classes such as stocks, bonds and also cryptocurrencies [18,19]. Instead of looking at the changes in time-series elements such as volumes, prices, returns and volatilities during the COVID-19 pandemic, in this study, we will investigate the impact of the pandemic by looking at the changes in *network structures* over time. Furthermore, based on these network's structures, we show how we can observe the corresponding community structures via community detection methods. The results from our experiment can be used to learn behaviours of investors in different periods of time, especially during downturn times in the financial market.

From the shortcomings of existing studies and utilizing the advantage of networkbased analysis, this study aims to investigate the network structure of cryptocurrencies without noise and trend effects and how this structure changes under the impact of the COVID-19 pandemic. Specifically, the research target is to answer these research questions:


It should be noted that we are not new to the subject of time-varying cryptocurrency network structure, we merely build on work by the team of Drozdz, Watorek, Kwapien [20,21] as well as, more recently, Nie [22]. However, our work expands the existing studies since we consider the investment decisions of investors based on the observed network structure and we acknowledge the negative effect of not only trend but also noise

presenting in cryptocurrencies. As suggested by Miceli [23], the trend and noise removal results in a filtered MST that better explains investment strategy and also potentially uncovers endogenous or exogenous factors that drive the price of cryptocurrencies

To solve these research questions, we use a tick-by-tick dataset which consists of 34 price time series corresponding to 34 cryptocurrencies traded on the HitBTC exchange during the period between 13 February 2019 and 6 April 2021. When it comes to network formation, we calculate the correlation between cryptocurrencies by adopting the linear similarity measurement named Pearson and then construct a Minimum Spanning Tree (MST) based on these correlation coefficients. The noise and trend removal is carried out by applying Random Matrix Theory (RMT). Community structure is found by using community detection methods. In addition, different metrics are used to analyze the network structures and support our findings.

The remainder of the article is organized as follows: Section 2 presents an overview of the relevant literature. Section 3 provides a description of the dataset. Section 4 describes terminologies, methods and preprocessing procedures. Section 5 discusses the experimental results followed by implications and hypotheses. Finally, the conclusion of this study is given in Section 7.
