Exploring the Relationship and Predictive Accuracy for the Tadawul All Share Index, Oil Prices, and Bitcoin Using Copulas and Machine Learning
<p>Log returns of TASI for the period from 17 September 2014 to 5 June 2023.</p> "> Figure 2
<p>Log returns of WTI index for the period from 17 September 2014 to 5 June 2023.</p> "> Figure 3
<p>Log returns of Bitcoin index for the period from 17 September 2014 to 5 June 2023.</p> "> Figure 4
<p>Student’s copula density of the TASI and BTC.</p> "> Figure 5
<p>Student’s copula density of the TASI and WTI.</p> "> Figure 6
<p>Frank copula density of the BTC and WTI.</p> "> Figure 7
<p>Forecasted values with the test data of the TASI returns.</p> "> Figure 8
<p>Forecasted values with the test data of the BTC returns.</p> "> Figure 9
<p>Forecasted values with the test data of the WTI returns.</p> "> Figure 10
<p>The training TASI returns with the forecasted values.</p> "> Figure 11
<p>The training BTC returns with the forecasted values.</p> "> Figure 12
<p>The training WTI returns with the forecasted values.</p> ">
Abstract
:1. Introduction
2. Literature Review
2.1. TASI and Oil Prices
2.2. Oil Prices and Bitcoin
2.3. TASI and Bitcoin
2.4. LSTM Networks and Financial Market Predictions
3. Methodology
3.1. Copulas Functions
3.1.1. Definitions and Properties
- 1.
- is non-decreasing in each component, .
- 2.
- The i-th marginal distribution is obtained by setting for , and since it is uniformly distributed,
- 3.
- C is grounded and N-increasing.
3.1.2. Gaussian Copula
3.1.3. Clayton Copula
3.1.4. Rotated Clayton Copula
3.1.5. Plackett Copula
3.1.6. Frank Copula
3.1.7. Gumbel Copula
3.1.8. Rotated-Gumbel Copula
Student’s Copula
3.1.9. Symmetrised Joe–Clayton Copula
3.1.10. Estimation of Copulas
3.2. LSTM Model Construction and Training
3.2.1. Model Construction
- Forget gate:
- Input gate:
- Cell candidate:
- Cell state:
- Output gate:
- Hidden state:
3.2.2. Training Process
3.3. Prediction Using Bivariate Copulas
3.4. Prediction Using LSTM
3.5. Comparison of Predictive Ability
4. Data and Variables
5. Empirical Results
5.1. Results of Copulas Models
5.2. Results of LSTM Model
5.3. Comparison between Copulas and LSTM Models
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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TASI | BTC | WTI | |
---|---|---|---|
Mean | −0.00048 | 0.003735 | −0.00252 |
Standard deviation | 0.027647 | 0.05139 | 0.09094 |
Kurstosis | 998.3401 | 8.579362 | 611.317 |
Skewness | −27.7652 | −0.0039 | −21.0552 |
Copula Family | Parameters | Lower Tale | Upper Tail | LL | AIC | BIC | |
---|---|---|---|---|---|---|---|
Normal Copula | 0.0149 | 0 | 0 | −0.1892 | −0.3772 | −0.374 | |
Clayton’s copula | 0.0343 | 0 | 0 | −1.0669 | −2.1327 | −2.1295 | |
Rotated Clayton copula | 0.0217 | 0 | 0 | −0.3845 | −0.7679 | −0.7647 | |
Plackett copula | 1.0169 | 0 | 0 | −0.0253 | −0.0494 | −0.0462 | |
Frank copula | 0.0326 | 0 | 0 | −0.0246 | −0.048 | −0.0448 | |
Gumbel copula | 1.0128 | 0 | 0.0174 | −0.4904 | −0.9796 | −0.9765 | |
Rotated Gumbel copula | 1.1 | 0.1221 | 0 | 11.7583 | 23.5177 | 23.5209 | |
Student’s t copula | 0.0107 | 12.37 | 0.003 | 0.003 | −5.214 | −10.4257 | −10.4194 |
Symmetrised Joe–Clayton copula | 0 | 0.0001 | 0.0001 | 0 | −1.1656 | −2.3289 | −2.3226 |
Optimal Copula | Student’s t copula |
Copula Family | Parameters | Lower Tale | Upper Tail | LL | AIC | BIC | |
---|---|---|---|---|---|---|---|
Normal Copula | 0.2088 | 0 | 0 | −38.0552 | −76.1093 | −76.1061 | |
Clayton’s copula | 0.2767 | 0.0817 | 0 | −42.7993 | −85.5975 | −85.5943 | |
Rotated Clayton copula | 0.2331 | 0 | 0.0511 | −31.9963 | −63.9915 | −63.9883 | |
Plackett copula | 1.9306 | 0 | 0 | −35.4105 | −70.8199 | −70.8167 | |
Frank copula | 1.209 | 0 | 0 | −31.741 | −63.4809 | −63.4777 | |
Gumbel copula | 1.1473 | 0 | 0.1703 | −43.884 | −87.7668 | −87.7636 | |
Rotated Gumbel copula | 1.1624 | 0.1846 | 0 | −54.4155 | −108.8297 | −108.8266 | |
Student’s t copula | 0.2013 | 4.3679 | 0.1135 | 0.1135 | −71.3387 | −142.6751 | −142.6687 |
Symmetrised Joe–Clayton copula | 0.0551 | 0.116 | 0.116 | 0.0551 | −56.7728 | −113.5432 | −113.5368 |
Optimal Copula | Student’s t copula |
Copula Family | Parameters | Lower Tale | Upper Tail | LL | AIC | BIC | |
---|---|---|---|---|---|---|---|
Normal Copula | 0.0617 | 0 | 0 | −3.2645 | −6.5279 | −6.5247 | |
Clayton’s copula | 0.0626 | 0 | 0 | −2.782 | −5.5629 | −5.5597 | |
Rotated Clayton copula | 0.0473 | 0 | 0 | −1.601 | −3.2008 | −3.1976 | |
Plackett copula | 1.2262 | 0 | 0 | −3.9794 | −7.9575 | −7.9544 | |
Frank copula | 0.4109 | 0 | 0 | −4.005 | −8.0087 | −8.0055 | |
Gumbel copula | 1.026 | 0 | 0.0348 | −2.0591 | −4.117 | −4.114 | |
Student’s t copula | 0.0626 | 99.9645 | 0 | 0 | −3.228 | −6.4537 | −6.4474 |
Symmetrised Joe–Clayton copula | 0 | 0.0015 | 0.0015 | 0 | −3.1517 | −6.3011 | −6.2947 |
Optimal Copula | Frank copula |
Student’s Copula (0.0107, 12.37) between TASI and BTC. | |||
---|---|---|---|
RMSE | MAE | MASE | |
TASI | 0.407 | 0.331 | 1.1 |
BTC | 0.414 | 0.337 | 1.03 |
Student’s Copula (0.2013, 4.3679) between TASI and WTI. | |||
---|---|---|---|
RMSE | MAE | MASE | |
TASI | 0.409 | 0.335 | 1.095 |
WTI | 0.410 | 0.333 | 1.002 |
Frank Copula (0.4909) between BTC and WTI. | |||
---|---|---|---|
RMSE | MAE | MASE | |
BTC | 0.417 | 0.342 | 1.032 |
WTI | 0.404 | 0.328 | 0.997 |
RMSE | MAE | MASE | |
---|---|---|---|
TASI | 0.015 | 0.0187 | 1.2 |
BTC | 0.051 | 0.0369 | 0.923 |
WTI | 0.039 | 0.1049 | 0.953 |
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Alokley, S.A.; Araichi, S.; Alomair, G. Exploring the Relationship and Predictive Accuracy for the Tadawul All Share Index, Oil Prices, and Bitcoin Using Copulas and Machine Learning. Energies 2024, 17, 3241. https://doi.org/10.3390/en17133241
Alokley SA, Araichi S, Alomair G. Exploring the Relationship and Predictive Accuracy for the Tadawul All Share Index, Oil Prices, and Bitcoin Using Copulas and Machine Learning. Energies. 2024; 17(13):3241. https://doi.org/10.3390/en17133241
Chicago/Turabian StyleAlokley, Sara Ali, Sawssen Araichi, and Gadir Alomair. 2024. "Exploring the Relationship and Predictive Accuracy for the Tadawul All Share Index, Oil Prices, and Bitcoin Using Copulas and Machine Learning" Energies 17, no. 13: 3241. https://doi.org/10.3390/en17133241