A Time-Varying Gerber Statistic: Application of a Novel Correlation Metric to Commodity Price Co-Movements †
Abstract
:1. Introduction
2. Materials and Methods
2.1. Dynamic Models
2.1.1. Historical Simulation
2.1.2. Conditional Auto-Regressive Multithreshold Logit Models
2.1.3. Dynamic Conditional Correlation Models
2.1.4. Filtered Historical Simulation
2.1.5. The Time-Varying Gerber Correlation
3. Empirical Analysis
3.1. Data Description
3.2. In-Sample Analysis
3.3. Out-of-Sample Analysis
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Selected Commodities | |
---|---|
Ticker | Description |
C1 Comdty | Generic 1st Corn No. 2 Yellow futures, US$ |
S1 Comdty | Generic 1st Soybean No. 2 Yellow futures, US$ |
W1 Comdty | Generic 1st Wheat futures, US$ |
CL1 Comdty | WTI crude oil |
NG1 Comdty | Natural Gas |
GC1 Comdty | Gold |
SI1 Comdty | Silver |
Remaining Agricultural Commodities | |
Ticker | Description |
KC1 Comdty | Generic 1st Coffee futures contract |
SB1 Comdty | Generic 1st Sugar No. 11 (raw) futures |
RR1 Comdty | Generic 1st Rice futures |
CC1 Comdty | Generic 1st Cocoa |
Remaining Energy Commodities | |
Ticker | Description |
CO1 Comdty | Brent Oil |
HO1 Comdty | Heating oil |
Remaining Metals | |
Ticker | Description |
HG1 Comdty | Copper |
Selected Commodities | |||||||
---|---|---|---|---|---|---|---|
C1 | S1 | W1 | CL1 | NG1 | GC1 | SI1 | |
Min. | −0.081 | −0.073 | −0.098 | −0.119 | −0.186 | −0.098 | −0.195 |
1st Qu | −0.008 | −0.007 | −0.010 | −0.010 | −0.015 | −0.004 | −0.007 |
Median | 0.000 | 0.000 | 0.000 | 0.000 | −0.001 | 0.001 | 0.001 |
Mean | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
3rd Qu | 0.009 | 0.007 | 0.010 | 0.010 | 0.014 | 0.006 | 0.009 |
Max. | 0.086 | 0.065 | 0.086 | 0.135 | 0.166 | 0.086 | 0.124 |
Std. Dev. | 0.016 | 0.013 | 0.018 | 0.020 | 0.026 | 0.011 | 0.019 |
Skewness | −0.043 | −0.252 | 0.034 | 0.030 | 0.141 | −0.475 | −0.916 |
Kurtosis | 5.411 | 5.818 | 5.033 | 7.013 | 5.862 | 10.335 | 11.132 |
JB stat. | 1214.252 | 1710.147 | 863.537 | 3360.445 | 1726.199 | 11,407.754 | 14,491.883 |
JB pval. | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Q1 | 652.816 | 667.872 | 577.179 | 765.575 | 796.927 | 777.274 | 846.418 |
Q5 | 961.155 | 1241.034 | 842.120 | 1436.187 | 1068.713 | 935.768 | 951.451 |
Q1 pval. | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Q5 pval. | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
LM1 | 5073.130 | 5761.032 | 4919.449 | 6467.057 | 4966.216 | 8230.659 | 7457.130 |
LM5 | 1567.114 | 1661.710 | 1531.263 | 1845.515 | 1577.667 | 2625.688 | 2431.796 |
LM1 pval. | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
LM5 pval. | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Remaining Agricultural Commodities | Remaining Energy Commodities | Remaining Metals | |||||
KC1 | SB1 | RR1 | CC1 | CO1 | HO1 | HG1 | |
Min. | −0.111 | −0.124 | −0.062 | −0.096 | −0.103 | −0.098 | −0.116 |
1st Qu | −0.010 | −0.009 | −0.007 | −0.009 | −0.009 | −0.009 | −0.007 |
Median | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Mean | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
3rd Qu | 0.010 | 0.009 | 0.007 | 0.009 | 0.009 | 0.009 | 0.008 |
Max. | 0.110 | 0.087 | 0.054 | 0.082 | 0.133 | 0.103 | 0.117 |
Std. Dev. | 0.017 | 0.018 | 0.012 | 0.016 | 0.019 | 0.017 | 0.016 |
Skewness | 0.047 | -0.313 | −0.003 | −0.210 | 0.047 | 0.064 | −0.043 |
Kurtosis | 5.104 | 6.087 | 4.298 | 5.472 | 7.267 | 6.115 | 7.703 |
JB stat. | 925.756 | 2071.051 | 351.917 | 1312.606 | 3800.539 | 2028.498 | 4615.341 |
JB pval. | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Q1 | 519.798 | 679.805 | 566.418 | 393.100 | 790.971 | 646.284 | 930.245 |
Q5 | 578.844 | 779.116 | 691.245 | 462.829 | 1514.100 | 1230.272 | 1894.352 |
Q1 pval. | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Q5 pval. | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
LM1 | 5203.071 | 5511.624 | 3811.809 | 6051.277 | 6428.943 | 5983.694 | 6486.196 |
LM5 | 1683.965 | 1809.333 | 1238.506 | 1962.049 | 1828.758 | 1717.633 | 1737.276 |
LM1 pval. | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
LM5 pval. | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
and | |||
---|---|---|---|
(GC1,CL1) | 3.245 | 1.229 | 1.152 |
(CL1,NG1) | 3.534 | 1.805 | 0.870 |
(GC1,SI1) | 0.461 | −0.512 | −0.270 |
(CL1,C1) | 3.689 | 1.979 | 1.120 |
(C1,W1) | 2.325 | 0.744 | −0.415 |
(C1,S1) | 0.220 | 0.294 | −3.201 |
and | |||
(GC1,CL1) | 1.553 | 2.827 | 1.149 |
(CL1,NG1) | 0.489 | 2.885 | −0.034 |
(GC1,SI1) | 1.818 | 0.064 | −0.125 |
(CL1,C1) | 3.418 | 4.242 | −0.373 |
(C1,W1) | 2.833 | 1.425 | −0.079 |
(C1,S1) | 0.526 | 0.873 | −2.625 |
and | |||
---|---|---|---|
NUM | 89 | 90 | 84 |
FREQ | 0.978 | 0.989 | 0.923 |
and | |||
NUM | 88 | 91 | 73 |
FREQ | 0.967 | 1.000 | 0.802 |
and | |||
NUM | 89 | 91 | 51 |
FREQ | 0.978 | 1.000 | 0.560 |
and | |||
NUM | 89 | 91 | 51 |
FREQ | 0.978 | 1.000 | 0.560 |
and | |||
---|---|---|---|
(GC1,CL1) | 3.280 | 2.568 | 2.125 |
(CL1,NG1) | 3.489 | 2.885 | 0.897 |
(GC1,SI1) | 1.270 | 0.064 | 0.970 |
(CL1,C1) | 3.418 | 4.242 | 1.373 |
(C1,W1) | 2.833 | 1.425 | 1.079 |
(C1,S1) | 1.896 | 2.843 | 0.297 |
and | |||
(GC1,CL1) | 1.297 | 2.272 | 0.791 |
(CL1,NG1) | 0.386 | 2.269 | −0.123 |
(GC1,SI1) | 1.192 | 0.164 | −0.070 |
(CL1,C1) | 2.942 | 3.722 | −0.373 |
(C1,W1) | 2.138 | 2.675 | −0.079 |
(C1,S1) | 0.397 | 0.973 | 0.059 |
and | |||
---|---|---|---|
NUM | 90 | 90 | 87 |
FREQ | 0.989 | 0.989 | 0.956 |
and | |||
NUM | 87 | 91 | 89 |
FREQ | 0.956 | 1.000 | 0.978 |
and | |||
NUM | 86 | 91 | 63 |
FREQ | 0.945 | 1.000 | 0.692 |
and | |||
NUM | 54 | 91 | 91 |
FREQ | 0.593 | 1.000 | 1.000 |
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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. https://doi.org/10.3390/forecast3020022
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(2):339-354. https://doi.org/10.3390/forecast3020022
Chicago/Turabian StyleAlgieri, Bernardina, Arturo Leccadito, and Pietro Toscano. 2021. "A Time-Varying Gerber Statistic: Application of a Novel Correlation Metric to Commodity Price Co-Movements" Forecasting 3, no. 2: 339-354. https://doi.org/10.3390/forecast3020022
APA StyleAlgieri, B., Leccadito, A., & Toscano, P. (2021). A Time-Varying Gerber Statistic: Application of a Novel Correlation Metric to Commodity Price Co-Movements. Forecasting, 3(2), 339-354. https://doi.org/10.3390/forecast3020022