Skewed Multifractal Cross-Correlations Between Green Bond Index and Energy Futures Markets: A New Perspective Based on Change Point
Abstract
1. Introduction
2. Literature Review
3. Skewed Multifractal Analysis Methodology
3.1. Change Point Test
3.2. Skewed Multifractal Cross-Correlation Analysis
3.3. Mean MF-DCCA Portfolio Construction
4. Data
5. Empirical Results and Discussion
5.1. Cross-Correlation Test
5.2. Skewed Multifractal Detrended Fluctuation Analysis
5.2.1. Results and Analysis of Change Point Identification
5.2.2. Skewed Multifractal Analysis
5.3. Portfolio Management Implications
5.4. Robustness Check of Change Points
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Green Bond | WTI Crude Oil | Natural Gas | Gasoline | |
---|---|---|---|---|
Mean | −0.1214 × 10−4 | −0.0001 | −0.0002 | −0.0003 |
Median | 0.0000 | 0.0008 | −0.0007 | 0.0010 |
Maximum | 0.0227 | 0.2374 | 0.4253 | 0.2686 |
Minimum | −0.0241 | −0.4808 | −0.1945 | −0.2638 |
Std. Dev. | 0.0038 | 0.0287 | 0.0362 | 0.0272 |
Skewness | −0.0835 | −2.1489 | 0.5932 | −0.5511 |
Kurtosis | 7.1020 | 45.5525 | 12.9178 | 18.0911 |
Jarque–Bera | 1766.2050 * | 191,683.5800 * | 10,455.1620 * | 23,992.7640 * |
N | 2515 | 2515 | 2515 | 2515 |
GB & WTI | GB & Gasoline | GB & Natural Gas | |
---|---|---|---|
Period 1 | 1 August 2014 to 20 April 2020 | 1 August 2014 to 6 March 2020 | 1 August 2014 to 22 September 2020 |
Period 2 | 21 April 2020 to 11 July 2022 | 9 March 2020 to 1 July 2022 | 23 September 2020 to 14 September 2022 |
Period 3 | 12 July 2022 to 28 August 2024 | 5 July 2022 to 28 August 2024 | 15 September 2022 to 28 August 2024 |
Entire period | 1 August 2014 to 28 August 2024 | 1 August 2014 to 28 August 2024 | 1 August 2014 to 28 August 2024 |
Entire period | Period 1 | |||||
q | GB&WTI | GB&Gasoline | GB&NG | GB&WTI | GB&Gasoline | GB&NG |
−10 | 0.6800 | 0.6796 | 0.6784 | 0.5888 | 0.6105 | 0.6067 |
−8 | 0.6689 | 0.6677 | 0.6632 | 0.5803 | 0.6006 | 0.5958 |
−6 | 0.6551 | 0.6532 | 0.6434 | 0.5715 | 0.5897 | 0.5822 |
−4 | 0.6378 | 0.6351 | 0.6179 | 0.5638 | 0.5792 | 0.5655 |
−2 | 0.6119 | 0.6085 | 0.5873 | 0.5596 | 0.5696 | 0.5458 |
0 | 0.5650 | 0.5591 | 0.5624 | 0.5485 | 0.5482 | 0.5160 |
2 | 0.4940 | 0.4831 | 0.5519 | 0.4385 | 0.4844 | 0.4510 |
4 | 0.4130 | 0.3940 | 0.5162 | 0.2740 | 0.4128 | 0.3815 |
6 | 0.3573 | 0.3360 | 0.4813 | 0.1841 | 0.3638 | 0.3335 |
8 | 0.3232 | 0.3011 | 0.4563 | 0.1359 | 0.3319 | 0.3019 |
10 | 0.3010 | 0.2783 | 0.4386 | 0.1069 | 0.3104 | 0.2805 |
ΔH | 0.3791 | 0.4012 | 0.2398 | 0.4818 | 0.3001 | 0.3262 |
Period 2 | Period 3 | |||||
q | GB&WTI | GB&Gasoline | GB&NG | GB&WTI | GB&Gasoline | GB&NG |
−10 | 0.7069 | 0.6441 | 0.7186 | 0.6173 | 0.6339 | 0.5913 |
−8 | 0.6968 | 0.6337 | 0.6976 | 0.6061 | 0.6240 | 0.5855 |
−6 | 0.6831 | 0.6202 | 0.6668 | 0.5900 | 0.6114 | 0.5797 |
−4 | 0.6632 | 0.6027 | 0.6227 | 0.5643 | 0.5943 | 0.5736 |
−2 | 0.6336 | 0.5827 | 0.5708 | 0.5177 | 0.5636 | 0.5609 |
0 | 0.6061 | 0.5808 | 0.5259 | 0.4398 | 0.4863 | 0.5145 |
2 | 0.5804 | 0.5770 | 0.4967 | 0.3615 | 0.3587 | 0.4361 |
4 | 0.5195 | 0.5269 | 0.4585 | 0.3130 | 0.2668 | 0.3793 |
6 | 0.4701 | 0.4876 | 0.4207 | 0.2804 | 0.2158 | 0.3432 |
8 | 0.4385 | 0.4620 | 0.3940 | 0.2568 | 0.1843 | 0.3183 |
10 | 0.4176 | 0.4446 | 0.3754 | 0.2393 | 0.1630 | 0.3003 |
ΔH | 0.2893 | 0.1995 | 0.3432 | 0.3780 | 0.4709 | 0.2910 |
Cross Correlation | αxy (0) | Wxy | Γ | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Entire Period | Period I | Period II | Period III | Entire Period | Period I | Period II | Period III | Entire Period | Period I | Period II | Period III | |
GB&WTI | 0.5619 | 0.5693 | 0.6078 | 0.4397 | 0.5171 | 0.6761 | 0.4167 | 0.4970 | 0.9203 | 1.1876 | 0.6856 | 1.1304 |
GB&Gasoline | 0.5558 | 0.5420 | 0.5821 | 0.4784 | 0.5442 | 0.4311 | 0.3147 | 0.6008 | 0.9791 | 0.7954 | 0.5407 | 1.2559 |
GB&NG | 0.5656 | 0.5107 | 0.5282 | 0.5096 | 0.3764 | 0.4599 | 0.5051 | 0.3911 | 0.6655 | 0.9006 | 0.9563 | 0.7675 |
Period | Portfolios | Weight: GB/WTI | SR | RRE | Weight: GB/Gasoline | SR | RRE | Weight: GB/NG | SR | RRE |
---|---|---|---|---|---|---|---|---|---|---|
Period 1 | energy only | 0/100 | −4.13 | - | 0/100 | −3.37 | - | 0/100 | −2.13 | - |
equal weighted | 50/50 | −4.69 | 49.81 | 50/50 | −3.84 | 49.72 | 50/50 | −2.49 | 49.61 | |
MV | 98.46/1.54 | −5.60 | 88.70 | 98.37/1.63 | −4.43 | 87.93 | 98.86/1.14 | −3.55 | 88.69 | |
MaxSR | 0/100 | −4.13 | 0.00 | 0/100 | −3.37 | 0.00 | 0/100 | −2.13 | 0.00 | |
MD | 99.04/0.96 | −5.41 | 88.69 | 98.47/1.53 | −4.40 | 87.93 | 99.07/0.93 | −3.52 | 88.69 | |
Mean-MF-DCCA MV | 97.27/2.73 | −0.80 | 92.79 | 98.34/1.66 | −1.17 | 91.03 | 94.31/5.69 | 0.12 | 91.86 | |
Mean-MF-DCCA MaxSR | 100/0 | −0.90 | 92.50 | 0/100 | 5.12 | 86.10 | 100/0 | −0.15 | 91.62 | |
Mean-MF-DCCA MD | 99.04/0.96 | −0.84 | 92.69 | 98.89/1.11 | −1.11 | 91.01 | 94.91/5.09 | −0.12 | 91.65 | |
Period 2 | energy only | 0/100 | 7.12 | - | 0/100 | 3.66 | - | 0/100 | 6.65 | - |
equal weighted | 50/50 | 5.92 | 49.54 | 50/50 | 2.30 | 49.29 | 50/50 | 5.25 | 49.88 | |
MV | 99.5/0.5 | −11.24 | 90.24 | 99.6/0.4 | −11.85 | 88.97 | 99.15/0.85 | −15.61 | 91.50 | |
MaxSR | 0/100 | 7.12 | 0.00 | 0/100 | 3.66 | 0.00 | 0/100 | 6.65 | 0.00 | |
MD | 98.9/1.1 | −10.71 | 90.22 | 99.65/0.35 | −11.87 | 88.97 | 98.61/1.39 | −15.07 | 91.49 | |
Mean-MF-DCCA MV | 98.4/1.6 | −0.50 | 90.19 | 92.33/7.67 | −1.67 | 92.14 | 96.54/3.46 | −0.03 | 92.07 | |
Mean-MF-DCCA MaxSR | 100/0 | −0.54 | 90.05 | 0/100 | 2.90 | 87.38 | 100/0 | −0.26 | 91.86 | |
Mean-MF-DCCA MD | 98.46/1.54 | −0.54 | 90.06 | 99.65/0.35 | −1.18 | 92.01 | 96.84/3.16 | −0.24 | 91.88 | |
Period 3 | energy only | 0/100 | −3.85 | - | 0/100 | −5.41 | - | 0/100 | −7.16 | - |
equal weighted | 50/50 | −3.63 | 48.32 | 50/50 | −5.28 | 48.56 | 50/50 | 1.10 | 49.40 | |
MV | 94.38/5.62 | −0.50 | 75.69 | 95.39/4.61 | −1.23 | 77.78 | 99.34/0.66 | 1.53 | 88.85 | |
MaxSR | 100/0 | 0.40 | 75.01 | 100/0 | −0.11 | 77.29 | 100/0 | −6.91 | 88.84 | |
MD | 94.94/5.06 | −0.41 | 75.68 | 96.87/3.13 | −0.87 | 77.73 | 99.66/0.34 | 1.31 | 88.85 | |
Mean-MF-DCCA MV | 96.84/3.16 | −0.44 | 91.38 | 94.99/5.01 | −2.29 | 94.39 | 96.3/3.7 | 0.52 | 96.71 | |
Mean-MF-DCCA MaxSR | 100/0 | −0.50 | 91.24 | 0/100 | 8.09 | 91.78 | 100/0 | −0.28 | 96.44 | |
Mean-MF-DCCA MD | 99.07/0.93 | −0.46 | 91.34 | 98.61/1.39 | −1.75 | 94.34 | 99.63/0.37 | 0.44 | 96.69 |
Multifractal Indicator | Period | Group | BEAST-Identified Sequence | Economic Event Sequence |
---|---|---|---|---|
Hurst exponent | 1 | GB&WTI | 0.4361 | 0.3941 |
GB&Gasoline | 0.4844 | 0.4711 | ||
GB&NG | 0.4510 | 0.4615 | ||
2 | GB&WTI | 0.5804 | 0.5138 | |
GB&Gasoline | 0.6097 | 0.5227 | ||
GB&NG | 0.4967 | 0.4017 | ||
3 | GB&WTI | 0.3615 | 0.3031 | |
GB&Gasoline | 0.3587 | 0.4520 | ||
GB&NG | 0.4361 | 0.4768 | ||
ΔH | 1 | GB&WTI | 0.5471 | 0.4650 |
GB&Gasoline | 0.3001 | 0.3341 | ||
GB&NG | 0.3262 | 0.3168 | ||
2 | GB&WTI | 0.2893 | 0.3891 | |
GB&Gasoline | 0.1945 | 0.2629 | ||
GB&NG | 0.3432 | 0.3971 | ||
3 | GB&WTI | 0.3780 | 0.5952 | |
GB&Gasoline | 0.4709 | 0.3053 | ||
GB&NG | 0.2910 | 0.2675 | ||
Wxy | 1 | GB&WTI | 0.6761 | 0.6043 |
GB&Gasoline | 0.4167 | 0.4770 | ||
GB&NG | 0.4970 | 0.4568 | ||
2 | GB&WTI | 0.4311 | 0.5442 | |
GB&Gasoline | 0.3147 | 0.3968 | ||
GB&NG | 0.6008 | 0.5449 | ||
3 | GB&WTI | 0.4599 | 0.7522 | |
GB&Gasoline | 0.5051 | 0.4175 | ||
GB&NG | 0.3911 | 0.3594 | ||
Γ | 1 | GB&WTI | 1.1876 | 1.2047 |
GB&Gasoline | 0.6856 | 0.7925 | ||
GB&NG | 1.1304 | 0.8178 | ||
2 | GB&WTI | 0.7954 | 0.9572 | |
GB&Gasoline | 0.5407 | 0.7547 | ||
GB&NG | 1.2559 | 0.8898 | ||
3 | GB&WTI | 0.9006 | 1.6849 | |
GB&Gasoline | 0.9563 | 0.8023 | ||
GB&NG | 0.7675 | 0.7560 |
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Tian, Y.; Li, Z.; Wang, J.; Wu, X.; Huang, H. Skewed Multifractal Cross-Correlations Between Green Bond Index and Energy Futures Markets: A New Perspective Based on Change Point. Fractal Fract. 2025, 9, 327. https://doi.org/10.3390/fractalfract9050327
Tian Y, Li Z, Wang J, Wu X, Huang H. Skewed Multifractal Cross-Correlations Between Green Bond Index and Energy Futures Markets: A New Perspective Based on Change Point. Fractal and Fractional. 2025; 9(5):327. https://doi.org/10.3390/fractalfract9050327
Chicago/Turabian StyleTian, Yun, Zhihui Li, Jue Wang, Xu Wu, and Huan Huang. 2025. "Skewed Multifractal Cross-Correlations Between Green Bond Index and Energy Futures Markets: A New Perspective Based on Change Point" Fractal and Fractional 9, no. 5: 327. https://doi.org/10.3390/fractalfract9050327
APA StyleTian, Y., Li, Z., Wang, J., Wu, X., & Huang, H. (2025). Skewed Multifractal Cross-Correlations Between Green Bond Index and Energy Futures Markets: A New Perspective Based on Change Point. Fractal and Fractional, 9(5), 327. https://doi.org/10.3390/fractalfract9050327