# The Impact of the COVID-19 Pandemic on the Unpredictable Dynamics of the Cryptocurrency Market

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Approximate Entropy (ApEn)

#### 2.2. Sample Entropy (SampEn)

#### 2.3. Lempel-Ziv Complexity (LZ)

## 3. Results

#### 3.1. Data

#### 3.2. Complexity Evolution by Time and Market Cap

#### 3.3. Comparison Test of Complexity Evolution

#### 3.4. Vaccination Effect on Complexity

## 4. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Scaled plot of 43 cryptocurrency markets from the bull market in 2017 to the recent COVID-19 pandemic.

**Figure 2.**Boxplots of the ApEn, SampEn, and LZ for the cryptocurrency markets from the bull to current COVID-19 pandemic. Each year includes 43 markets. Diamond symbols are outliers.

**Figure 3.**Boxplots of the ApEn for each market cap from the bull to current COVID-19 pandemic year. Each group includes 11 markets approximately.

**Figure 4.**Boxplots of the SampEn for each market cap from the bull to current COVID-19 pandemic year. Each group includes 11 markets approximately.

**Figure 5.**Boxplots of the LZ for each market cap from the bull to current COVID-19 pandemic year. Each group includes 11 markets approximately.

**Figure 6.**Time evolution of ApEn, SampEn, and LZ. The black line is the average value of 43 cryptocurrencies in market, and the gray shade is the 95% confidence interval.

Market Cap | Name | Abbreviation | Market Cap | Name | Abbreviation | Market Cap | Name | Abbreviation | Market Cap | Name | Abbreviation |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | Bitcoin | BTC-USD | 12 | EthereumClassic | ETC-USD | 23 | Ardor | ARDR-USD | 34 | Blocknet | BLOCK-USD |

2 | Ethereum | ETH-USD | 13 | Waves | WAVES-USD | 24 | BitShares | BTS-USD | 35 | Factom | FCT-USD |

3 | XRP | XRP-USD | 14 | Dogecoin | DOGE-USD | 25 | Steem | STEEM-USD | 36 | Nxt | NXT-USD |

4 | Tether | USDT-USD | 15 | DigiByte | DGB-USD | 26 | MaidSafeCoin | MAID-USD | 37 | Vertcoin | VTC-USD |

5 | Litecoin | LTC-USD | 16 | Decred | DCR-USD | 27 | Syscoin | SYS-USD | 38 | NavCoin | NAV-USD |

6 | Stellar | XLM-USD | 17 | Augur | REP-USD | 28 | Zcoin | XZC-USD | 39 | GameCredits | GAME-USD |

7 | Monero | XMR-USD | 18 | Lisk | LSK-USD | 29 | Bytecoin | BCN-USD | 40 | Counterparty | XCP-USD |

8 | NEM | XEM-USD | 19 | Siacoin | SC-USD | 30 | PIVX | PIVX-USD | 41 | SingularDTV | SNGLS-USD |

9 | NEO | NEO-USD | 20 | Verge | XVG-USD | 31 | Obyte | GBYTE-USD | 42 | NoLimitCoin | NLC2-USD |

10 | Dash | DASH-USD | 21 | Golem | GNT-USD | 32 | DigixDAO | DGD-USD | 43 | IOCoin | IOC-USD |

11 | Zcash | ZEC-USD | 22 | MonaCoin | MONA-USD | 33 | Nexus | NXS-USD |

(a) Market cap: Top “1–25%” | |||||

Algorithm | Null Hypothesis | “2017 = 2020” | “2018 = 2020” | “2019 = 2020” | “2017 = 2018 = 2019 = 2020” |

Approximate Entropy | left = right | 0.00 * | 0.19 | 0.32 | - |

left > right | 0.00 * | 0.09 * | 0.85 | - | |

left < right | 1.00 | 0.92 | 0.16 | - | |

same mean | - | - | - | 0.00 * | |

same variance | - | - | - | 0.66 | |

Sample Entropy | left = right | 0.00 * | 0.05 * | 0.43 | - |

left > right | 0.00 * | 0.02 * | 0.80 | - | |

left < right | 1.00 | 0.98 | 0.22 | - | |

same mean | - | - | - | 0.00 * | |

same variance | - | - | - | 0.59 | |

Lemple-Ziv Complexity | left = right | 0.04 * | 0.03 * | 0.60 | - |

left > right | 0.02 * | 0.01 * | 0.30 | - | |

left < right | 0.98 | 0.99 | 0.72 | - | |

same mean | - | - | - | 0.02 * | |

same variance | - | - | - | 0.98 | |

(b) Market cap: Top “26–50%” | |||||

Algorithm | Null Hypothesis | “2017 = 2020” | “2018 = 2020” | “2019 = 2020” | “2017 = 2018 = 2019 = 2020” |

Approximate Entropy | left = right | 0.00 * | 0.00 * | 0.36 | - |

left > right | 0.00 * | 0.00 * | 0.18 | - | |

left < right | 1.00 | 1.00 | 0.84 | - | |

same mean | - | - | - | 0.00 * | |

same variance | - | - | - | 0.85 | |

Sample Entropy | left = right | 0.00 * | 0.00 * | 0.26 | - |

left > right | 0.00 * | 0.00 * | 0.13 | - | |

left < right | 1.00 | 1.00 | 0.88 | - | |

same mean | - | - | - | 0.00 * | |

same variance | - | - | - | 0.43 | |

Lemple-Ziv Complexity | left = right | 0.00 * | 0.00 * | 0.21 | - |

left > right | 0.00 * | 0.00 * | 0.11 | - | |

left < right | 1.00 | 1.00 | 0.91 | - | |

same mean | - | - | - | 0.00 * | |

same variance | - | - | - | 0.51 |

(a) Market cap: Top “51–75%” | |||||

Algorithm | Null Hypothesis | “2017 = 2020” | “2018 = 2020” | “2019 = 2020” | “2017 = 2018 = 2019 = 2020” |

Approximate Entropy | left = right | 0.00 * | 0.00 * | 0.32 | - |

left > right | 0.00 * | 0.00 * | 0.16 | - | |

left < right | 1.00 | 1.00 | 0.85 | - | |

same mean | - | - | - | 0.00 * | |

same variance | - | - | - | 0.00 * | |

Sample Entropy | left = right | 0.00 * | 0.00 * | 0.26 | - |

left > right | 0.00 * | 0.00 * | 0.13 | - | |

left < right | 1.00 | 1.00 | 0.88 | - | |

same mean | - | - | - | 0.00 * | |

same variance | - | - | - | 0.00 * | |

Lemple-Ziv Complexity | left = right | 0.32 | 0.16 | 0.00 * | - |

left > right | 0.86 | 0.93 | 1.00 | - | |

left < right | 0.16 | 0.08 * | 0.00 * | - | |

same mean | - | - | - | 0.00 * | |

same variance | - | - | - | 0.72 | |

(b) Market cap: Top “76–100%” | |||||

Algorithm | Null Hypothesis | “2017 = 2020” | “2018 = 2020” | “2019 = 2020” | “2017 = 2018 = 2019 = 2020” |

Approximate Entropy | left = right | 0.01 * | 0.00 * | 0.10 * | - |

left > right | 0.00 * | 0.00 * | 0.05 * | - | |

left < right | 1.00 | 1.00 | 0.96 | - | |

same mean | - | - | - | 0.00 * | |

same variance | - | - | - | 0.08 * | |

Sample Entropy | left = right | 0.01 * | 0.00 * | 0.12 | - |

left > right | 0.00 * | 0.00 * | 0.06 * | - | |

left < right | 1.00 | 1.00 | 0.95 | - | |

same mean | - | - | - | 0.00 * | |

same variance | - | - | - | 0.02 * | |

Lemple-Ziv Complexity | left = right | 0.79 | 0.34 | 0.03 * | - |

left > right | 0.40 | 0.85 | 0.99 | - | |

left < right | 0.63 | 0.17 | 0.02 * | - | |

same mean | - | - | - | 0.03 * | |

same variance | - | - | - | 0.50 |

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**MDPI and ACS Style**

Kim, K.; Lee, M.
The Impact of the COVID-19 Pandemic on the Unpredictable Dynamics of the Cryptocurrency Market. *Entropy* **2021**, *23*, 1234.
https://doi.org/10.3390/e23091234

**AMA Style**

Kim K, Lee M.
The Impact of the COVID-19 Pandemic on the Unpredictable Dynamics of the Cryptocurrency Market. *Entropy*. 2021; 23(9):1234.
https://doi.org/10.3390/e23091234

**Chicago/Turabian Style**

Kim, Kyungwon, and Minhyuk Lee.
2021. "The Impact of the COVID-19 Pandemic on the Unpredictable Dynamics of the Cryptocurrency Market" *Entropy* 23, no. 9: 1234.
https://doi.org/10.3390/e23091234