# Modeling and Forecasting Cryptocurrency Closing Prices with Rao Algorithm-Based Artificial Neural Networks: A Machine Learning Approach

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## Abstract

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## 1. Introduction

- We are designing an efficient ANN forecast for the nearly precise prediction of cryptocurrencies such as Bitcoin, Litecoin, Ethereum, CMC 200, Tether, and Ripple.
- Suitable tuning of ANN parameters (i.e., weight and bias) by RA, thus forming a hybrid model (i.e., RA + ANN) to overcome the limitations of derivative-based optimization techniques.
- We are evaluating the performance of the RA + ANN forecast through two performance metrics, MAPE and ARV.

## 2. Artificial Neural Network

## 3. Proposed RA + ANN Based Forecasting

- ${W}_{j,k,i}$ = the value of ${j}^{th}$ variable of ${k}^{th}$ solution ($k=1,2,3,\cdots ,n$) at ${i}^{th}$ iteration.
- ${W}_{j,k,i}^{\prime}$ = the modified value of ${j}^{th}$ variable of ${k}^{th}$ solution ($k=1,2,3,\cdots ,n$) at ${i}^{th}$ iteration.
- ${W}_{j,best,i}$ = ${j}^{th}$ variable value of the best solution in ${i}^{th}$ iteration.
- ${W}_{j,worst,i}$ = ${j}^{th}$ variable value of the worst solution ${i}^{th}$ iteration.
- $ran{d}_{1,j,i}$ and $ran{d}_{2,j,i}$ are two random values in [0,1].

Algorithm 1: RA + ANN-based forecasting. |

1. Set population size (n), No. of design variables (m), and Termination criteria. 2. Initialization of population. 3. Set training and test data using sliding window. 4. Normalization of training and test data. /* Model Training */ 5. While (! = termination criteria) For each candidate solution (W) in the population. Supply train data and W to ANN. Compute ANN output. Error = expected output–estimated output Fitness = accumulated error. End Identify best and worst solution. Update population using any Equations (8)–(10). 6. End /* Model Testing */ 7. Feed test data and best solution to ANN. Calculate the model output error value. 8. Reiterate Steps 2–6 for all training and test patterns and preserve total error. |

## 4. Cryptocurrency Data

## 5. Experimental Results and Analysis

#### 5.1. Model Input Selection and Normalization

#### 5.2. Performance Evaluation Metrics

#### 5.3. Experimental Setting

#### 5.4. Simulation Results and Discussion

- The RA + ANN-based forecast was found quite capable in capturing the inherent dynamism and uncertainties associated with cryptocurrency data.
- The hybridization of RA and ANN achieved improved forecasting accuracy compared to others.
- The outcomes from the statistical test justified the significant difference between RA + ANN and others.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Statistic | Bitcoin | Litecoin | Ethereum | Ripple | CMC 200 | Tether |
---|---|---|---|---|---|---|

Minimum | 68.4300 | 1.1600 | 0.4348 | 0.0028 | 0.9742 | 0.9742 |

Mean | 1.4826 × 10^{3} | 20.4966 | 147.7843 | 0.0984 | 1.0029 | 1.0029 |

Median | 482.8100 | 3.9100 | 12.0200 | 0.0079 | 1.0017 | 1.0017 |

Variance | 8.7535 × 10^{6} | 2.2240 × 10^{3} | 6.9765 × 10^{4} | 0.1028 | 2.5621 × 10^{−5} | 2.5621 × 10^{−5} |

Maximum | 1.9497 × 10^{4} | 358.3400 | 1.3964 × 10^{3} | 3.3800 | 1.0536 | 1.0536 |

Standard deviation | 2.9593 × 10^{3} | 47.1594 | 264.1308 | 0.3206 | 0.0051 | 0.0051 |

Skewness | 3.5394 | 4.1627 | 2.3844 | 5.8039 | 1.9417 | 1.9417 |

Kurtosis | 15.9671 | 21.5925 | 8.5122 | 42.9469 | 19.3797 | 19.3797 |

Correlation coefficient | 0.00130 | 0.00211 | −0.0052 | 0.0027 | 0.0039 | 0.0035 |

MODEL | BITCOIN | RIPPLE | EHTEREUM | LITECOIN | CMC200 | TETHER | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

MAPE | ARV | MAPE | ARV | MAPE | ARV | MAPE | ARV | MAPE | ARV | MAPE | ARV | |

RA + ANN | 0.0300 | 0.0057 | 0.0397 | 0.0051 | 0.0385 | 0.0039 | 0.0322 | 0.0054 | 0.0275 | 0.0027 | 0.0065 | 0.0055 |

GA + ANN | 0.0322 | 0.0075 | 0.0457 | 0.0143 | 0.0495 | 0.0057 | 0.0454 | 0.0058 | 0.0299 | 0.0053 | 0.0087 | 0.0173 |

PSO + ANN | 0.0454 | 0.0061 | 0.0473 | 0.0053 | 0.0439 | 0.0063 | 0.0394 | 0.0079 | 0.0287 | 0.0164 | 0.0082 | 0.0094 |

SVM | 0.0394 | 0.0065 | 0.0476 | 0.0068 | 0.0463 | 0.0059 | 0.0837 | 0.0060 | 0.0428 | 0.0342 | 0.0093 | 0.0107 |

MLP | 0.0472 | 0.0077 | 0.0497 | 0.0174 | 0.0593 | 0.0467 | 0.1726 | 0.0246 | 0.0479 | 0.0277 | 0.0329 | 0.0637 |

ARIMA | 0.0606 | 0.0083 | 0.0828 | 0.0163 | 0.0758 | 0.0193 | 0.0940 | 0.0095 | 0.1327 | 0.0336 | 0.0852 | 0.2953 |

LSE | 0.0946 | 0.1005 | 0.0876 | 0.1373 | 0.2557 | 0.0736 | 0.2163 | 0.0266 | 0.5283 | 0.2734 | 0.1086 | 0.4066 |

Proposed Forecast | Comparative Forecast | p and h Values from Wilcoxon Signed Test | ||||
---|---|---|---|---|---|---|

NASDAQ | BSE | DJIA | HSI | NIKKEI | ||

RA + ANN | GA + ANN | 2.5034 × 10^{−5}(h = 1) | 3.1432 × 10^{−4}(h = 1) | 2.2441 × 10^{−3}(h = 1) | 3.0134 × 10^{−5}(h = 1) | 2.2763 × 10^{−4}(h = 1) |

PSO + ANN | 3.1362 × 10^{−3}(h = 1) | 4.2634 × 10^{−5}(h = 1) | 4.3004 × 10^{−3}(h = 1) | 6.2515 × 10^{−3}(h = 1) | 1.7253 × 10^{−2}(h = 1) | |

SVM | 4.2418 × 10^{−4}(h = 1) | 2.1505 × 10^{−3}(h = 1) | 3.3410 × 10^{−2}(h = 1) | 2.990152 (h = 0) | 1.6728 × 10^{−1}(h = 1) | |

MLP | 1.5728 × 10^{−3}(h = 1) | 0.008524 (h = 0) | 6.2803 × 10^{−2}(h = 1) | 7.2095 × 10^{−2}(h = 1) | 4.2021 × 10^{−3}(h = 1) | |

ARIMA | 4.3007 × 10^{−4}(h = 1) | 3.7726 × 10^{−2}(h = 1) | 1.7362 × 10^{−5}(h = 1) | 3.3282 × 10^{−3}(h = 1) | 1.7062 × 10^{−4}(h = 1) | |

LSE | 1.5338 × 10^{−3}(h = 1) | 0.01821 (h = 0) | 6.2033 × 10^{−2}(h = 1) | 7.0025 × 10^{−2}(h = 1) | 3.2521 × 10^{−3}(h = 1) | |

p and h values from Diebold–Mariano test | ||||||

GA + ANN | 2.09755 (h = 1) | 2.34220 (h = 1) | 2.0007 (h = 1) | 1.9820 (h = 1) | 2.2037 (h = 1) | |

PSO + ANN | 2.22043 (h = 1) | 2.36020 (h = 1) | 1.9873 (h = 1) | 1.9815 (h = 1) | −1.9900 (h = 1) | |

SVM | 2.36105 (h = 1) | 1.99247 (h = 1) | 1.97695 (h = 1) | 1.98577 (h = 1) | 1.9792 (h = 1) | |

MLP | 2.7329 (h = 1) | 1.9800 (h = 1) | −3.05263 (h = 1) | −1.99265 (h = 1) | 2.52655 (h = 1) | |

ARIMA | 1.9909 (h = 1) | 2.61227 (h = 1) | −3.40582 (h = 1) | 1.96035 (h = 0) | 2.45884 (h = 1) | |

LSE | 2.0728 × 10^{−3}(h = 1) | 2.88524 (h = 1) | 3.2800 × 10^{−2}(h = 1) | 5.1095 × 10^{−2}(h = 1) | 4.32171 × 10^{−3}(h = 1) |

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**MDPI and ACS Style**

Nayak, S.K.; Nayak, S.C.; Das, S.
Modeling and Forecasting Cryptocurrency Closing Prices with Rao Algorithm-Based Artificial Neural Networks: A Machine Learning Approach. *FinTech* **2022**, *1*, 47-62.
https://doi.org/10.3390/fintech1010004

**AMA Style**

Nayak SK, Nayak SC, Das S.
Modeling and Forecasting Cryptocurrency Closing Prices with Rao Algorithm-Based Artificial Neural Networks: A Machine Learning Approach. *FinTech*. 2022; 1(1):47-62.
https://doi.org/10.3390/fintech1010004

**Chicago/Turabian Style**

Nayak, Sanjib Kumar, Sarat Chandra Nayak, and Subhranginee Das.
2022. "Modeling and Forecasting Cryptocurrency Closing Prices with Rao Algorithm-Based Artificial Neural Networks: A Machine Learning Approach" *FinTech* 1, no. 1: 47-62.
https://doi.org/10.3390/fintech1010004