A Monte Carlo Approach to Bitcoin Price Prediction with Fractional Ornstein–Uhlenbeck Lévy Process
Abstract
:1. Introduction
2. Materials and Methods
- The process is likely to reverse the trend over the time frame considered.
- The process is random in which knowing one data point does not provide insight into predicting future data points.
- The process is persistent in the sense that a future data point is likely to be similar to a data point preceding it.
2.1. Fractional Brownian Motion
2.2. Lévy Process
2.2.1. Infinitely Divisible Distributions
2.2.2. Continuous-Time Stochastic Processes
- The random variables are independent for all and (independent increments);
- has the same distribution as for all (stationary increments);
- L is stochastically continuous; that is, for all and .
- The paths are right-continuous with left limits (cadlag-continue á droite et limite á gauche).
2.2.3. Normal Inverse Gaussian
- iv) (Poisson distribution).
2.3. Fractional Ornstein–Uhlenbeck Lévy Process
3. Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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29 July | 8 August | 18 August | |
---|---|---|---|
Quantiles | 10 Day | 20 Day | 30 Day |
25% | 9812 | 9590 | 8915 |
50% | 10,360 | 10,283 | 9956 |
75% | 10,841 | 11,029 | 11,161 |
90% | 11,342 | 11,818 | 12,049 |
95% | 11,881 | 12,245 | 13,157 |
99% | 11,963 | 12,885 | 13,600 |
mean | 10,085.65 | 10,085.66 | 10,085.68 |
skweness | −0.0899 | −0.0891 | −0.0626 |
kurtosis | 1.1390 | 0.5511 | 0.3755 |
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Mba, J.C.; Mwambi, S.M.; Pindza, E. A Monte Carlo Approach to Bitcoin Price Prediction with Fractional Ornstein–Uhlenbeck Lévy Process. Forecasting 2022, 4, 409-419. https://doi.org/10.3390/forecast4020023
Mba JC, Mwambi SM, Pindza E. A Monte Carlo Approach to Bitcoin Price Prediction with Fractional Ornstein–Uhlenbeck Lévy Process. Forecasting. 2022; 4(2):409-419. https://doi.org/10.3390/forecast4020023
Chicago/Turabian StyleMba, Jules Clément, Sutene Mwambetania Mwambi, and Edson Pindza. 2022. "A Monte Carlo Approach to Bitcoin Price Prediction with Fractional Ornstein–Uhlenbeck Lévy Process" Forecasting 4, no. 2: 409-419. https://doi.org/10.3390/forecast4020023