# Multifractal Detrended Cross-Correlations between Green Bonds and Commodity Markets: An Exploration of the Complex Connections between Green Finance and Commodities from the Econophysics Perspective

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Materials and Methods

#### 3.1. Data

#### 3.2. MFDCCA Method

#### 3.3. Cross-Correlation Significance Test

#### 3.4. DCCA Coefficient

## 4. Findings and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Zhang, D.; Zhang, Z.; Managi, S. A Bibliometric Analysis on Green Finance: Current Status, Development, and Future Directions. Finance Res. Lett.
**2019**, 29, 425–430. [Google Scholar] [CrossRef] - Reboredo, J.C.; Ugolini, A. Price Connectedness between Green Bond and Financial Markets. Econ. Model.
**2020**, 88, 25–38. [Google Scholar] [CrossRef] - Climate Bond Initiative Sustainable Debt Global State of the Market Report 2022. 2023. Available online: https://www.climatebonds.net/resources/reports/global-state-market-report-2022 (accessed on 13 February 2024).
- MacAskill, S.; Roca, E.; Liu, B.; Stewart, R.A.; Sahin, O. Is There a Green Premium in the Green Bond Market? Systematic Literature Review Revealing Premium Determinants. J. Clean. Prod.
**2021**, 280, 124491. [Google Scholar] [CrossRef] - Banga, J. The Green Bond Market: A Potential Source of Climate Finance for Developing Countries. J. Sustain. Finance Investig.
**2019**, 9, 17–32. [Google Scholar] [CrossRef] - Basak, S.; Pavlova, A. A Model of Financialization of Commodities. J. Finance
**2016**, 71, 1511–1556. [Google Scholar] [CrossRef] - Acikgoz, T.; Alp, O.S.; Alkan, N.B. Dynamics of a Newly Established Agricultural Commodities Market: Financialization, Hedging and Portfolio Diversification in Turkey. Ann. Finance Econ.
**2023**, 18, 2350005. [Google Scholar] [CrossRef] - Tang, K.; Xiong, W. Index Investment and the Financialization of Commodities. Finance Anal. J.
**2012**, 68, 54–74. [Google Scholar] [CrossRef] - Nguyen, T.T.H.; Naeem, M.A.; Balli, F.; Balli, H.O.; Vo, X.V. Time-Frequency Comovement among Green Bonds, Stocks, Commodities, Clean Energy, and Conventional Bonds. Finance Res. Lett.
**2021**, 40, 101739. [Google Scholar] [CrossRef] - Arif, M.; Naeem, M.A.; Farid, S.; Nepal, R.; Jamasb, T. Diversifier or More? Hedge and Safe Haven Properties of Green Bonds during COVID-19. Energy Policy
**2022**, 168, 113102. [Google Scholar] [CrossRef] [PubMed] - Naeem, M.A.; Adekoya, O.B.; Oliyide, J.A. Asymmetric Spillovers between Green Bonds and Commodities. J. Clean. Prod.
**2021**, 314, 128100. [Google Scholar] [CrossRef] - Naeem, M.A.; Nguyen, T.T.H.; Nepal, R.; Ngo, Q.-T.; Taghizadeh–Hesary, F. Asymmetric Relationship between Green Bonds and Commodities: Evidence from Extreme Quantile Approach. Finance Res. Lett.
**2021**, 43, 101983. [Google Scholar] [CrossRef] - Tsagkanos, A.; Sharma, A.; Ghosh, B. Green Bonds and Commodities: A New Asymmetric Sustainable Relationship. Sustainability
**2022**, 14, 6852. [Google Scholar] [CrossRef] - Carter, C.A.; Rausser, G.C.; Smith, A. Commodity Booms and Busts. Annu. Rev. Resour. Econ.
**2011**, 3, 87–118. [Google Scholar] [CrossRef] - Acar, S.; Yeldan, E. Handbook of Green Economics; Academic Press: Cambridge, MA, USA, 2019; ISBN 0128166444. [Google Scholar]
- Reboredo, J.C. Green Bond and Financial Markets: Co-Movement, Diversification and Price Spillover Effects. Energy Econ.
**2018**, 74, 38–50. [Google Scholar] [CrossRef] - Reboredo, J.C.; Ugolini, A.; Aiube, F.A.L. Network Connectedness of Green Bonds and Asset Classes. Energy Econ.
**2020**, 86, 104629. [Google Scholar] [CrossRef] - Khamis, M.; Aassouli, D. The Eligibility of Green Bonds as Safe Haven Assets: A Systematic Review. Sustainability
**2023**, 15, 6841. [Google Scholar] [CrossRef] - Research Department, International Monetary Fund. World Economic Outlook, October 2020: A Long and Difficult Ascent; International Monetary Fund: Washington, DC, USA, 2020; ISBN 9781513556055. [Google Scholar]
- Mezghani, T.; Ben Hamadou, F.; Boujelbène-Abbes, M. Network Connectedness and Portfolio Hedging of Green Bonds, Stock Markets and Commodities. Int. J. Emerg. Mark. 2023; ahead-of-print. [Google Scholar] [CrossRef]
- Fama, E.F. Efficient Capital Markets: A Review of Theory and Empirical Work. J. Finance
**1970**, 25, 383–417. [Google Scholar] [CrossRef] - Peters, E.E. Fractal Market Analysis: Applying Chaos Theory to Investment and Economics; John Wiley & Sons: Hoboken, NJ, USA, 1994; Volume 24. [Google Scholar]
- Mandelbrot, B. The Variation of Certain Speculative Prices. J. Bus.
**1963**, 36, 394–419. [Google Scholar] [CrossRef] - Mandelbrot, B.B. A Multifractal Walk down Wall Street. Sci. Am.
**1999**, 280, 70–73. [Google Scholar] [CrossRef] - Mandelbrot, B.B.; Van Ness, J.W. Fractional Brownian Motions, Fractional Noises and Applications. SIAM Rev.
**1968**, 10, 422–437. [Google Scholar] [CrossRef] - Peng, C.-K.; Buldyrev, S.V.; Havlin, S.; Simons, M.; Stanley, H.E.; Goldberger, A.L. Mosaic Organization of DNA Nucleotides. Phys. Rev. E
**1994**, 49, 1685–1689. [Google Scholar] [CrossRef] - Kantelhardt, J.W.; Zschiegner, S.A.; Koscielny-Bunde, E.; Havlin, S.; Bunde, A.; Stanley, H.E. Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series. Phys. A Stat. Mech. Its Appl.
**2002**, 316, 87–114. [Google Scholar] [CrossRef] - Podobnik, B.; Stanley, H.E. Detrended Cross-Correlation Analysis: A New Method for Analyzing Two Nonstationary Time Series. Phys. Rev. Lett.
**2008**, 100, 84102. [Google Scholar] [CrossRef] [PubMed] - Zhou, W.-X. Multifractal Detrended Cross-Correlation Analysis for Two Nonstationary Signals. Phys. Rev. E
**2008**, 77, 66211. [Google Scholar] [CrossRef] [PubMed] - Pan, Y.; Hou, L.; Pan, X. Interplay between Stock Trading Volume, Policy, and Investor Sentiment: A Multifractal Approach. Phys. A Stat. Mech. Its Appl.
**2022**, 603, 127706. [Google Scholar] [CrossRef] - Li, X.; Su, F. The Dynamic Effects of COVID-19 and the March 2020 Crash on the Multifractality of NASDAQ Insurance Stock Markets. Fractal Fract.
**2023**, 7, 91. [Google Scholar] [CrossRef] - Fernandes, L.H.S.; Silva, J.W.L.; Quintino, D.D.; De Araujo, F.H.A.; Tabak, B.M. Multifractal Cross-Correlations Risk among WTI and Financial Assets. Fractals
**2022**, 30, 2250191. [Google Scholar] [CrossRef] - Shao, Y.-H.; Liu, Y.-L.; Yang, Y.-H. The Short-Term Effect of COVID-19 Pandemic on China’s Crude Oil Futures Market: A Study Based on Multifractal Analysis. Fluct. Noise Lett.
**2022**, 22, 2340001. [Google Scholar] [CrossRef] - Aslam, F.; Zil-E-Huma; Bibi, R.; Ferreira, P. The Nexus Between Twitter-Based Uncertainty and Cryptocurrencies: A Multifractal Analysis. Fractals
**2023**, 31, 2350027. [Google Scholar] [CrossRef] - Ruan, Q.; Meng, L.; Lv, D. Effect of Introducing Bitcoin Futures on the Underlying Bitcoin Market Efficiency: A Multifractal Analysis. Chaos Solitons Fractals
**2021**, 153, 111576. [Google Scholar] [CrossRef] - Ma, J.; Wang, T.; Zhao, R. Quantifying Cross-Correlations between Economic Policy Uncertainty and Bitcoin Market: Evidence from Multifractal Analysis. Discrete Dyn. Nat. Soc.
**2022**, 2022, 1072836. [Google Scholar] [CrossRef] - Ali, H.; Aslam, F.; Ferreira, P. Modeling Dynamic Multifractal Efficiency of US Electricity Market. Energies
**2021**, 14, 6145. [Google Scholar] [CrossRef] - Fu, Z.; Niu, H.; Wang, W. Market Efficiency and Cross-Correlations of Chinese New Energy Market with Other Assets: Evidence from Multifractality Analysis. Comput. Econ.
**2023**, 62, 1287–1311. [Google Scholar] [CrossRef] [PubMed] - Yang, W.; Ruan, Q.; Yin, L. Non-Linear Impact of Chinese Treasury Bond Futures on the Information Content of IRS. Fluct. Noise Lett.
**2021**, 20, 2150051. [Google Scholar] [CrossRef] - Wang, J.; Jiang, W.; Yan, Y.; Shao, W.; Wu, X.; Hua, Z. Exploring the Asymmetric Multifractal Characteristics of Price–Volume Cross-Correlation in the Chinese Rebar Futures Market Based on MF-ADCCA. Fluct. Noise Lett.
**2023**, 22, 2350029. [Google Scholar] [CrossRef] - Fernandes, L.H.S.; Silva, J.W.L.; de Araujo, F.H.A.; Tabak, B.M. Multifractal Cross-Correlations between Green Bonds and Financial Assets. Finance Res. Lett.
**2023**, 53, 103603. [Google Scholar] [CrossRef] - Shishlov, I.; Morel, R.; Cochran, I. Beyond Transparency: Unlocking the Full Potential of Grene Bonds. Inst. Clim. Change
**2016**, 2, 1–28. [Google Scholar] - Flaherty, M.; Gevorkyan, A.; Radpour, S.; Semmler, W. Financing Climate Policies through Climate Bonds—A Three Stage Model and Empirics. Res. Int. Bus. Finance
**2017**, 42, 468–479. [Google Scholar] [CrossRef] - Flammer, C. Corporate Green Bonds. J. Finance Econ.
**2021**, 142, 499–516. [Google Scholar] [CrossRef] - Guo, D.; Zhou, P. Green Bonds as Hedging Assets before and after COVID: A Comparative Study between the US and China. Energy Econ.
**2021**, 104, 105696. [Google Scholar] [CrossRef] - Jiang, Y.; Wang, J.; Ao, Z.; Wang, Y. The Relationship between Green Bonds and Conventional Financial Markets: Evidence from Quantile-on-Quantile and Quantile Coherence Approaches. Econ. Model.
**2022**, 116, 106038. [Google Scholar] [CrossRef] - Han, Y.; Li, J. Should Investors Include Green Bonds in Their Portfolios? Evidence for the USA and Europe. Int. Rev. Finance Anal.
**2022**, 80, 101998. [Google Scholar] [CrossRef] - Ren, B.; Lucey, B.; Luo, Q. An Examination of Green Bonds as a Hedge and Safe Haven for International Equity Markets. Glob. Finance J.
**2023**, 58, 100894. [Google Scholar] [CrossRef] - Tang, D.Y.; Zhang, Y. Do Shareholders Benefit from Green Bonds? J. Corp. Finance
**2020**, 61, 101427. [Google Scholar] [CrossRef] - Pham, L. Is It Risky to Go Green? A Volatility Analysis of the Green Bond Market. J. Sustain. Finance Investig.
**2016**, 6, 263–291. [Google Scholar] [CrossRef] - Gao, Y.; Li, Y.; Wang, Y. Risk Spillover and Network Connectedness Analysis of China’s Green Bond and Financial Markets: Evidence from Financial Events of 2015–2020. N. Am. J. Econ. Finance
**2021**, 57, 101386. [Google Scholar] [CrossRef] - Oświȩcimka, P.; Drożdż, S.; Forczek, M.; Jadach, S.; Kwapień, J. Detrended Cross-Correlation Analysis Consistently Extended to Multifractality. Phys. Rev. E
**2014**, 89, 23305. [Google Scholar] [CrossRef] - Kwapień, J.; Oświęcimka, P.; Drożdż, S. Detrended Fluctuation Analysis Made Flexible to Detect Range of Cross-Correlated Fluctuations. Phys. Rev. E
**2015**, 92, 52815. [Google Scholar] [CrossRef] - He, L.-Y.; Chen, S.-P. Nonlinear Bivariate Dependency of Price–Volume Relationships in Agricultural Commodity Futures Markets: A Perspective from Multifractal Detrended Cross-Correlation Analysis. Phys. A Stat. Mech. Its Appl.
**2011**, 390, 297–308. [Google Scholar] [CrossRef] - Li, Z.; Lu, X. Cross-Correlations between Agricultural Commodity Futures Markets in the US and China. Phys. A Stat. Mech. Its Appl.
**2012**, 391, 3930–3941. [Google Scholar] [CrossRef] - Cai, Y.; Lu, X.; Ren, Y.; Qu, L. Exploring the Dynamic Relationship between Crude Oil Price and Implied Volatility Indices: A MF-DCCA Approach. Phys. A Stat. Mech. Its Appl.
**2019**, 536, 120973. [Google Scholar] [CrossRef] - Charutha, S.; Gopal Krishna, M.; Manimaran, P. Multifractal Analysis of Indian Public Sector Enterprises. Phys. A Stat. Mech. Its Appl.
**2020**, 557, 124881. [Google Scholar] [CrossRef] - Zou, S.; Zhang, T. Multifractal Detrended Cross-Correlation Analysis of the Relation between Price and Volume in European Carbon Futures Markets. Phys. A Stat. Mech. Its Appl.
**2020**, 537, 122310. [Google Scholar] [CrossRef] - Fernandes, L.H.S.; Silva, J.W.L.; de Araujo, F.H.A.; Ferreira, P.; Aslam, F.; Tabak, B.M. Interplay Multifractal Dynamics among Metal Commodities and US-EPU. Phys. A Stat. Mech. Its Appl.
**2022**, 606, 128126. [Google Scholar] [CrossRef] - Telli, Ş.; Chen, H. Multifractal Behavior Relationship between Crypto Markets and Wikipedia-Reddit Online Platforms. Chaos Solitons Fractals
**2021**, 152, 111331. [Google Scholar] [CrossRef] - Zhuang, X.; Wei, Y.; Zhang, B. Multifractal Detrended Cross-Correlation Analysis of Carbon and Crude Oil Markets. Phys. A Stat. Mech. Its Appl.
**2014**, 399, 113–125. [Google Scholar] [CrossRef] - Podobnik, B.; Jiang, Z.-Q.; Zhou, W.-X.; Stanley, H.E. Statistical Tests for Power-Law Cross-Correlated Processes. Phys. Rev. E
**2011**, 84, 66118. [Google Scholar] [CrossRef] [PubMed] - Zebende, G.F. DCCA Cross-Correlation Coefficient: Quantifying Level of Cross-Correlation. Phys. A Stat. Mech. Its Appl.
**2011**, 390, 614–618. [Google Scholar] [CrossRef] - Zhang, S.; Guo, Y.; Cheng, H.; Zhang, H. Cross-Correlations between Price and Volume in China’s Crude Oil Futures Market: A Study Based on Multifractal Approaches. Chaos Solitons Fractals
**2021**, 144, 110642. [Google Scholar] [CrossRef] - Lin, Y.; Wang, R.; Gong, X.; Jia, G. Cross-Correlation and Forecast Impact of Public Attention on USD/CNY Exchange Rate: Evidence from Baidu Index. Phys. A Stat. Mech. Its Appl.
**2022**, 604, 127686. [Google Scholar] [CrossRef] - Ferreira, P.; Dionísio, A.; Movahed, S.M.S. Assessment of 48 Stock Markets Using Adaptive Multifractal Approach. Phys. A Stat. Mech. Its Appl.
**2017**, 486, 730–750. [Google Scholar] [CrossRef] - Saâdaoui, F. Testing for Multifractality of Islamic Stock Markets. Phys. A Stat. Mech. Its Appl.
**2018**, 496, 263–273. [Google Scholar] [CrossRef] - Matia, K.; Ashkenazy, Y.; Stanley, H.E. Multifractal Properties of Price Fluctuations of Stocks and Commodities. Europhys. Lett.
**2003**, 61, 422. [Google Scholar] [CrossRef] - Sadegh Movahed, M.; Jafari, G.R.; Ghasemi, F.; Rahvar, S.; Reza Rahimi Tabar, M. Multifractal Detrended Fluctuation Analysis of Sunspot Time Series. J. Stat. Mech. Theory Exp.
**2006**, 2006, P02003. [Google Scholar] [CrossRef] - Zhou, W.-X. The Components of Empirical Multifractality in Financial Returns. Europhys. Lett.
**2009**, 88, 28004. [Google Scholar] [CrossRef] - Ruan, Q.; Jiang, W.; Ma, G. Cross-Correlations between Price and Volume in Chinese Gold Markets. Phys. A Stat. Mech. Its Appl.
**2016**, 451, 10–22. [Google Scholar] [CrossRef] - Shen, N.; Chen, J.Y. Multifractal Analysis of the Impact of COVID-19 on NASDAQ, CIOPI, and WTI Crude Oil Market. Fluct. Noise Lett.
**2022**, 21, 2250041. [Google Scholar] [CrossRef]

**Figure 1.**The data graphs of (

**i**) level, (

**ii**) return, and (

**iii**) volatility series (1 November 2013–24 November 2023).

**Figure 2.**${\mathit{Q}}_{\mathit{c}\mathit{c}}\left(\mathit{m}\right)$ test results of return series.

**Figure 7.**Singularity strength ${\alpha}_{xy}\left(q\right)$ vs. multifractal spectrum $f\left({\alpha}_{xy}\right)$.

Agriculture | Livestock | Energy | Industrial_Metals | Precious_Metals | gbi | |
---|---|---|---|---|---|---|

Mean | 0.00 | 0.01 | −0.01 | 0.01 | 0.02 | 0.00 |

Median | −0.03 | 0.04 | 0.11 | 0.00 | 0.02 | 0.00 |

Min. | −5.25 | −6.23 | −30.18 | −4.11 | −5.43 | −2.41 |

Max. | 4.96 | 5.30 | 15.99 | 5.16 | 5.72 | 2.27 |

Std. Dev. | 1.10 | 1.06 | 2.33 | 1.09 | 0.98 | 0.37 |

Skewness | 0.00 | −0.30 | −1.30 | −0.03 | −0.12 | −0.16 |

Kurtosis | 1.82 | 2.33 | 19.84 | 1.12 | 3.76 | 4.35 |

# of Obs. | 2534 | 2534 | 2534 | 2534 | 2534 | 2534 |

Window Size | s = 16 | s = 32 | s = 64 | s = 126 | s = 256 | s = 512 | s = 1024 |
---|---|---|---|---|---|---|---|

gbi-agriculture | 0.57 | 0.57 | 0.56 | 0.53 | 0.53 | 0.61 | 0.68 |

gbi-livestock | 0.57 | 0.58 | 0.53 | 0.52 | 0.60 | 0.68 | 0.66 |

gbi-energy | 0.54 | 0.61 | 0.57 | 0.55 | 0.62 | 0.70 | 0.73 |

gbi-industrial_metals | 0.63 | 0.63 | 0.65 | 0.66 | 0.69 | 0.71 | 0.75 |

gbi-precious_metals | 0.69 | 0.71 | 0.71 | 0.66 | 0.70 | 0.72 | 0.79 |

Window Size | s = 16 | s = 32 | s = 64 | s = 126 | s = 256 | s = 512 | s = 1024 |
---|---|---|---|---|---|---|---|

gbi-agriculture | 0.39 | 0.41 | 0.45 | 0.41 | 0.28 | 0.54 | 0.71 |

gbi-livestock | 0.44 | 0.49 | 0.48 | 0.91 | 0.93 | 0.91 | 0.84 |

gbi-energy | 0.32 | 0.44 | 0.60 | 0.79 | 0.92 | 0.92 | 0.91 |

gbi-industrial_metals | 0.48 | 0.55 | 0.58 | 0.48 | 0.62 | 0.73 | 0.75 |

gbi-precious_metals | 0.48 | 0.61 | 0.52 | 0.87 | 0.92 | 0.65 | 0.85 |

Return Pairs | $\mathbf{Min}\left({\mathit{h}}_{\mathit{x}\mathit{y}}\right(\mathit{q}\left)\right)$ | $\mathbf{Max}\left({\mathit{h}}_{\mathit{x}\mathit{y}}\right(\mathit{q}\left)\right)$ | $\mathsf{\Delta}{\mathit{h}}_{\mathit{x}\mathit{y}}\left(\mathit{q}\right)$ | $\mathbf{Min}\left({\mathit{\alpha}}_{\mathit{x}\mathit{y}}\right(\mathit{q}\left)\right)$ | $\mathbf{Max}\left({\mathit{\alpha}}_{\mathit{x}\mathit{y}}\right(\mathit{q}\left)\right)$ | $\mathsf{\Delta}{\mathit{\alpha}}_{\mathit{x}\mathit{y}}\left(\mathit{q}\right)$ |
---|---|---|---|---|---|---|

gbi-agricultuıre | 0.4231 | 0.6390 | 0.2159 | 0.3381 | 0.6854 | 0.3472 |

gbi-livestock | 0.3892 | 0.7010 | 0.3118 | 0.2819 | 0.7498 | 0.4679 |

gbi-energy | 0.3733 | 0.8008 | 0.4275 | 0.2660 | 0.8684 | 0.6024 |

gbi-industrial_metals | 0.4405 | 0.7403 | 0.2998 | 0.3553 | 0.7867 | 0.4314 |

gbi-precious_metals | 0.3454 | 0.6936 | 0.3481 | 0.2502 | 0.7531 | 0.5029 |

Volatility Pairs | $\mathrm{min}\left({h}_{xy}\right(q\left)\right)$ | $\mathrm{max}\left({h}_{xy}\right(q\left)\right)$ | $\mathsf{\Delta}{h}_{xy}\left(q\right)$ | $\mathrm{min}\left({\alpha}_{xy}\right(q\left)\right)$ | $\mathrm{max}\left({\alpha}_{xy}\right(q\left)\right)$ | $\mathsf{\Delta}{\alpha}_{xy}\left(q\right)$ |

gbi-agricultuıre | 0.9024 | 1.5898 | 0.6874 | 0.8108 | 1.6699 | 0.8591 |

gbi-livestock | 0.7350 | 1.5741 | 0.8391 | 0.6301 | 1.6447 | 1.0147 |

gbi-energy | 0.7711 | 1.9267 | 1.1555 | 0.6652 | 2.0088 | 1.3436 |

gbi-industrial_metals | 0.9337 | 1.8406 | 0.9070 | 0.8201 | 1.9394 | 1.1193 |

gbi-precious_metals | 0.8630 | 1.8560 | 0.9930 | 0.7565 | 1.9317 | 1.1752 |

Return Pairs | Volatility Pairs | |||||
---|---|---|---|---|---|---|

$\mathsf{\Delta}{h}_{original}$ | $\mathsf{\Delta}{h}_{shuffled}$ | $\mathsf{\Delta}{h}_{surrogated}$ | $\mathsf{\Delta}{h}_{original}$ | $\mathsf{\Delta}{h}_{shuffled}$ | $\mathsf{\Delta}{h}_{surrogated}$ | |

gbi-agriculture | 0.2159 | 0.0852 | 0.0909 | 0.6874 | 0.1972 | 0.2647 |

gbi-livestock | 0.3118 | 0.1326 | 0.0759 | 0.8391 | 0.2516 | 0.3225 |

gbi-energy | 0.4275 | 0.1425 | 0.0602 | 1.1555 | 0.3017 | 0.2728 |

gbi-industrial_metals | 0.2998 | 0.0779 | 0.0339 | 0.9070 | 0.1982 | 0.2468 |

gbi-precious_metals | 0.3481 | 0.1846 | 0.0406 | 0.9930 | 0.1028 | 0.3589 |

$\mathsf{\Delta}{\alpha}_{original}$ | $\mathsf{\Delta}{\alpha}_{shuffled}$ | $\mathsf{\Delta}{\alpha}_{surrogated}$ | $\mathsf{\Delta}{\alpha}_{original}$ | $\mathsf{\Delta}{\alpha}_{shuffled}$ | $\mathsf{\Delta}{\alpha}_{surrogated}$ | |

gbi-agriculture | 0.3472 | 0.1537 | 0.1654 | 0.8591 | 0.3208 | 0.3988 |

gbi-livestock | 0.4679 | 0.2234 | 0.1462 | 1.0147 | 0.3630 | 0.4682 |

gbi-energy | 0.6024 | 0.2445 | 0.1225 | 1.3436 | 0.4343 | 0.4020 |

gbi-industrial_metals | 0.4314 | 0.1430 | 0.0955 | 1.1193 | 0.3114 | 0.3741 |

gbi-precious_metals | 0.5029 | 0.3030 | 0.0938 | 1.1752 | 0.1817 | 0.5136 |

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**MDPI and ACS Style**

Acikgoz, T.; Gokten, S.; Soylu, A.B.
Multifractal Detrended Cross-Correlations between Green Bonds and Commodity Markets: An Exploration of the Complex Connections between Green Finance and Commodities from the Econophysics Perspective. *Fractal Fract.* **2024**, *8*, 117.
https://doi.org/10.3390/fractalfract8020117

**AMA Style**

Acikgoz T, Gokten S, Soylu AB.
Multifractal Detrended Cross-Correlations between Green Bonds and Commodity Markets: An Exploration of the Complex Connections between Green Finance and Commodities from the Econophysics Perspective. *Fractal and Fractional*. 2024; 8(2):117.
https://doi.org/10.3390/fractalfract8020117

**Chicago/Turabian Style**

Acikgoz, Turker, Soner Gokten, and Abdullah Bugra Soylu.
2024. "Multifractal Detrended Cross-Correlations between Green Bonds and Commodity Markets: An Exploration of the Complex Connections between Green Finance and Commodities from the Econophysics Perspective" *Fractal and Fractional* 8, no. 2: 117.
https://doi.org/10.3390/fractalfract8020117