# Exploring Dependence Relationships between Bitcoin and Commodity Returns: An Assessment Using the Gerber Cross-Correlation

^{1}

^{2}

^{3}

^{4}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The Gerber Statistic

#### 2.2. The Gerber Cross-Correlation

#### Inference Methods

## 3. Data and Empirical Results

#### 3.1. Data Description

#### 3.2. Rolling Window Estimation of Gerber Cross-Correlations

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Almeida, J.; Gonçalves, T.C. A Systematic Literature Review of Volatility and Risk Management on Cryptocurrency Investment: A Methodological Point of View. Risks
**2022**, 10, 107. [Google Scholar] [CrossRef] - Kristoufek, L. What Are the Main Drivers of the Bitcoin Price? Evidence from Wavelet Coherence Analysis. PLoS ONE
**2015**, 10, e0123923. [Google Scholar] - Kjærland, F.; Khazal, A.; Krogstad, E.A.; Nordstrøm, F.B.G.; Oust, A. An Analysis of Bitcoin’s Price Dynamics. J. Risk Financ. Manag.
**2018**, 11, 63. [Google Scholar] - Huynh, T.L.D.; Nasir, M.A.; Vo, X.V.; Nguyen, T.T. “Small things matter most”: The spillover effects in the cryptocurrency market and gold as a silver bullet. N. Am. J. Econ. Financ.
**2020**, 54, 101277. [Google Scholar] - Klein, T.; Pham Thu, H.; Walther, T. Bitcoin is not the New Gold—A comparison of volatility, correlation, and portfolio performance. Int. Rev. Financ. Anal.
**2018**, 59, 105–116. [Google Scholar] [CrossRef] - Wu, S. Co-movement and return spillover: Evidence from Bitcoin and traditional assets. SN Bus. Econ.
**2021**, 1, 1–16. [Google Scholar] [CrossRef] - Elsayed, A.H.; Gozgor, G.; Yarovaya, L. Volatility and return connectedness of cryptocurrency, gold, and uncertainty: Evidence from the cryptocurrency uncertainty indices. Financ. Res. Lett.
**2022**, 47, 102732. [Google Scholar] - Conrad, C.; Custovic, A.; Ghysels, E. Long- and Short-Term Cryptocurrency Volatility Components: A GARCH-MIDAS Analysis. J. Risk Financ. Manag.
**2018**, 11, 23. [Google Scholar] [CrossRef] - Dai, M.; Qamruzzaman, M.; Hamadelneel Adow, A. An Assessment of the Impact of Natural Resource Price and Global Economic Policy Uncertainty on Financial Asset Performance: Evidence From Bitcoin. Front. Environ. Sci.
**2022**, 10, 897496. [Google Scholar] [CrossRef] - Gerber, S.; Markowitz, H.; Ernst, P.A.; Miao, Y.; Javid, B.; Sargen, P. The Gerber Statistic: A Robust Co-Movement Measure for Portfolio Optimization. J. Portf. Manag.
**2022**, 48, 87–102. [Google Scholar] - Algieri, B.; Leccadito, A.; Toscano, P. A Time-Varying Gerber Statistic: Application of a Novel Correlation Metric to Commodity Price Co-Movements. Forecasting
**2021**, 3, 339–354. [Google Scholar] [CrossRef] - Zaremba, A.; Umar, Z.; Mikutowski, M. Commodity financialisation and price co-movement: Lessons from two centuries of evidence. Financ. Res. Lett.
**2021**, 38, 101492. [Google Scholar] [CrossRef] - Politis, D.N.; Romano, J.P. The Stationary Bootstrap. J. Am. Stat. Assoc.
**1994**, 89, 1303–1313. [Google Scholar] [CrossRef] - Patton, A.; Politis, D.N.; White, H. Correction to “Automatic Block-Length Selection for the Dependent Bootstrap” by D. Politis and H. White. Econom. Rev.
**2009**, 28, 372–375. [Google Scholar] [CrossRef] - Ameur, H.B.; Ftiti, Z.; Louhichi, W. Revisiting the relationship between spot and futures markets: Evidence from commodity markets and NARDL framework. Ann. Oper. Res.
**2022**, 313, 171–189. [Google Scholar] [CrossRef] - Algieri, B.; Leccadito, A. Assessing contagion risk from energy and non-energy commodity markets. Energy Econ.
**2017**, 62, 312–322. [Google Scholar] [CrossRef] - Algieri, B.; Leccadito, A. Ask CARL: Forecasting tail probabilities for energy commodities. Energy Econ.
**2019**, 84. [Google Scholar] [CrossRef] - Baur, D.G.; Dimpfl, T.; Kuck, K. Bitcoin, gold and the US dollar—A replication and extension. Financ. Res. Lett.
**2018**, 25, 103–110. [Google Scholar] [CrossRef] - Baur, D.G.; Hoang, L. The Bitcoin gold correlation puzzle. J. Behav. Exp. Financ.
**2021**, 32, 100561. [Google Scholar] [CrossRef] - Bouri, E.; Gupta, R.; Lahiani, A.; Shahbaz, M. Testing for asymmetric nonlinear short- and long-run relationships between bitcoin, aggregate commodity and gold prices. Resour. Policy
**2018**, 57, 224–235. [Google Scholar] [CrossRef] - Jareño, F.; de la O. González, M.; López, R.; Ramos, A.R. Cryptocurrencies and oil price shocks: A NARDL analysis in the COVID-19 pandemic. Resour. Policy
**2021**, 74, 102281. [Google Scholar] [CrossRef] - Aloui, R.; Aïssa, M.S.B.; Nguyen, D.K. Global financial crisis, extreme interdependences, and contagion effects: The role of economic structure? J. Bank. Financ.
**2011**, 35, 130–141. [Google Scholar] [CrossRef]

**Figure 1.**Whole Sample Gerber cross-correlations between Bitcoin (BTC) and each commodity. Note: Thresholds are ${H}_{i}={\sigma}_{i}/2$ where ${\sigma}_{i}$ are the (unconditional) return volatilities for $i=1,2$.

**Figure 2.**The 3-year trailing Gerber cross-correlations and 99% confidence bands, ${y}_{1}$ = BTC, ${y}_{2}$ = WTI. Note: Thresholds are ${H}_{i}={\sigma}_{i}/2$ where ${\sigma}_{i}$ are the (unconditional) return volatilities for $i=1,2$.

**Figure 3.**The 3-year trailing Gerber cross-correlations and 99% confidence bands, ${y}_{1}$ = WTI, ${y}_{2}$ = BTC. Note: Thresholds are ${H}_{i}={\sigma}_{i}/2$ where ${\sigma}_{i}$ are the (unconditional) return volatilities for $i=1,2$.

**Figure 4.**The 3-year trailing Gerber cross-correlations and 99% confidence bands, ${y}_{1}$ = BTC, ${y}_{2}$ = Platinum. Note: Thresholds are ${H}_{i}={\sigma}_{i}/2$ where ${\sigma}_{i}$ are the (unconditional) return volatilities for $i=1,2$.

**Figure 5.**The 3-year trailing Gerber cross-correlations and 99% confidence bands, ${y}_{1}$ = Platinum, ${y}_{2}$ = BTC. Note: Thresholds are ${H}_{i}={\sigma}_{i}/2$ where ${\sigma}_{i}$ are the (unconditional) return volatilities for $i=1,2$.

**Figure 6.**The 3-year trailing Gerber cross-correlations and 99% confidence bands, ${y}_{1}$ = BTC, ${y}_{2}$ = Wheat. Note: Thresholds are ${H}_{i}={\sigma}_{i}/2$ where ${\sigma}_{i}$ are the (unconditional) return volatilities for $i=1,2$.

**Figure 7.**The 3-year trailing Gerber cross-correlations and 99% confidence bands, ${y}_{1}$ = Wheat, ${y}_{2}$ = BTC. Note: Thresholds are ${H}_{i}={\sigma}_{i}/2$ where ${\sigma}_{i}$ are the (unconditional) return volatilities for $i=1,2$.

**Figure 8.**The 3-year trailing Gerber cross-correlations and 99% confidence bands, ${y}_{1}$ = BTC, ${y}_{2}$ = Gold. Note: Thresholds are ${H}_{i}={\sigma}_{i}/2$ where ${\sigma}_{i}$ are the (unconditional) return volatilities for $i=1,2$.

**Figure 9.**The 3-year trailing Gerber cross-correlations and 99% confidence bands, ${y}_{1}$ = Gold, ${y}_{2}$ = BTC. Note: Thresholds are ${H}_{i}={\sigma}_{i}/2$ where ${\sigma}_{i}$ are the (unconditional) return volatilities for $i=1,2$.

Selected Commodities | |
---|---|

Ticker | Description |

CL1 Comdty | Generic 1st Crude Oil WTI Futures |

PL1 Comdty | Generic 1st Platinum futures |

W1 Comdty | Generic 1st Wheat futures |

GC1 Comdty | Generic 1st Gold futures |

BTC | WTI | Platinum | Wheat | Gold | |
---|---|---|---|---|---|

Mean | 0.0015 | 0.0001 | −0.0002 | 0.0004 | 0.0002 |

Standard Deviation | 0.0422 | 0.0325 | 0.0168 | 0.0193 | 0.0093 |

Median | 0.0019 | 0.0013 | 0.0002 | −0.0002 | 0.0003 |

Minimum | −0.4647 | −0.3454 | −0.1231 | −0.1130 | −0.0511 |

Maximum | 0.2252 | 0.3196 | 0.1118 | 0.1970 | 0.0577 |

Standard Error | 0.0010 | 0.0007 | 0.0004 | 0.0004 | 0.0002 |

Skewness | −0.8523 | −0.7362 | −0.2743 | 0.5836 | −0.0783 |

Kurtosis | 14.0416 | 29.3225 | 7.9913 | 10.2708 | 7.2735 |

JB Stat | 10162.5935 | 56588.1481 | 2052.8205 | 4414.9624 | 1488.8657 |

JB pval | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |

${\mathit{y}}_{1}$ = BTC, ${\mathit{y}}_{2}$ = WTI | ${\mathit{y}}_{1}$ = BTC, ${\mathit{y}}_{2}$ = Platinum | ${\mathit{y}}_{1}$ = BTC, ${\mathit{y}}_{2}$ = Wheat | ${\mathit{y}}_{1}$ = BTC, ${\mathit{y}}_{2}$ = Gold | |||||

${\mathit{k}}_{\mathbf{max}}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ |

1 | 2.8590 | 0.4570 | 2.7277 | 0.5500 | 0.0083 | 0.9600 | 3.8789 | 0.5790 |

5 | 28.8201 | 0.4320 | 11.9621 | 0.9000 | 40.5485 | 0.7110 | 13.3090 | 0.9120 |

10 | 46.9309 | 0.6870 | 53.2732 | 0.9080 | 74.0836 | 0.8400 | 31.3360 | 0.9640 |

25 | 137.9548 | 0.9130 | 112.1169 | 0.9880 | 166.4217 | 0.9670 | 120.1614 | 0.9920 |

${\mathit{y}}_{\mathbf{1}}\mathbf{=}$WTI, ${\mathit{y}}_{\mathbf{2}}\mathbf{=}$BTC | ${\mathit{y}}_{\mathbf{1}}\mathbf{=}$Platinum, ${\mathit{y}}_{\mathbf{2}}\mathbf{=}$BTC | ${\mathit{y}}_{\mathbf{1}}\mathbf{=}$Wheat, ${\mathit{y}}_{\mathbf{2}}\mathbf{=}$BTC | ${\mathit{y}}_{\mathbf{1}}\mathbf{=}$Gold, ${\mathit{y}}_{\mathbf{2}}\mathbf{=}$BTC | |||||

${\mathit{k}}_{\mathbf{max}}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ |

1 | 20.2080 | 0.0410 | 8.6844 | 0.5050 | 3.4788 | 0.4300 | 0.3950 | 0.7700 |

5 | 43.5911 | 0.2180 | 26.5014 | 0.8040 | 15.2411 | 0.8270 | 12.5860 | 0.8540 |

10 | 85.0695 | 0.2350 | 44.3850 | 0.9250 | 31.5308 | 0.9300 | 28.6693 | 0.9560 |

25 | 108.5652 | 0.8880 | 66.4093 | 0.9980 | 97.5479 | 0.9880 | 97.3701 | 0.9930 |

${\mathit{y}}_{1}\mathbf{=}$ BTC${}^{2}$, ${\mathit{y}}_{2}\mathbf{=}$ WTI | ${\mathit{y}}_{1}\mathbf{=}$ BTC${}^{2}$, ${\mathit{y}}_{2}\mathbf{=}$ Platinum | ${\mathit{y}}_{1}\mathbf{=}$ BTC${}^{2}$, ${\mathit{y}}_{2}\mathbf{=}$ Wheat | ${\mathit{y}}_{1}\mathbf{=}$ BTC${}^{2}$, ${\mathit{y}}_{2}\mathbf{=}$ Gold | |||||

${\mathit{k}}_{\mathbf{max}}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ |

1 | 12.0200 | 0.5480 | 0.9370 | 0.7950 | 16.1488 | 0.3110 | 13.1282 | 0.3170 |

5 | 58.6704 | 0.7580 | 14.5683 | 0.9510 | 52.9512 | 0.6780 | 97.1572 | 0.3190 |

10 | 178.7206 | 0.7110 | 75.9803 | 0.8770 | 94.2911 | 0.8270 | 260.5584 | 0.1840 |

25 | 672.2332 | 0.8990 | 183.1941 | 0.9870 | 275.7607 | 0.9490 | 684.0197 | 0.2120 |

${\mathit{y}}_{\mathbf{1}}\mathbf{=}$WTI,${\mathit{y}}_{\mathbf{2}}\mathbf{=}$BTC${}^{\mathbf{2}}$ | ${\mathit{y}}_{\mathbf{1}}\mathbf{=}$Platinum,${\mathit{y}}_{\mathbf{2}}\mathbf{=}$BTC${}^{\mathbf{2}}$ | ${\mathit{y}}_{\mathbf{1}}\mathbf{=}$Wheat,${\mathit{y}}_{\mathbf{2}}\mathbf{=}$BTC${}^{\mathbf{2}}$ | ${\mathit{y}}_{\mathbf{1}}\mathbf{=}$Gold,${\mathit{y}}_{\mathbf{2}}\mathbf{=}$BTC${}^{\mathbf{2}}$ | |||||

${\mathit{k}}_{\mathbf{max}}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ |

1 | 4.2667 | 0.6090 | 19.5400 | 0.1990 | 0.1041 | 0.9280 | 1.0248 | 0.7990 |

5 | 72.4407 | 0.6180 | 71.6663 | 0.4770 | 25.2471 | 0.8870 | 72.1157 | 0.4660 |

10 | 229.8511 | 0.3820 | 152.8596 | 0.5500 | 63.1620 | 0.9220 | 191.9757 | 0.2990 |

25 | 506.2262 | 0.5990 | 295.6690 | 0.9330 | 339.1286 | 0.8870 | 510.9055 | 0.3830 |

${\mathit{y}}_{1}\mathbf{=}$BTC${}^{2}$,${\mathit{y}}_{2}\mathbf{=}$ WTI${}^{2}$ | ${\mathit{y}}_{1}\mathbf{=}$BTC${}^{2}$,${\mathit{y}}_{2}\mathbf{=}$ Platinum${}^{2}$ | ${\mathit{y}}_{1}\mathbf{=}$BTC${}^{2}$,${\mathit{y}}_{2}\mathbf{=}$ Wheat${}^{2}$ | ${\mathit{y}}_{1}\mathbf{=}$BTC${}^{2}$,${\mathit{y}}_{2}\mathbf{=}$ Gold${}^{2}$ | |||||

${\mathit{k}}_{\mathbf{max}}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ |

1 | 1.8448 | 0.2820 | 16.9378 | 0.0000 | 9.4301 | 0.0380 | 17.7234 | 0.0000 |

5 | 17.9767 | 0.2060 | 60.2868 | 0.0020 | 69.5256 | 0.0000 | 74.4307 | 0.0000 |

10 | 31.2844 | 0.2050 | 118.3702 | 0.0000 | 137.8887 | 0.0000 | 135.3187 | 0.0000 |

25 | 53.1649 | 0.2070 | 308.7823 | 0.0000 | 333.0107 | 0.0000 | 316.5219 | 0.0000 |

${\mathit{y}}_{\mathbf{1}}\mathbf{=}$WTI${}^{\mathbf{2}}$,${\mathit{y}}_{\mathbf{2}}\mathbf{=}$ BTC${}^{\mathbf{2}}$ | ${\mathit{y}}_{\mathbf{1}}\mathbf{=}$Platinum${}^{\mathbf{2}}$,${\mathit{y}}_{\mathbf{2}}\mathbf{=}$ BTC${}^{\mathbf{2}}$ | ${\mathit{y}}_{\mathbf{1}}\mathbf{=}$Wheat${}^{\mathbf{2}}$,${\mathit{y}}_{\mathbf{2}}\mathbf{=}$ BTC${}^{\mathbf{2}}$ | ${\mathit{y}}_{\mathbf{1}}\mathbf{=}$Gold${}^{\mathbf{2}}$,${\mathit{y}}_{\mathbf{2}}\mathbf{=}$ BTC${}^{\mathbf{2}}$ | |||||

${\mathit{k}}_{\mathbf{max}}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{Q}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ | $\widehat{\mathit{p}}\mathbf{\left(}{\mathit{k}}_{\mathbf{max}}\mathbf{\right)}$ |

1 | 3.0219 | 0.2290 | 9.8020 | 0.0430 | 9.9330 | 0.0470 | 14.4043 | 0.0000 |

5 | 23.6538 | 0.1600 | 71.9153 | 0.0000 | 72.8432 | 0.0010 | 73.0970 | 0.0000 |

10 | 44.6466 | 0.1700 | 144.1266 | 0.0000 | 138.5131 | 0.0010 | 134.3093 | 0.0000 |

25 | 104.3157 | 0.1820 | 326.3295 | 0.0030 | 348.7731 | 0.0020 | 308.8461 | 0.0000 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lawuobahsumo, K.K.; Algieri, B.; Iania, L.; Leccadito, A.
Exploring Dependence Relationships between Bitcoin and Commodity Returns: An Assessment Using the Gerber Cross-Correlation. *Commodities* **2022**, *1*, 34-49.
https://doi.org/10.3390/commodities1010004

**AMA Style**

Lawuobahsumo KK, Algieri B, Iania L, Leccadito A.
Exploring Dependence Relationships between Bitcoin and Commodity Returns: An Assessment Using the Gerber Cross-Correlation. *Commodities*. 2022; 1(1):34-49.
https://doi.org/10.3390/commodities1010004

**Chicago/Turabian Style**

Lawuobahsumo, Kokulo K., Bernardina Algieri, Leonardo Iania, and Arturo Leccadito.
2022. "Exploring Dependence Relationships between Bitcoin and Commodity Returns: An Assessment Using the Gerber Cross-Correlation" *Commodities* 1, no. 1: 34-49.
https://doi.org/10.3390/commodities1010004