# The Cryptocurrency Market in Transition before and after COVID-19: An Opportunity for Investors?

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## Abstract

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## 1. Introduction

- RQ1. Is there evidence of the existence of noise and trend effects in the cryptocurrency market? If yes, how do noise and trend effects influence the interactions between cryptocurrencies? What does the network structure of these cryptocurrencies look like after removing noise and trend effects?
- RQ2. Does the network structure change when the level of granularity changes? If this is the case, what level of granularity should we use to obtain the true network structure?
- RQ3. Is there evidence that historical events such as the COVID-19 pandemic and the global downturn in 2020 changed the overall cryptocurrency network structure? If this is the case, how did they change it? Moreover, is there any possibility that this change was caused by a change in investors’ investment strategy? In other words, does the way investors react to a downturn change the interactions between cryptocurrencies?

## 2. Related Works

#### 2.1. Correlation-Based Analysis in the Financial Markets

#### 2.2. How the COVID-19 Pandemic Intervened on the Economy Worldwide

## 3. Data Description

#### 3.1. A Note on Data Sampling and Missing Data

#### 3.2. Aggregational Gaussianity

## 4. Research Methodology

#### 4.1. Correlation Matrix Based on Pearson Coefficients and Random Matrix Theory

- Firstly, we make use of cryptocurrency returns in order to retain the statistical nature of the associated time series. While some authors have proposed addressing the nonlinearity problem (e.g., Spearman [59] and Kendall [53]), these have the disadvantage of converting rational numbers into integer rankings, with the potential to lose out on critical information from financial time series [60]. Moreover, it has been shown that rank correlation metrics also suffer from the nonlinearity issue in some cases [58].
- Thirdly, rank-based correlation metrics require independent observations. This is a known weakness of non-linear correlation methods such as Spearman and Kendall [60]. On the other hand, Pearson works well for time series with duplicate observations (because there is no requirement for independent observations), as is the case in financial time series. For example, the price of a cryptocurrency can be unchanged for a period of time.

#### 4.2. Cleaning Trend and Noise Effects in the Cryptocurrency Market

#### 4.2.1. Noise and Trend

#### 4.2.2. Cleaning Method

#### 4.3. Distance Matrix and Its Minimum Spanning Tree

**D**be a distance matrix deriving from ${\mathbf{C}}_{cleaned}$, then:

**D**, with 0 indicates the complete similarity between 2 nodes while 2 indicates the complete difference between 2 nodes. From the Equation (3), we can prove that: (1) ${d}_{ij}\ge 0$, (2) ${d}_{ij}=0$ if $i=j$ and (3) ${d}_{ij}={d}_{ji}$, i.e., the requirements of a metric are satisfied [85]. By using the distance matrix, we can derive a network (graph) of cryptocurrencies (nodes) with a specific topology, where similar cryptocurrencies are close to each other and cryptocurrencies with different behaviors are far away from each other, the link (edge) between each pair of cryptocurrencies is their distance value. Thanks to this topology, different communities of cryptocurrencies can be observed.

#### 4.4. Community Detection in the Cryptocurrency Market

#### 4.5. Time Window Division

## 5. Experimental Results and Discussion

#### 5.1. The Response of Network Structures to Noise and Trend Effects

- Residuality Coefficient [93]: This compares the relative strength of the connections above and below a threshold distance value. In this experiment, we use the highest distance value ensuring connectivity of the MST as the threshold, denoted L:$$R=\frac{{\Sigma}_{[{d}_{ij}>L]}{d}_{ij}^{-1}}{{\Sigma}_{[{d}_{ij}\le L]}{d}_{ij}^{-1}}$$
- MST-based mean distance [111]: this calculates the average distance of the MST:$$M=\frac{1}{N-1}{\Sigma}_{{d}_{ij}\in MST}{d}_{ij}$$

#### 5.2. Real Network Structures in Different Levels of Granularity: An Experiment on Cleaned Data

#### 5.2.1. The Evolution of the Cryptocurrency Network According to Timescales

#### 5.2.2. Louvain vs. Girvan–Newman for Community Structure Detection

#### 5.3. Analysis of Investors’ Investment Decisions Based on the Time-Varying Network Structure

#### 5.3.1. The Changes in Crypto Network Structure during Times of Crisis

#### 5.3.2. Learning the Investment Decision of Crypto Traders Based on Ranking Distribution

## 6. Limitations and Future Works

#### 6.1. Limitations

#### 6.2. Future Works

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The reaction of general public and global economy to the COVID-19 pandemic. Four factors are considered: (

**a**) Worldwide attention to the pandemic, (

**b**) Global GDP growth, (

**c**) VIX index, (

**d**) $S\&P500$ index.

**Figure 2.**Cryptocurrency network structures using daily data. For each time window, Louvain method is applied to both original and cleaned data to detect existing communities. The illustrations on the left and right hand side are for the original and cleaned data, respectively, for 3 time windows referring to normal, downturn and recovery times, respectively.

**Figure 3.**Network structure for the first time window, community detection is applied using Louvain method. Four different timescales are used, e.g., (

**a**) 30 min, (

**b**) 6 h, (

**c**) 12 h, (

**d**) 24 h.

**Figure 4.**Network structure for the second time window, community detection is applied using Louvain method. Four different timescales are used, e.g., (

**a**) 30 min, (

**b**) 6 h, (

**c**) 12 h, (

**d**) 24 h.

**Figure 5.**Network structure for the third time window, community detection is applied using Louvain method. Four different timescales are used, e.g., (

**a**) 30 min, (

**b**) 6 h, (

**c**) 12 h, (

**d**) 24 h.

**Figure 6.**Cryptocurrency’s rankings distributions in three different phases of time. Each community is represented by a circular shape while the rankings of cryptocurrencies in this community are given by the blue color intensity, i.e., the darker the blue, the lower the cryptocurrency’s rank.

Cryptocurrencies | |||||
---|---|---|---|---|---|

Argur (REP) | Bitcoin SV (BSV) | Ethereum Classic (ETC) | MaidSafeCoin (MAID) | Ontology (ONT) | Tron (TRX) |

Bancor (BNT) | Cardano (ADA) | FunToken (FUN) | Maker (MKR) | Ox (ZRX) | Verge (XVG) |

Basic Attention Token(BAT) | Decentraland (MANA) | ICON (ICX) | Monero (XMR) | QTUM | Zcash (ZEC) |

Bitcoin (BTC) | Dogecoin (DOGE) | IOST | Nem (XEM) | Ripple (XRP) | Zilliqa (ZIL) |

Bitcoin Cash (BCH) | EOS | Lisk (LSK) | NEO | Stellar (XLM) | |

Bitcoin Gold (BTG) | Ethereum (ETH) | Litecoin (LTC) | OMG Network (OMG) | Tezos (XTZ) |

Level of Granularity | # Data Points | # Missing Values |
---|---|---|

30 min | 37,632 | 289 (0.8%) |

6 h | 3136 | 24 (0.8%) |

12 h | 1568 | 12 (0.8%) |

24 h | 784 | 0 (0%) |

**Table 3.**Three time windows used in this work (time windows split to take into consideration the COVID-19 pandemic).

Time Window | Stage | Time Span | # Days |
---|---|---|---|

1 | Normal time | 13 February 2019–31 December 2019 | 322 days |

2 | Downturn time | 1 January 2020–30 June 2020 | 182 days |

3 | Recovery time | 1 July 2020–6 April 2021 | 280 days |

**Table 4.**Cryptocurrency network connection strength through three time windows measured by Residuality Coefficient and Mean Distance. Four different granularity levels are considered, each with datasets, including original and cleaned dataset after removing noise and trend effects.

Metric | Data Type | Time Window | Granularity | |||
---|---|---|---|---|---|---|

30 min | 6 h | 12 h | 24 h | |||

ResidualityCoefficient | Original Data | 1 | 0.41 | 0.11 | 0.16 | 0.08 |

2 | 0.28 | 0.111 | 0.06 | 0.05 | ||

3 | 0.14 | 0.05 | 0.07 | 0.34 | ||

Cleaned data | 1 | 1.69 | 6.66 | 14.82 | 14.40 | |

2 | 5.98 | 8.90 | 14.41 | 15.34 | ||

3 | 2.32 | 2.99 | 1.88 | 1.05 | ||

Meandistance | Original Data | 1 | 1.08 | 0.82 | 0.80 | 0.76 |

2 | 0.99 | 0.71 | 0.65 | 0.56 | ||

3 | 0.98 | 0.57 | 0.46 | 0.45 | ||

Cleaned data | 1 | 1.29 | 1.38 | 1.42 | 1.42 | |

2 | 1.40 | 1.42 | 1.42 | 1.42 | ||

3 | 1.29 | 1.12 | 1.01 | 1.22 |

Granularity | ||||
---|---|---|---|---|

30 min | 6 h | 12 h | 24 h | |

Time window 1 | 0.88 | 1.00 | 1.00 | 1.00 |

Time window 2 | 1.00 | 1.00 | 1.00 | 1.00 |

Time window 3 | 0.87 | 0.82 | 0.91 | 1.00 |

**Table 6.**The growth of network structures over time measured by Betweenness Centrality and Degree Assortativity.

Metrics | Time Window 1 | Time Window 2 | Time Window 3 |
---|---|---|---|

Betweenness centrality | 0.15 | 0.05 | 0.16 |

Degree Assortativity | −0.49 | −0.72 | −0.51 |

**Table 7.**Similarity in network structures between different phases of the cryptocurrency market measured by three metrics. A higher value of $\mathit{v}-\mathit{measure}$ indicates a greater similarity between two structures, whereas, higher values of $\mathit{degreecentrality}$ and $\mathit{eigenvaluemethod}$ indicate more dissimilarity between two structures.

Time Window | 1 vs. 2 | 1 vs. 3 | 2 vs. 3 | |
---|---|---|---|---|

Metrics | ||||

Degree centrality | 0.5 | 0.09 | 0.42 | |

Eigenvalue method | 844.45 | 4.59 | 759.16 | |

v-measure | 0.04 | 0.32 | 0.02 |

**Table 8.**Distributions of rankings in each community during different phases of the financial market: normal time, downturn time and recovery time. The rankings are sorted in ascending order. Bold values are minimum and maximum ranks in each period.

1l | Group | Cryptocurrencies | Rankings |
---|---|---|---|

Normal time | 1 | ADA, XLM, BAT, ZIL | 10, 13, 32, 99 |

2 | BTG, IOST, XTZ, ZRX, ETC | 12, 21, 45, 57, 83 | |

3 | LSK, OMG, REP, FUN, MKR | 26,54, 58, 70, 168 | |

4 | NEO, MANA, BNT, XVG, XEM, QTUM | 19, 31, 41, 86, 117, 184 | |

5 | ONT, ZEC, XMR, XRP, EOS, TRX, LTC | 3, 6, 7, 11, 16, 29, 35 | |

6 | ICX, MAID, DOGE, BTC, BSV, ETH, BCH | 1, 2, 5, 9, 34, 84, 130 | |

Downturn time | 1 | DOGE, ICX, BNT, MANA, ZRX, FUN, MAID, BAT, XVG, ONT | 32, 33, 40, 45, 60, 81, 105, 124, 139, 196 |

2 | ADA, BCH, BSV, BTC, BTG, EOS, ETH, ETC, IOST, LSK, LTC, MKR, NEO, OMG, QTUM, REP, TRX, XEM, XLM, XMR, XRP, XTZ, ZEC, ZIL | 1, 2, 4, 5, 6, 7, 9,11, 12, 15, 17, 18, 21, 22, 27, 30, 34, 48, 51, 53, 54, 62, 65, 91 | |

Recovery time | 1 | BTG, MANA, BAT, ZEC | 56, 62, 67, 107 |

2 | ONT, QTUM, EOS, BSV, MKR | 24, 31, 53, 75, 88 | |

3 | XVG, ZIL, XEM, MAID, BTC, ETH | 1, 2, 38, 48, 109, 136 | |

4 | ADA, DOGE, XRP, BCH, XLM, LTC | 6, 7, 9, 15, 16, 20 | |

5 | OMG, BNT, IOST, REP, ICX, LSK | 68, 78, 85, 100, 101, 140 | |

6 | ETC, ZRX, TRX, NEO, XMR, FUN, XTZ | 17, 27, 33, 35, 64, 76, 129 |

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## Share and Cite

**MDPI and ACS Style**

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

**AMA Style**

Nguyen APN, Mai TT, Bezbradica M, Crane M.
The Cryptocurrency Market in Transition before and after COVID-19: An Opportunity for Investors? *Entropy*. 2022; 24(9):1317.
https://doi.org/10.3390/e24091317

**Chicago/Turabian Style**

Nguyen, An Pham Ngoc, Tai Tan Mai, Marija Bezbradica, and Martin Crane.
2022. "The Cryptocurrency Market in Transition before and after COVID-19: An Opportunity for Investors?" *Entropy* 24, no. 9: 1317.
https://doi.org/10.3390/e24091317