A Comparison of the Risk Quantification in Traditional and Renewable Energy Markets
Abstract
:1. Introduction
2. Literature Review: Risk Quantification
3. Materials and Methods
3.1. Dynamics of VaR/ES with Mean and Variance Models
3.2. Risk Measures under Different Distributions
3.3. VaR Backtesting
3.4. ES Backtesting
3.4.1. Z1 Test
3.4.2. Z2 Test
3.4.3. ZES Test
3.4.4. Algorithm 1: Critical Values for ES Backtesting under Student’s t Distributions
Algorithm 1 |
1. Simulation of under normal, skew-normal, Student’s t, skewed -t, GED and SGED distributions, and M = 10,000 times. The value indicates the test (). |
2. Calculation of the statistics, using the data simulated in step 1. |
3. Estimation of critical values (cv) at 5%, . |
4. Resampling the critical values for the different skewness, degrees of freedom and shape parameters. |
4. Data
5. Empirical Results
5.1. Conditional Mean and Variance Models in Sample Estimations
5.2. Backtesting of 99%-VaR
5.3. Backtesting of 97.5%-VaR
5.4. Backtesting of 97.5%-ES
5.4.1. Z1 Test
5.4.2. Z2 Test
5.4.3. ZES Test
6. Discussion
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
Stock | Index | Description |
---|---|---|
EPISTAR | NEX | Epistar Corporation manufactures and markets light-emitting diode (LED) chips and epitaxial wafers. The Company sells its products in Taiwan and exports worldwide. |
Kingspan Group PLC | NEX | Kingspan Group PLC is a global market player in high-performance insulation and building envelope technologies. |
Boralex Inc. | NEX | Boralex Inc. is an electricity producer whose core business is the development and operation of renewable energy power stations. The Corporation operates assets in the following power generation types—wind, hydroelectric, thermal and solar-based in Canada, the Northeastern United States, and France. |
NIBE Industrier | NEX | NIBE Industrier AB is an international heating technology company. The Company is organized around three business areas, all united under a shared vision to create world-class solutions in sustainable energy. NIBE produces and sells heat pumps, boiler and water heaters, electrical heating elements as well as freestanding fireplaces. |
Exxon Mobil Corporation | BWEI | Exxon Mobil Corporation operates petroleum and petrochemical businesses on a worldwide basis. The Company operations include exploration and production of oil and gas, electric power generation, and coal and mineral operations. Exxon Mobil also manufactures and markets fuels, lubricants and chemicals. |
Chevron Corporation | BWEI | Chevron Corporation is an integrated energy company with operations in countries located around the world. The Company produces and transports crude oil and natural gas. Chevron also refines, markets, and distributes fuels, as well as is involved in chemical and mining operations, power generation and energy services. |
TOTAL S.A. | BWEI | TOTAL S.A. explores for, produces, refines, transports, and markets oil and natural gas. The Company also operates a chemical division that produces polypropylene, polyethylene, polystyrene, rubber, paint, ink, adhesives, and resins. TOTAL operates gasoline filling stations in Europe, the United States and Africa. |
Schlumberger Limited | BWEI | Schlumberger Limited is an oil services company. The Company, through its subsidiaries, provides a wide range of services, including technology, project management, and information solutions to the international petroleum industry as well as advanced acquisition and data processing surveys. |
NEX stands for WilderHill New Energy Global Innovation index, and BWEI stands for Bloomberg World Energy index. Source: Bloomberg LP. |
Appendix B. Tables and Figures
Epistar | Kingspan | Boralex | Nibe | Exxon | Chevron | Total | Schlumberger | |
---|---|---|---|---|---|---|---|---|
Coefficient | Normal Distribution | |||||||
μ | 0.0000 (0.001) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) |
ϕ | 0.0499 (0.019) | 0.0283 (0.020) | −0.0524 (0.019) | 0.0017 (0.020) | −0.0517 (0.019) | −0.0342 (0.019) | −0.0172 (0.019) | −0.0267 (0.019) |
ω | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) |
α | 0.0414 (0.007) | 0.0952 (0.017) | 0.0319 (0.004) | 0.0931 (0.014) | 0.0812 (0.010) | 0.0837 (0.010) | 0.0758 (0.010) | 0.0496 (0.006) |
β | 0.9433 (0.010) | 0.8894 (0.020) | 0.9659 (0.004) | 0.8652 (0.020) | 0.8989 (0.012) | 0.9012 (0.011) | 0.9074 (0.012) | 0.9428 (0.007) |
Skew-Normal Distribution | ||||||||
μ | 0.0001 (0.0005) | 0.0012 (0.0004) | 0.0007 (0.0003) | 0.0013 (0.0004) | 0.0004 (0.0002) | 0.0005 (0.0002) | 0.0004 (0.0003) | 0.0007 (0.0003) |
ϕ | 0.0531 (0.0197) | 0.0298 (0.0198) | −0.0593 (0.0192) | 0.0001 (0.0207) | −0.0611 (0.0198) | −0.0409 (0.0195) | −0.0219 (0.0196) | −0.0235 (0.0198) |
ω | 0.0000 (0.0000) | 0.0000 (0.0000) | 0.0000 (0.0000) | 0.0000 (0.0000) | 0.0000 (0.0000) | 0.0000 (0.0000) | 0.0000 (0.0000) | 0.0000 (0.0000) |
α | 0.0405 (0.0028) | 0.0485 (0.0182) | 0.0317 (0.0022) | 0.0862 (0.0142) | 0.0857 (0.0093) | 0.0866 (0.0111) | 0.0682 (0.0095) | 0.0507 (0.0076) |
β | 0.9435 (0.0050) | 0.9456 (0.0217) | 0.9663 (0.0020) | 0.8740 (0.0207) | 0.8945 (0.0123) | 0.8997 (0.0125) | 0.9184 (0.0119) | 0.9412 0.0089 |
ξ | 1.0119 (0.0235) | 1.0162 (0.0221) | 1.0032 (0.0194) | 1.0340 (0.0212) | 0.9062 (0.0211) | 0.8597 (0.0225) | 0.9295 (0.0216) | 0.9729 (0.0226) |
Student’s t Distribution | ||||||||
μ | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) |
ϕ | 0.0274 (0.019) | 0.0216 (0.018) | −0.0653 (0.018) | −0.0065 (0.0019) | −0.0524 (0.018) | −0.0352 (0.019) | −0.0196 (0.018) | −0.0285 (0.018) |
ω | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) |
α | 0.0500 (0.008) | 0.0446 (0.009) | 0.1131 (0.028) | 0.0883 (0.019) | 0.0831 (0.013) | 0.0805 (0.011) | 0.0689 (0.011) | 0.0478 (0.007) |
β | 0.9421 (0.010) | 0.9497 (0.010) | 0.8494 (0.039) | 0.8762 (0.026) | 0.9026 (0.014) | 0.9089 (0.011) | 0.9151 (0.014) | 0.9484 (0.007) |
8.7578 (1.529) | 5.2540 (0.498) | 5.8807 (0.298) | 5.2573 (0.488) | 6.6061 (0.766) | 10.000 (1.452) | 7.6678 (1.035) | 7.8742 (1.028) | |
Skewed-t Distribution | ||||||||
μ | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) |
ϕ | 0.0286 (0.019) | 0.0216 (0.018) | −0.0653 (0.018) | −0.0030 (0.019) | −0.0572 (0.019) | −0.0427 (0.019) | −0.0268 (0.018) | −0.0285 (0.018) |
ω | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) |
α | 0.0501 (0.008) | 0.0445 (0.009) | 0.1132 (0.027) | 0.0887 (0.018) | 0.0833 (0.012) | 0.0809 (0.011) | 0.0670 (0.011) | 0.0478 (0.007) |
β | 0.9421 (0.010) | 0.9497 (0.010) | 0.8491 (0.038) | 0.8762 (0.025) | 0.9018 (0.014) | 0.9093 (0.011) | 0.9172 (0.014) | 0.9484 (0.007) |
ν | 8.6184 (1.478) | 5.2529 (0.498) | 5.8799 (0.298) | 5.2686 (0.489) | 6.7975 (0.812) | 10.000 (1.422) | 7.6179 (1.031) | 7.8740 (1.028) |
λ | 1.0288 (0.025) | 0.9987 (0.025) | 1.0167 (0.024) | 1.0483 (0.027) | 0.9385 (0.024) | 0.882 (0.024) | 0.9253 (0.023) | 1.0003 (0.026) |
GED | ||||||||
μ | −0.0003 (0.000) | 0.0009 (0.000) | 0.0003 (0.000) | 0.0007 (0.000) | 0.0005 (0.000) | 0.0007 (0.000) | 0.0006 (0.000) | 0.0007 (0.000) |
ϕ | 0.0220 (0.019) | 0.0103 (0.019) | −0.0676 (0.015) | −0.0165 (0.019) | −0.0490 (0.019) | −0.0356 (0.019) | −0.023 (0.020) | −0.0283 (0.019) |
ω | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) |
α | 0.0444 (0.004) | 0.0431 (0.008) | 0.0394 (0.006) | 0.0760 (0.017) | 0.0851 (0.013) | 0.0852 (0.012) | 0.0676 (0.012) | 0.0501 (0.018) |
β | 0.9443 (0.006) | 0.9516 (0.009) | 0.9521 (0.007) | 0.8873 (0.027) | 0.8977 (0.015) | 0.9014 (0.014) | 0.9188 (0.015) | 0.9439 (0.021) |
η | 1.4626 (0.053) | 1.2959 (0.046) | 1.1214 (0.038) | 1.2557 (0.041) | 1.4437 (0.051) | 1.6629 (0.061) | 1.4599 (0.054) | 1.4819 (0.056) |
SGED | ||||||||
μ | −0.0001 (0.001) | 0.0010 (0.000) | 0.0005 (0.000) | 0.0010 (0.000) | 0.0003 (0.000) | 0.0005 (0.000) | 0.0004 (0.000) | 0.0006 (0.000) |
ϕ | 0.0224 (0.019) | 0.0111 (0.016) | −0.0695 (0.013) | −0.0124 (0.022) | −0.0601 (0.020) | −0.0429 (0.019) | −0.0287 (0.019) | −0.0290 (0.019) |
ω | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) |
α | 0.0446 (0.004) | 0.0436 (0.009) | 0.0394 (0.006) | 0.0777 (0.017) | 0.0850 (0.013) | 0.0846 (0.013) | 0.0649 (0.012) | 0.0500 (0.018) |
β | 0.9439 (0.006) | 0.9511 (0.010) | 0.9520 (0.007) | 0.8865 (0.026) | 0.8972 (0.015) | 0.9025 (0.015) | 0.9217 (0.016) | 0.9440 (0.021) |
η | 1.4597 (0.023) | 1.2970 (0.020) | 1.1220 (0.019) | 1.2533 (0.028) | 1.4618 (0.023) | 1.7051 (0.023) | 1.4639 (0.023) | 1.4834 (0.025) |
ζ | 1.0266 (0.053) | 1.0128 (0.046) | 1.019 (0.038)0 | 1.0576 (0.040) | 0.9339 (0.052) | 0.8713 (0.064) | 0.9331 (0.054) | 0.9920 (0.057) |
Epistar | Kingspan | Boralex | Nibe | Exxon | Chevron | Total | Schlumberger | |
---|---|---|---|---|---|---|---|---|
Coefficient | Normal Distribution | |||||||
μ | 0.0000 (0.0009) | 0.0000 (0.0004) | 0.0000 (0.0004) | 0.0000 (0.0003) | 0.0000 (0.0002) | 0.0000 (0.0002) | 0.0000 (0.0002) | 0.0000 (0.0003) |
ϕ | 0.055 (0.077) | 0.019 (0.020) | −0.052 (0.020) | −0.002 (0.003) | −0.051 (0.020) | −0.022 (0.011) | −0.007 (0.019) | −0.027 (0.019) |
ω | −2.025 (0.491) | −0.307 (0.061) | −0.390 (0.075) | −0.258 (0.027) | −0.213 (0.021) | −0.157 (0.035) | −0.335 (0.043) | −0.329 (0.045) |
α | −0.095 (0.022) | −0.042 (0.013) | −0.069 (0.011) | −0.060 (0.011) | −0.069 (0.011) | −0.078 (0.012) | −0.104 (0.005) | −0.060 (0.012) |
β | 0.712 (0.070) | 0.957 (0.008) | 0.948 (0.010) | 0.965 (0.004) | 0.975 (0.002) | 0.981 (0.004) | 0.959 (0.005) | 0.957 (0.006) |
γ | 0.278 (0.019) | 0.232 (0.026) | 0.188 (0.005) | 0.154 (0.038) | 0.177 (0.016) | 0.158 (0.041) | 0.160 (0.005) | 0.178 (0.020) |
Skew-Normal Distribution | ||||||||
μ | −0.0001 (0.0006) | 0.0007 (0.0003) | 0.0002 (0.0002) | 0.0011 (0.0004) | 0.0001 (0.0002) | 0.0002 (0.0003) | 0.0001 (0.0003) | 0.0003 (0.0003) |
ϕ | 0.0488 (0.0192) | 0.0219 (0.0172) | −0.0591 (0.0152) | −0.0085 (0.0196) | −0.0570 (0.0188) | −0.0232 (0.0189) | −0.0155 (0.0188) | −0.0225 (0.0191) |
ω | −0.1515 (0.0086) | −0.0308 (0.0005) | −0.0195 (0.0004) | −0.2447 (0.0089) | −0.2277 (0.0235) | −0.1516 (0.0328) | −0.1556 (0.0089) | −0.0828 (0.0011) |
α | −0.0324 (0.0079) | −0.0327 (0.0065) | −0.0456 (0.0047) | −0.0585 (0.0060) | −0.0700 (0.0111) | −0.0784 (0.0112) | −0.0803 (0.0107) | −0.0413 (0.0078) |
β | 0.9782 (0.0012) | 0.9955 (0.0001) | 0.9968 (0.0001) | 0.9667 (0.0013) | 0.9731 (0.0027) | 0.9820 (0.0039) | 0.9808 (0.0011) | 0.9890 (0.0002) |
γ | 0.0935 (0.0118) | 0.0770 (0.00275 | 0.0690 (0.0027) | 0.1481 (0.0156) | 0.1822 (0.0165) | 0.1561 (0.0423) | 0.1107 (0.0202) | 0.1008 (0.0036) |
ξ | 1.0226 (0.0240) | 1.0219 (0.0219) | 1.0123 (0.0193) | 1.0390 (0.0211) | 0.9006 (0.0212) | 0.8569 (0.0230) | 0.9351 (0.0219) | 0.9757 (0.0226) |
Student’s t Distribution | ||||||||
μ | 0.000 (0.001) | 0.000 (0.000) | 0.000 (0.000) | 0.000 (0.000) | 0.000 (0.000) | 0.000 (0.000) | 0.000 (0.000) | 0.000 (0.000) |
ϕ | 0.036 (0.020) | 0.023 (0.020) | −0.069 (0.019) | −0.007 (0.018) | −0.052 (0.018) | −0.027 (0.019) | −0.014 (0.020) | −0.025 (0.019) |
ω | −1.491 (0.341) | −0.562 (0.605) | −1.550 (0.534) | −0.311 (0.026) | −0.150 (0.013) | −0.138 (0.029) | −0.176 (0.002) | −0.068 (0.003) |
α | −0.095 (0.021) | −0.069 (0.029) | −0.038 (0.027) | −0.066 (0.015) | −0.063 (0.012) | −0.072 (0.013) | −0.083 (0.011) | −0.051 (0.009) |
β | 0.788 (0.049) | 0.925 (0.081) | 0.798 (0.070) | 0.959 (0.003) | 0.983 (0.002) | 0.984 (0.004) | 0.979 (0.000) | 0.991 (0.000) |
γ | 0.289 (0.019) | 0.290 (0.148) | 0.414 (0.035) | 0.174 (0.024) | 0.172 (0.020) | 0.150 (0.055) | 0.118 (0.009) | 0.104 (0.011) |
ν | 9.972 (2.372) | 5.947 (0.574) | 5.621 (0.242) | 5.344 (0.505) | 7.021 (0.898) | 13.361 (5.56) | 8.410 (1.176) | 8.356 (0.801) |
Skewed-t Distribution | ||||||||
μ | 0.000 (0.001) | 0.000 (0.000) | 0.000 (0.000) | 0.000 (0.000) | 0.000 (0.000) | 0.000 (0.000) | 0.000 (0.000) | 0.000 (0.000) |
ϕ | −0.008 (0.018) | 0.011 (0.018) | −0.070 (0.019) | −0.005 (0.023) | −0.057 (0.018) | −0.041 (0.019) | −0.027 (0.018) | −0.025 (0.015) |
ω | −0.117 (0.072) | −0.132 (0.075) | −1.574 (0.530) | −0.313 (0.026) | −0.150 (0.013) | −0.350 (0.093) | −0.365 (0.110) | −0.068 (0.002) |
α | −0.698 (0.116) | −0.558 (0.175) | −0.038 (0.027) | −0.066 (0.015) | −0.063 (0.012) | −1.083 (0.278) | −1.417 (0.200) | −0.051 (0.009) |
β | 0.935 (0.032) | 0.942 (0.028) | 0.795 (0.070) | 0.959 (0.003) | 0.983 (0.001) | 0.889 (0.027) | 0.888 (0.032) | 0.991 (0.000) |
γ | 2.410 (0.330) | 2.553 (0.517) | 0.416 (0.034) | 0.176 (0.024) | 0.171 (0.020) | 3.587 (0.145) | 2.464 (0.155) | 0.104 (0.011) |
ν | 4.010 (0.001) | 5.456 (0.000) | 5.613 (0.242) | 5.354 (0.506 | 7.229 (0.957) | 5.812 (0.001) | 4.513 (0.000) | 8.357 (0.808) |
λ | 1.034 (0.029) | 0.988 (0.023) | 1.011 (0.025) | 1.045 (0.027) | 0.935 (0.024) | 0.926 (0.028) | 0.945 (0.025) | 0.995 (0.026) |
GED | ||||||||
μ | −0.0005 (0.001) | 0.0007 (0.000) | 0.0002 (0.000) | 0.0004 (0.000) | 0.0003 (0.000) | 0.0003 (0.000) | 0.0003 (0.000) | 0.0004 (0.000) |
ϕ | 0.0191 (0.014) | 0.0073 (0.015) | −0.0685 (0.021) | −0.0180 (0.020) | −0.0477 (0.021) | −0.0232 (0.019) | −0.0215 (0.019) | −0.0245 (0.019) |
ω | −0.1301 (0.004) | −0.0371 (0.001) | −0.0612 (0.001) | −0.2399 (0.037) | −0.2105 (0.024) | −0.1526 (0.019) | −0.1609 (0.003) | −0.0761 (0.002) |
α | −0.0328 (0.009) | −0.0337 (0.008) | −0.0395 (0.009) | −0.0613 (0.014) | −0.0688 (0.014) | −0.0772 (0.012) | −0.0800 (0.010) | −0.0471 (0.009) |
β | 0.9816 (0.001) | 0.9952 (0.000) | 0.9922 (0.000) | 0.9684 (0.005) | 0.9759 (0.003) | 0.9823 (0.002) | 0.9807 (0.001) | 0.9903 (0.000) |
γ | 0.1035 (0.008) | 0.0796 (0.007) | 0.0924 (0.009) | 0.1409 (0.040) | 0.1804 (0.019) | 0.1570 (0.023) | 0.1144 (0.009) | 0.1016 (0.001) |
η | 1.4724 (0.057) | 1.3183 (0.046) | 1.1360 (0.037) | 1.2649 (0.041) | 1.4612 (0.054) | 1.7093 (0.068) | 1.5078 (0.055) | 1.4797 (0.051) |
SGED | ||||||||
μ | −0.0003 (0.001) | 0.0008 (0.000) | 0.0003 (0.000) | 0.0007 (0.000) | 0.0001 (0.000) | 0.0002 (0.000) | 0.0001 (0.000) | 0.0003 (0.000) |
ϕ | 0.0181 (0.020) | 0.0075 (0.016) | −0.0698 (0.013) | −0.0159 (0.019) | −0.0579 (0.019) | −0.0275 (0.019) | −0.0239 (0.019) | −0.0254 (0.019) |
ω | −0.1310 (0.004) | −0.0369 (0.001) | −0.0608 (0.001) | −0.2357 (0.030) | −0.2234 (0.042) | −0.1475 (0.028) | −0.1566 (0.001) | −0.0766 (0.002) |
α | −0.0332 (0.009) | −0.0335 (0.008) | −0.0390 (0.009) | −0.0593 (0.014) | −0.0712 (0.014) | −0.0764 (0.012) | −0.0794 (0.010) | −0.0470 (0.009) |
β | 0.9815 (0.001) | 0.9952 (0.000) | 0.9923 (0.000) | 0.9690 (0.004) | 0.9743 (0.005) | 0.9827 (0.003) | 0.9811 (0.000) | 0.9902 (0.000) |
γ | 0.1039 (0.008) | 0.0800 (0.007) | 0.0923 (0.009) | 0.1446 (0.033) | 0.1815 (0.021) | 0.1534 (0.038) | 0.1092 (0.007) | 0.1014 (0.001) |
η | 1.4707 (0.057) | 1.3192 (0.046) | 1.1362 (0.037) | 1.2652 (0.041) | 1.4805 (0.055) | 1.7464 (0.082) | 1.5056 (0.055) | 1.4806 (0.051) |
ζ | 1.0310 (0.024) | 1.0063 (0.020) | 1.0131 (0.019) | 1.0514 (0.026) | 0.9247 (0.022) | 0.8641 (0.024) | 0.9294 (0.022) | 0.9879 (0.025) |
Epistar | Kingspan | Boralex | Nibe | Exxon | Chevron | Total | Schlumberger | |
---|---|---|---|---|---|---|---|---|
Coefficient | Normal Distribution | |||||||
μ | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) |
ϕ | 0.0463 (0.018) | 0.0145 (0.014) | −0.0511 (0.019) | 0.0019 (0.019) | −0.0529 (0.020) | −0.0246 (0.020) | −0.0151 (0.016) | −0.0218 (0.19) |
ω | 0.0005 (0.000) | 0.0003 (0.000) | 0.0000 (0.000) | 0.0018 (0.000) | 0.0001 (0.000) | 0.0001 (0.000) | 0.0009 (0.000) | 0.0000 (0.000) |
α | 0.0498 (0.007) | 0.0361 (0.05) | 0.0307 (0.005) | 0.0844 (0.010) | 0.0881 (0.011) | 0.0802 (0.010) | 0.0653 (0.009) | 0.0500 (0.007) |
β | 0.9396 (0.010) | 0.9690 (0.003) | 0.9697 (0.003) | 0.9020 (0.013) | 0.8988 (0.011) | 0.9124 (0.009) | 0.9279 (0.011) | 0.9471 (0.006) |
γ | 0.3283 (0.094) | 0.4062 (0.150) | 0.4534 (0.108) | 0.4670 (0.106) | 0.3935 (0.076) | 0.5248 (0.097) | 0.8203 (0.112) | 0.3714 (0.098) |
δ | 1.0739 (0.263) | 0.7834 (0.253) | 1.6283 (0.232) | 0.7959 (0.159) | 1.3440 (0.214) | 1.2293 (0.202) | 0.8168 (0.167) | 1.4029 (0.226) |
Skew-Normal Distribution | ||||||||
μ | −0.0001 (0.0005) | 0.0007 (0.0003) | 0.0004 (0.0003) | 0.0011 (0.0002) | 0.0001 (0.0002) | 0.0002 (0.0002) | 0.0000 (0.0001) | 0.0004 (0.0003) |
ϕ | 0.0498 (0.0215) | 0.0206 (0.0130) | −0.0590 (0.0190) | −0.0029 (0.0038) | −0.0553 (0.0196) | −0.0262 (0.0195) | −0.0167 (0.0042) | −0.0188 (0.0194) |
ω | 0.0005 (0.0005) | 0.0002 (0.0000) | 0.0000 (0.0000) | 0.0018 (0.0012) | 0.0001 (0.0001) | 0.0001 (0.0001) | 0.0010 (0.0007) | 0.0001 (0.0001) |
α | 0.0495 (0.0103) | 0.0373 (0.0013) | 0.0305 (0.0020) | 0.0795 (0.0108) | 0.0947 (0.0114) | 0.0807 (0.0103) | 0.0544 (0.0155) | 0.0499 (0.0066) |
β | 0.9378 (0.0156) | 0.9675 (0.0003) | 0.9682 (0.0015) | 0.9062 (0.0132) | 0.8916 (0.0117) | 0.9118 (0.0100) | 0.9422 (0.0216) | 0.9474 (0.0061) |
γ | 0.3413 (0.1006) | 0.4763 (0.0991) | 0.4041 (0.0759) | 0.4901 (0.1130) | 0.3914 (0.0754) | 0.4775 (0.0945) | 0.9037 (0.1513) | 0.3765 (0.1012) |
δ | 1.0937 (0.2763) | 0.8959 (0.0482) | 1.7392 (0.0380) | 0.7835 (0.1661) | 1.3313 (0.2018) | 1.2970 (0.1934) | 0.7297 (0.2298) | 1.3378 (0.2035) |
ξ | 1.0235 (0.0239) | 1.0258 (0.0220) | 1.0135 (0.0198) | 1.0402 (0.0215) | 0.8990 (0.0212) | 0.8575 (0.0225) | 0.9351 (0.0219) | 0.9732 (0.0226) |
Student’s t Distribution | ||||||||
μ | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) |
ϕ | 0.0240 (0.019) | 0.0169 (0.019) | −0.0660 (0.018) | −0.0056 (0.017) | −0.0516 (0.018) | −0.0295 (0.019) | −0.0196 (0.020) | −0.0228 (0.018) |
ω | 0.0003 (0.000) | 0.0002 (0.000) | 0.0001 (0.000) | 0.0011 (0.000) | 0.0001 (0.000) | 0.0001 (0.000) | 0.0010 (0.000) | 0.0001 (0.000) |
α | 0.0599 (0.009) | 0.0440 (0.008) | 0.1036 (0.029) | 0.0842 (0.014) | 0.0940 (0.014) | 0.0764 (0.011) | 0.0629 (0.009) | 0.0514 (0.008) |
β | 0.9374 (0.010) | 0.9611 (0.006) | 0.8826 (0.037) | 0.9087 (0.016) | 0.8995 (0.013) | 0.9190 (0.010) | 0.9309 (0.012) | 0.9494 (0.007) |
γ | 0.2804 (0.090) | 0.4878 (0.140) | 0.1524 (0.073) | 0.4344 (0.112) | 0.3965 (0.089) | 0.4985 (0.108) | 0.8705 (0.115) | 0.4807 (0.115) |
δ | 1.1112 (0.253) | 0.9558 (0.173) | 1.6047 (0.266) | 0.8777 (0.182) | 1.2454 (0.235) | 1.2586 (0.227) | 0.7786 (0.180) | 1.2967 (0.230) |
ν | 8.9644 (0.1609) | 5.4858 (0.534) | 5.9731 (0.315) | 5.3611 (0.500) | 7.0192 (0.854) | 10.000 1.381 | 8.5843 (1.272) | 8.1418 (1.068) |
Skewed-t Distribution | ||||||||
μ | 0.0000 (0.001) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) | 0.0000 (0.000) |
ϕ | 0.0247 (0.020) | 0.0170 (0.019) | −0.0663 (0.018) | −0.0042 (0.018) | −0.0547 (0.020) | −0.0335 (0.019) | −0.0226 (0.014) | −0.0227 (0.018) |
ω | 0.0003 (0.000) | 0.0002 (0.000) | 0.0001 (0.000) | 0.0010 (0.000) | 0.0001 (0.000) | 0.0001 (0.000) | 0.0010 (0.000) | 0.0001 (0.000) |
α | 0.0604 (0.009) | 0.0440 (0.008) | 0.1040 (0.029) | 0.0850 (0.014) | 0.0939 (0.014) | 0.0759 (0.011) | 0.0613 (0.009) | 0.0514 (0.008) |
β | 0.9369 (0.011) | 0.9611 (0.006) | 0.8819 (0.037) | 0.9084 (0.016) | 0.8985 (0.013) | 0.9200 (0.010) | 0.9324 (0.012) | 0.9494 (0.007) |
γ | 0.2915 (0.091) | 0.4885 (0.141) | 0.1508 (0.074) | 0.4317 (0.112) | 0.3997 (0.089) | 0.4903 (0.108) | 0.8812 (0.116) | 0.4808 (0.116) |
δ | 1.0959 (0.251) | 0.9560 (0.173) | 1.6053 (0.266) | 0.8782 (0.183) | 1.2520 (0.233) | 1.2570 (0.219) | 0.7915 (0.183) | 1.2972 (0.231) |
ν | 8.8193 (1.553) | 5.4835 (0.534) | 5.9717 (0.315) | 5.3631 (0.500) | 7.2550 (0.914) | 10.0000 (1.352) | 8.4353 (1.239) | 8.1419 (1.068) |
λ | 1.0373 (0.026) | 0.9979 (0.025) | 1.0150 (0.024) | 1.0496 (0.028) | 0.9347 (0.024) | 0.8833 (0.025) | 0.9256 (0.023) | 1.0023 (0.026) |
GED | ||||||||
μ | −0.0005 (0.000) | 0.0007 (0.000) | 0.0002 (0.000) | 0.0004 (0.000) | 0.0003 (0.000) | 0.0004 (0.000) | 0.0002 (0.000) | 0.0004 (0.000) |
ϕ | 0.0192 (0.015) | 0.0069 (0.018) | −0.0684 (0.017) | −0.0151 (0.020) | −0.0483 (0.019) | −0.0270 (0.020) | −0.0245 (0.005) | −0.0232 (0.019) |
ω | 0.0005 (0.000) | 0.0001 (0.000) | 0.0000 (0.000) | 0.0010 (0.001) | 0.0001 (0.000) | 0.0001 (0.000) | 0.0011 (0.002) | 0.0001 (0.000) |
α | 0.0550 (0.013) | 0.0386 (0.002) | 0.0412 (0.010) | 0.0770 (0.014) | 0.0933 (0.013) | 0.0807 (0.011) | 0.0551 (0.043) | 0.0505 (0.007) |
β | 0.9378 (0.018) | 0.9657 (0.000) | 0.9536 (0.003) | 0.9094 (0.018) | 0.8958 (0.013) | 0.9116 (0.011) | 0.9416 (0.060) | 0.9488 (0.006) |
γ | 0.3166 (0.104) | 0.4740 (0.124) | 0.2562 (0.067) | 0.4785 (0.132) | 0.3864 (0.088) | 0.4722 (0.102) | 0.8899 (0.355) | 0.4355 (0.116) |
δ | 1.0750 (0.289) | 0.9619 (0.060) | 1.7863 (0.045) | 0.9253 (0.210) | 1.3296 (0.232) | 1.2952 (0.218) | 0.7131 (0.607) | 1.2793 (0.223) |
η | 1.4721 (0.059) | 1.3237 (0.046) | 1.1369 (0.038) | 1.2715 (0.041) | 1.4668 (0.052) | 1.7166 (0.064) | 1.5221 (0.056) | 1.4899 (0.052) |
SGED | ||||||||
μ | −0.0003 (0.001) | 0.0008 (0.000) | 0.0003 (0.000) | 0.0007 (0.000) | 0.0001 (0.000) | 0.0002 (0.000) | 0.0001 (0.000) | 0.0004 (0.000) |
ϕ | 0.0184 (0.020) | 0.0075 (0.018) | −0.0704 (0.017) | −0.0130 (0.010) | −0.0565 (0.020) | −0.0303 (0.020) | −0.0258(0.006) | −0.0241 (0.019) |
ω | 0.0005 (0.000) | 0.0001 (0.000) | 0.0000 (0.000) | 0.0010 (0.001) | 0.0001 (0.000) | 0.0001 (0.000) | 0.0011 (0.001) | 0.0001 (0.000) |
α | 0.0552 (0.014) | 0.0388 (0.002) | 0.0409 (0.018) | 0.0785 (0.014) | 0.0946 (0.014) | 0.0794 (0.011) | 0.0532 (0.003) | 0.0504 (0.007) |
β | 0.9373 (0.019) | 0.9656 (0.000) | 0.9537 (0.002) | 0.9088 (0.017) | 0.8936 (0.013) | 0.9133 (0.011) | 0.9438 (0.003) | 0.9488 (0.006) |
γ | 0.3225 (0.105) | 0.4689 (0.124) | 0.2533 (0.011) | 0.4546 (0.124) | 0.3995 (0.088) | 0.4713 (0.101) | 0.9123 (0.024) | 0.4366 (0.116) |
δ | 1.0626 (0.289) | 0.9603 (0.060) | 1.7912 (0.109) | 0.9259 (0.178) | 1.3185 (0.234) | 1.3070 (0.209) | 0.7026 (0.129) | 1.2759 (0.223) |
η | 1.4705 (0.059) | 1.3252 (0.046) | 1.1374 (0.038) | 1.2718 (0.041) | 1.4876 (0.053) | 1.7570 (0.067) | 1.5176 (0.056) | 1.4911 (0.052) |
ζ | 1.0316 (0.024) | 1.0082 (0.021) | 1.0160 (0.023) | 1.0526 (0.024) | 0.9239 (0.023) | 0.8652 (0.023) | 0.9278 (0.022) | 0.9878 (0.024) |
Normal Distribution | |||||||||
---|---|---|---|---|---|---|---|---|---|
AR(1)-GARCH(1,1) | AR(1)-EGARCH(1,1) | AR(1)-APARCH(1,1) | |||||||
KS test | Skewness | Kurtosis | KS test | Skewness | Kurtosis | KS test | Skewness | Kurtosis | |
Epistar | 0.34974 | −0.02509 | 3.56091 | 0.58578 | 0.01060 | 3.51367 | 0.56405 | 0.01369 | 3.52055 |
Kingspan | 0.00001 | −0.02622 | 5.97671 | 0.00013 | 0.04630 | 5.45896 | 0.00011 | 0.05806 | 5.42608 |
Boralex | 0.00644 | −0.10020 | 6.77246 | 0.01180 | 0.01380 | 6.06245 | 0.00768 | 0.01185 | 6.06490 |
Nibe | 0.00128 | 0.02981 | 8.25770 | 0.00157 | 0.09467 | 8.13498 | 0.00085 | 0.09749 | 7.76289 |
Exxon Mobil | 0.00001 | −0.32429 | 4.45371 | 0.00017 | −0.33825 | 4.47172 | 0.00015 | −0.33922 | 4.43026 |
Chevron | 0.00001 | −0.35244 | 3.87062 | 0.00003 | −0.34835 | 3.76999 | 0.00003 | −0.34522 | 3.73576 |
Total S.A | 0.00095 | −0.19559 | 4.09768 | 0.00914 | −0.15077 | 3.87862 | 0.01180 | −0.14697 | 3.83074 |
Schlumberger | 0.00077 | −0.14672 | 4.84447 | 0.00281 | −0.13005 | 5.28481 | 0.00157 | −0.15377 | 5.20671 |
Skew-Normal Distribution | |||||||||
AR(1)-GARCH(1,1) | AR(1)-EGARCH(1,1) | AR(1)-APARCH(1,1) | |||||||
KS test | Skewness | Kurtosis | KS test | Skewness | Kurtosis | KS test | Skewness | Kurtosis | |
Epistar | 0.34974 | −0.02473 | 3.55932 | 0.54257 | 0.01167 | 3.51233 | 0.52138 | 0.01507 | 3.51885 |
Kingspan | 0.00001 | −0.02368 | 5.96416 | 0.00009 | 0.04878 | 5.45697 | 0.00009 | 0.06210 | 5.42004 |
Boralex | 0.00492 | −0.09972 | 6.76391 | 0.01085 | 0.01532 | 6.05871 | 0.00704 | 0.01297 | 6.05604 |
Nibe | 0.00069 | 0.03401 | 8.26214 | 0.00095 | 0.10223 | 8.14003 | 0.00045 | 0.10469 | 7.75844 |
Exxon Mobil | 0.00002 | −0.32679 | 4.45798 | 0.00026 | −0.34130 | 4.47621 | 0.00029 | −0.34287 | 4.43726 |
Chevron | 0.00001 | −0.35726 | 3.88138 | 0.00005 | −0.35196 | 3.78288 | 0.00004 | −0.34844 | 3.74654 |
Total S.A | 0.00128 | −0.19884 | 4.10454 | 0.01515 | −0.15259 | 3.88038 | 0.01180 | −0.14812 | 3.83148 |
Schlumberger | 0.00095 | −0.14735 | 4.84126 | 0.00309 | −0.13118 | 5.27491 | 0.00191 | −0.15441 | 5.19833 |
Student’s t Distribution | |||||||||
AR(1)-GARCH(1,1) | AR(1)-EGARCH(1,1) | AR(1)-APARCH(1,1) | |||||||
KS test | Skewness | Kurtosis | KS test | Skewness | Kurtosis | KS test | Skewness | Kurtosis | |
Epistar | 0.56405 | −0.03986 | 3.70186 | 0.78183 | 0.00493 | 3.63943 | 0.73966 | 0.00840 | 3.64400 |
Kingspan | 0.00007 | −0.03756 | 6.03803 | 0.00033 | 0.06306 | 5.46181 | 0.00037 | 0.07129 | 5.44417 |
Boralex | 0.07290 | −0.19773 | 9.38079 | 0.05533 | −0.11641 | 7.51664 | 0.07797 | −0.10244 | 8.02954 |
Nibe | 0.01284 | 0.04234 | 8.33048 | 0.03583 | 0.12275 | 8.24616 | 0.02645 | 0.12479 | 7.96779 |
Exxon Mobil | 0.00000 | −0.32580 | 4.48021 | 0.00003 | −0.33700 | 4.48218 | 0.00002 | −0.33900 | 4.45428 |
Chevron | 0.00000 | −0.35661 | 3.88572 | 0.00001 | −0.35261 | 3.78892 | 0.00001 | −0.34927 | 3.75188 |
Total S.A | 0.00077 | −0.19871 | 4.10470 | 0.00492 | −0.15234 | 3.88005 | 0.00538 | −0.14787 | 3.83225 |
Schlumberger | 0.00041 | −0.13753 | 4.89148 | 0.00173 | −0.11563 | 5.50872 | 0.00142 | −0.14305 | 5.42437 |
Skewed-t Distribution | |||||||||
AR(1)-GARCH(1,1) | AR(1)-EGARCH(1,1) | AR(1)-APARCH(1,1) | |||||||
KS test | Skewness | Kurtosis | KS test | Skewness | Kurtosis | KS test | Skewness | Kurtosis | |
Epistar | 0.34974 | −0.03887 | 3.69955 | 0.60772 | 0.00666 | 3.63809 | 0.58578 | 0.01031 | 3.64268 |
Kingspan | 0.00003 | −0.03578 | 6.02867 | 0.00021 | 0.06330 | 5.46192 | 0.00023 | 0.07161 | 5.44377 |
Boralex | 0.02264 | −0.19364 | 9.33015 | 0.03325 | −0.11992 | 7.56109 | 0.04153 | −0.10409 | 8.04632 |
Nibe | 0.00173 | 0.04592 | 8.33099 | 0.00538 | 0.12563 | 8.23526 | 0.00340 | 0.12700 | 7.95628 |
Exxon Mobil | 0.00002 | −0.32652 | 4.48299 | 0.00011 | −0.33788 | 4.48242 | 0.00012 | −0.34041 | 4.45491 |
Chevron | 0.00001 | −0.35987 | 3.89653 | 0.00004 | −0.35530 | 3.79812 | 0.00002 | −0.35118 | 3.75814 |
Total S.A | 0.00173 | −0.20179 | 4.11535 | 0.01932 | −0.15329 | 3.88020 | 0.01515 | −0.14829 | 3.83103 |
Schlumberger | 0.00041 | −0.13768 | 4.89171 | 0.00173 | −0.11566 | 5.50729 | 0.00142 | −0.14302 | 5.42275 |
GED | |||||||||
AR(1)-GARCH(1,1) | AR(1)-EGARCH(1,1) | AR(1)-APARCH(1,1) | |||||||
KS test | Skewness | Kurtosis | KS test | Skewness | Kurtosis | KS test | Skewness | Kurtosis | |
Epistar | 0.71801 | −0.03908 | 3.65905 | 0.62978 | 0.00483 | 3.60380 | 0.62978 | 0.00927 | 3.60931 |
Kingspan | 0.00002 | −0.03973 | 6.04344 | 0.00011 | 0.05276 | 5.46952 | 0.00011 | 0.06141 | 5.44694 |
Boralex | 0.01782 | −0.12891 | 7.32284 | 0.01395 | −0.04801 | 6.60500 | 0.00838 | −0.02864 | 6.57144 |
Nibe | 0.01395 | 0.03481 | 8.26940 | 0.03325 | 0.10989 | 8.18071 | 0.02857 | 0.11132 | 7.89423 |
Exxon Mobil | 0.00000 | −0.32378 | 4.46475 | 0.00006 | −0.33762 | 4.47545 | 0.00004 | −0.33892 | 4.44059 |
Chevron | 0.00000 | −0.35507 | 3.87463 | 0.00001 | −0.35064 | 3.77825 | 0.00001 | −0.34756 | 3.74339 |
Total S.A | 0.00037 | −0.19835 | 4.09900 | 0.00309 | −0.15231 | 3.87994 | 0.00492 | −0.14817 | 3.83287 |
Schlumberger | 0.00062 | −0.14245 | 4.86641 | 0.00173 | −0.12185 | 5.39927 | 0.00128 | −0.14757 | 5.31753 |
SGED | |||||||||
AR(1)-GARCH(1,1) | AR(1)-EGARCH(1,1) | AR(1)-APARCH(1,1) | |||||||
KS test | Skewness | Kurtosis | KS test | Skewness | Kurtosis | KS test | Skewness | Kurtosis | |
Epistar | 0.50054 | −0.03816 | 3.65581 | 0.60772 | 0.00624 | 3.60313 | 0.56405 | 0.01103 | 3.60817 |
Kingspan | 0.00001 | −0.03759 | 6.03233 | 0.00008 | 0.05335 | 5.46925 | 0.00007 | 0.06230 | 5.44584 |
Boralex | 0.00838 | −0.12663 | 7.30907 | 0.00644 | −0.04804 | 6.60818 | 0.00538 | −0.02765 | 6.56856 |
Nibe | 0.00142 | 0.03907 | 8.27474 | 0.00644 | 0.11483 | 8.17757 | 0.00538 | 0.11561 | 7.89235 |
Exxon Mobil | 0.00003 | −0.32639 | 4.46975 | 0.00023 | −0.33964 | 4.47782 | 0.00017 | −0.34140 | 4.44407 |
Chevron | 0.00001 | −0.35879 | 3.88791 | 0.00005 | −0.35397 | 3.79038 | 0.00003 | −0.35002 | 3.75210 |
Total S.A | 0.00142 | −0.20169 | 4.11009 | 0.01395 | −0.15356 | 3.88053 | 0.01515 | −0.14836 | 3.83142 |
Schlumberger | 0.00085 | −0.14257 | 4.86469 | 0.00173 | −0.12218 | 5.39494 | 0.00157 | −0.14773 | 5.31342 |
Normal Distribution | ||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
AR(1)-GARCH(1,1) | AR(1)-EGARCH(1,1) | AR(1)-APARCH(1,1) | ||||||||||||||||||||||
m | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | Kingspan | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger |
1 | 0.75 | 0.57 | 0.66 | 0.60 | 0.64 | 0.97 | 0.66 | 0.66 | 0.63 | 0.65 | 0.85 | 0.60 | 0.90 | 0.52 | 0.96 | 0.68 | 0.64 | 0.61 | 0.93 | 0.75 | 0.73 | 0.65 | 0.98 | 0.74 |
2 | 0.94 | 0.68 | 0.90 | 0.79 | 0.86 | 0.40 | 0.85 | 0.50 | 0.89 | 0.61 | 0.97 | 0.81 | 0.99 | 0.50 | 0.97 | 0.55 | 0.90 | 0.59 | 1.00 | 0.88 | 0.92 | 0.52 | 0.97 | 0.54 |
3 | 0.93 | 0.78 | 0.97 | 0.63 | 0.59 | 0.46 | 0.85 | 0.20 | 0.89 | 0.73 | 0.99 | 0.65 | 0.71 | 0.63 | 0.89 | 0.21 | 0.90 | 0.70 | 1.00 | 0.74 | 0.61 | 0.62 | 0.87 | 0.18 |
4 | 0.58 | 0.31 | 0.99 | 0.27 | 0.71 | 0.58 | 0.92 | 0.29 | 0.57 | 0.35 | 1.00 | 0.27 | 0.81 | 0.73 | 0.96 | 0.28 | 0.58 | 0.36 | 1.00 | 0.31 | 0.71 | 0.71 | 0.95 | 0.26 |
5 | 0.71 | 0.10 | 0.48 | 0.31 | 0.44 | 0.67 | 0.97 | 0.30 | 0.70 | 0.10 | 0.53 | 0.33 | 0.64 | 0.84 | 0.98 | 0.35 | 0.71 | 0.10 | 0.52 | 0.37 | 0.59 | 0.82 | 0.98 | 0.31 |
6 | 0.77 | 0.08 | 0.59 | 0.43 | 0.56 | 0.47 | 0.94 | 0.19 | 0.77 | 0.06 | 0.66 | 0.45 | 0.75 | 0.59 | 0.97 | 0.20 | 0.78 | 0.07 | 0.64 | 0.49 | 0.70 | 0.56 | 0.97 | 0.17 |
7 | 0.64 | 0.11 | 0.70 | 0.37 | 0.59 | 0.57 | 0.97 | 0.26 | 0.62 | 0.09 | 0.76 | 0.36 | 0.75 | 0.69 | 0.99 | 0.25 | 0.63 | 0.10 | 0.75 | 0.38 | 0.73 | 0.67 | 0.98 | 0.23 |
8 | 0.58 | 0.15 | 0.12 | 0.47 | 0.49 | 0.45 | 0.77 | 0.27 | 0.54 | 0.12 | 0.10 | 0.47 | 0.57 | 0.59 | 0.82 | 0.29 | 0.55 | 0.14 | 0.11 | 0.48 | 0.59 | 0.55 | 0.84 | 0.25 |
12 | 0.84 | 0.09 | 0.11 | 0.27 | 0.58 | 0.61 | 0.44 | 0.29 | 0.82 | 0.06 | 0.08 | 0.27 | 0.69 | 0.69 | 0.50 | 0.33 | 0.84 | 0.06 | 0.09 | 0.25 | 0.69 | 0.65 | 0.49 | 0.28 |
20 | 0.45 | 0.08 | 0.23 | 0.23 | 0.49 | 0.45 | 0.52 | 0.40 | 0.44 | 0.04 | 0.21 | 0.22 | 0.59 | 0.58 | 0.67 | 0.43 | 0.46 | 0.05 | 0.24 | 0.23 | 0.61 | 0.55 | 0.68 | 0.41 |
Skew-Normal Distribution | ||||||||||||||||||||||||
AR(1)-GARCH(1,1) | AR(1)-EGARCH(1,1) | AR(1)-APARCH(1,1) | ||||||||||||||||||||||
m | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | Kingspan | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger |
1 | 0.78 | 0.59 | 0.67 | 0.63 | 0.39 | 0.54 | 0.46 | 0.58 | 0.66 | 0.66 | 0.83 | 0.61 | 0.63 | 0.79 | 0.95 | 0.64 | 0.67 | 0.61 | 0.92 | 0.76 | 0.61 | 0.92 | 0.99 | 0.70 |
2 | 0.95 | 0.69 | 0.91 | 0.81 | 0.67 | 0.34 | 0.71 | 0.48 | 0.91 | 0.61 | 0.97 | 0.81 | 0.89 | 0.59 | 0.96 | 0.54 | 0.91 | 0.59 | 0.99 | 0.88 | 0.86 | 0.57 | 0.96 | 0.53 |
3 | 0.93 | 0.79 | 0.97 | 0.64 | 0.50 | 0.41 | 0.76 | 0.19 | 0.90 | 0.73 | 0.99 | 0.65 | 0.68 | 0.71 | 0.89 | 0.21 | 0.90 | 0.70 | 1.00 | 0.74 | 0.60 | 0.66 | 0.87 | 0.18 |
4 | 0.59 | 0.32 | 0.99 | 0.28 | 0.63 | 0.53 | 0.87 | 0.28 | 0.58 | 0.35 | 1.00 | 0.27 | 0.78 | 0.80 | 0.96 | 0.28 | 0.59 | 0.36 | 1.00 | 0.31 | 0.70 | 0.75 | 0.95 | 0.26 |
5 | 0.71 | 0.11 | 0.48 | 0.32 | 0.39 | 0.64 | 0.94 | 0.30 | 0.70 | 0.10 | 0.53 | 0.33 | 0.63 | 0.89 | 0.98 | 0.35 | 0.71 | 0.10 | 0.52 | 0.37 | 0.59 | 0.85 | 0.98 | 0.31 |
6 | 0.77 | 0.08 | 0.59 | 0.44 | 0.51 | 0.44 | 0.91 | 0.19 | 0.77 | 0.06 | 0.65 | 0.45 | 0.73 | 0.64 | 0.97 | 0.20 | 0.78 | 0.07 | 0.64 | 0.50 | 0.70 | 0.58 | 0.97 | 0.17 |
7 | 0.64 | 0.12 | 0.70 | 0.37 | 0.54 | 0.55 | 0.95 | 0.26 | 0.62 | 0.09 | 0.76 | 0.37 | 0.74 | 0.73 | 0.99 | 0.25 | 0.63 | 0.10 | 0.74 | 0.38 | 0.73 | 0.69 | 0.98 | 0.23 |
8 | 0.58 | 0.15 | 0.12 | 0.48 | 0.45 | 0.43 | 0.74 | 0.26 | 0.55 | 0.12 | 0.10 | 0.47 | 0.56 | 0.62 | 0.82 | 0.29 | 0.55 | 0.14 | 0.11 | 0.48 | 0.59 | 0.57 | 0.84 | 0.25 |
12 | 0.84 | 0.10 | 0.11 | 0.28 | 0.54 | 0.60 | 0.42 | 0.28 | 0.83 | 0.06 | 0.08 | 0.27 | 0.68 | 0.73 | 0.51 | 0.33 | 0.84 | 0.06 | 0.09 | 0.25 | 0.69 | 0.67 | 0.50 | 0.28 |
20 | 0.45 | 0.08 | 0.23 | 0.23 | 0.46 | 0.44 | 0.50 | 0.39 | 0.44 | 0.04 | 0.21 | 0.22 | 0.57 | 0.60 | 0.67 | 0.43 | 0.46 | 0.05 | 0.23 | 0.24 | 0.61 | 0.56 | 0.69 | 0.41 |
Student’s t Distribution | ||||||||||||||||||||||||
AR(1)-GARCH(1,1) | AR(1)-EGARCH(1,1) | AR(1)-APARCH(1,1) | ||||||||||||||||||||||
m | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | Kingspan | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger |
1 | 0.17 | 0.23 | 0.20 | 0.39 | 0.61 | 0.82 | 0.53 | 0.55 | 0.13 | 0.27 | 0.16 | 0.56 | 0.88 | 0.73 | 0.79 | 0.65 | 0.13 | 0.27 | 0.23 | 0.60 | 0.77 | 0.88 | 0.81 | 0.63 |
2 | 0.38 | 0.38 | 0.38 | 0.61 | 0.84 | 0.40 | 0.76 | 0.45 | 0.32 | 0.38 | 0.35 | 0.75 | 0.98 | 0.59 | 0.94 | 0.52 | 0.32 | 0.37 | 0.43 | 0.77 | 0.93 | 0.59 | 0.95 | 0.49 |
3 | 0.54 | 0.52 | 0.56 | 0.54 | 0.58 | 0.46 | 0.79 | 0.18 | 0.47 | 0.52 | 0.54 | 0.64 | 0.69 | 0.69 | 0.87 | 0.18 | 0.47 | 0.50 | 0.61 | 0.69 | 0.60 | 0.66 | 0.85 | 0.15 |
4 | 0.36 | 0.19 | 0.72 | 0.23 | 0.70 | 0.58 | 0.89 | 0.26 | 0.32 | 0.24 | 0.71 | 0.29 | 0.79 | 0.79 | 0.95 | 0.24 | 0.33 | 0.25 | 0.77 | 0.31 | 0.71 | 0.75 | 0.94 | 0.21 |
5 | 0.49 | 0.05 | 0.36 | 0.28 | 0.45 | 0.68 | 0.95 | 0.29 | 0.45 | 0.07 | 0.35 | 0.36 | 0.63 | 0.88 | 0.98 | 0.32 | 0.45 | 0.08 | 0.40 | 0.39 | 0.59 | 0.85 | 0.98 | 0.28 |
6 | 0.58 | 0.04 | 0.48 | 0.39 | 0.57 | 0.47 | 0.92 | 0.19 | 0.54 | 0.04 | 0.47 | 0.48 | 0.74 | 0.64 | 0.96 | 0.19 | 0.55 | 0.05 | 0.53 | 0.51 | 0.71 | 0.60 | 0.96 | 0.16 |
7 | 0.47 | 0.06 | 0.60 | 0.33 | 0.60 | 0.58 | 0.96 | 0.25 | 0.44 | 0.07 | 0.59 | 0.40 | 0.75 | 0.73 | 0.98 | 0.24 | 0.44 | 0.08 | 0.64 | 0.41 | 0.73 | 0.70 | 0.98 | 0.21 |
8 | 0.43 | 0.08 | 0.18 | 0.43 | 0.49 | 0.45 | 0.75 | 0.27 | 0.39 | 0.10 | 0.13 | 0.50 | 0.57 | 0.63 | 0.80 | 0.28 | 0.39 | 0.11 | 0.17 | 0.52 | 0.59 | 0.59 | 0.83 | 0.23 |
12 | 0.73 | 0.06 | 0.11 | 0.27 | 0.57 | 0.62 | 0.43 | 0.30 | 0.70 | 0.05 | 0.09 | 0.30 | 0.69 | 0.73 | 0.47 | 0.33 | 0.72 | 0.05 | 0.11 | 0.29 | 0.69 | 0.69 | 0.47 | 0.27 |
20 | 0.39 | 0.05 | 0.22 | 0.22 | 0.50 | 0.45 | 0.51 | 0.40 | 0.38 | 0.03 | 0.19 | 0.24 | 0.59 | 0.59 | 0.65 | 0.43 | 0.39 | 0.03 | 0.24 | 0.25 | 0.62 | 0.56 | 0.67 | 0.40 |
Skewed-t Distribution | ||||||||||||||||||||||||
AR(1)-GARCH(1,1) | AR(1)-EGARCH(1,1) | AR(1)-APARCH(1,1) | ||||||||||||||||||||||
m | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | Kingspan | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger |
1 | 0.17 | 0.23 | 0.20 | 0.39 | 0.61 | 0.82 | 0.53 | 0.55 | 0.13 | 0.27 | 0.16 | 0.56 | 0.88 | 0.73 | 0.79 | 0.65 | 0.13 | 0.27 | 0.23 | 0.60 | 0.77 | 0.88 | 0.81 | 0.63 |
2 | 0.38 | 0.38 | 0.38 | 0.61 | 0.84 | 0.40 | 0.76 | 0.45 | 0.32 | 0.38 | 0.35 | 0.75 | 0.98 | 0.59 | 0.94 | 0.52 | 0.32 | 0.37 | 0.43 | 0.77 | 0.93 | 0.59 | 0.95 | 0.49 |
3 | 0.54 | 0.52 | 0.56 | 0.54 | 0.58 | 0.46 | 0.79 | 0.18 | 0.47 | 0.52 | 0.54 | 0.64 | 0.69 | 0.69 | 0.87 | 0.18 | 0.47 | 0.50 | 0.61 | 0.69 | 0.60 | 0.66 | 0.85 | 0.15 |
4 | 0.36 | 0.19 | 0.72 | 0.23 | 0.70 | 0.58 | 0.89 | 0.26 | 0.32 | 0.24 | 0.71 | 0.29 | 0.79 | 0.79 | 0.95 | 0.24 | 0.33 | 0.25 | 0.77 | 0.31 | 0.71 | 0.75 | 0.94 | 0.21 |
5 | 0.49 | 0.05 | 0.36 | 0.28 | 0.45 | 0.68 | 0.95 | 0.29 | 0.45 | 0.07 | 0.35 | 0.36 | 0.63 | 0.88 | 0.98 | 0.32 | 0.45 | 0.08 | 0.40 | 0.39 | 0.59 | 0.85 | 0.98 | 0.28 |
6 | 0.58 | 0.04 | 0.48 | 0.39 | 0.57 | 0.47 | 0.92 | 0.19 | 0.54 | 0.04 | 0.47 | 0.48 | 0.74 | 0.64 | 0.96 | 0.19 | 0.55 | 0.05 | 0.53 | 0.51 | 0.71 | 0.60 | 0.96 | 0.16 |
7 | 0.47 | 0.06 | 0.60 | 0.33 | 0.60 | 0.58 | 0.96 | 0.25 | 0.44 | 0.07 | 0.59 | 0.40 | 0.75 | 0.73 | 0.98 | 0.24 | 0.44 | 0.08 | 0.64 | 0.41 | 0.73 | 0.70 | 0.98 | 0.21 |
8 | 0.43 | 0.08 | 0.18 | 0.43 | 0.49 | 0.45 | 0.75 | 0.27 | 0.39 | 0.10 | 0.13 | 0.50 | 0.57 | 0.63 | 0.80 | 0.28 | 0.39 | 0.11 | 0.17 | 0.52 | 0.59 | 0.59 | 0.83 | 0.23 |
12 | 0.73 | 0.06 | 0.11 | 0.27 | 0.57 | 0.62 | 0.43 | 0.30 | 0.70 | 0.05 | 0.09 | 0.30 | 0.69 | 0.73 | 0.47 | 0.33 | 0.72 | 0.05 | 0.11 | 0.29 | 0.69 | 0.69 | 0.47 | 0.27 |
20 | 0.39 | 0.05 | 0.22 | 0.22 | 0.50 | 0.45 | 0.51 | 0.40 | 0.38 | 0.03 | 0.19 | 0.24 | 0.59 | 0.59 | 0.65 | 0.43 | 0.39 | 0.03 | 0.24 | 0.25 | 0.62 | 0.56 | 0.67 | 0.40 |
GED | ||||||||||||||||||||||||
AR(1)-GARCH(1,1) | AR(1)-EGARCH(1,1) | AR(1)-APARCH(1,1) | ||||||||||||||||||||||
m | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | Kingspan | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger |
1 | 0.07 | 0.15 | 0.38 | 0.21 | 0.79 | 0.73 | 0.43 | 0.43 | 0.05 | 0.23 | 0.37 | 0.33 | 0.99 | 0.77 | 0.74 | 0.54 | 0.05 | 0.22 | 0.47 | 0.36 | 0.89 | 0.93 | 0.71 | 0.53 |
2 | 0.18 | 0.27 | 0.68 | 0.41 | 0.92 | 0.39 | 0.69 | 0.41 | 0.16 | 0.33 | 0.67 | 0.56 | 1.00 | 0.60 | 0.92 | 0.49 | 0.15 | 0.32 | 0.76 | 0.59 | 0.96 | 0.60 | 0.92 | 0.46 |
3 | 0.30 | 0.40 | 0.84 | 0.39 | 0.62 | 0.45 | 0.74 | 0.16 | 0.26 | 0.46 | 0.84 | 0.51 | 0.71 | 0.71 | 0.85 | 0.18 | 0.25 | 0.44 | 0.90 | 0.57 | 0.62 | 0.67 | 0.83 | 0.15 |
4 | 0.20 | 0.15 | 0.94 | 0.16 | 0.73 | 0.57 | 0.85 | 0.24 | 0.18 | 0.21 | 0.93 | 0.22 | 0.80 | 0.80 | 0.94 | 0.24 | 0.18 | 0.21 | 0.96 | 0.25 | 0.72 | 0.76 | 0.93 | 0.22 |
5 | 0.30 | 0.04 | 0.45 | 0.20 | 0.46 | 0.67 | 0.93 | 0.27 | 0.28 | 0.06 | 0.48 | 0.29 | 0.64 | 0.89 | 0.97 | 0.32 | 0.27 | 0.06 | 0.50 | 0.32 | 0.60 | 0.86 | 0.97 | 0.28 |
6 | 0.38 | 0.03 | 0.57 | 0.29 | 0.58 | 0.47 | 0.90 | 0.17 | 0.36 | 0.03 | 0.61 | 0.40 | 0.74 | 0.65 | 0.96 | 0.18 | 0.36 | 0.04 | 0.63 | 0.43 | 0.71 | 0.60 | 0.96 | 0.15 |
7 | 0.31 | 0.05 | 0.68 | 0.25 | 0.61 | 0.57 | 0.95 | 0.24 | 0.29 | 0.05 | 0.72 | 0.33 | 0.75 | 0.74 | 0.98 | 0.23 | 0.28 | 0.06 | 0.74 | 0.35 | 0.74 | 0.71 | 0.98 | 0.20 |
8 | 0.28 | 0.06 | 0.14 | 0.34 | 0.50 | 0.46 | 0.72 | 0.25 | 0.25 | 0.08 | 0.13 | 0.43 | 0.57 | 0.64 | 0.79 | 0.27 | 0.25 | 0.08 | 0.14 | 0.45 | 0.59 | 0.60 | 0.82 | 0.23 |
12 | 0.57 | 0.04 | 0.11 | 0.21 | 0.58 | 0.62 | 0.40 | 0.28 | 0.55 | 0.04 | 0.09 | 0.26 | 0.69 | 0.74 | 0.46 | 0.32 | 0.55 | 0.04 | 0.10 | 0.26 | 0.69 | 0.69 | 0.46 | 0.27 |
20 | 0.28 | 0.04 | 0.23 | 0.18 | 0.50 | 0.45 | 0.49 | 0.38 | 0.28 | 0.02 | 0.21 | 0.21 | 0.59 | 0.60 | 0.64 | 0.43 | 0.28 | 0.03 | 0.24 | 0.23 | 0.62 | 0.57 | 0.66 | 0.40 |
SGED | ||||||||||||||||||||||||
AR(1)-GARCH(1,1) | AR(1)-EGARCH(1,1) | AR(1)-APARCH(1,1) | ||||||||||||||||||||||
m | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | Kingspan | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger |
1 | 0.07 | 0.16 | 0.33 | 0.30 | 0.42 | 0.47 | 0.29 | 0.41 | 0.05 | 0.23 | 0.34 | 0.39 | 0.59 | 0.96 | 0.63 | 0.51 | 0.05 | 0.23 | 0.41 | 0.43 | 0.57 | 0.92 | 0.66 | 0.49 |
2 | 0.19 | 0.29 | 0.62 | 0.52 | 0.69 | 0.32 | 0.54 | 0.40 | 0.14 | 0.33 | 0.63 | 0.63 | 0.87 | 0.62 | 0.87 | 0.48 | 0.14 | 0.33 | 0.71 | 0.66 | 0.83 | 0.58 | 0.88 | 0.45 |
3 | 0.31 | 0.42 | 0.80 | 0.47 | 0.51 | 0.39 | 0.63 | 0.16 | 0.24 | 0.46 | 0.81 | 0.55 | 0.66 | 0.73 | 0.83 | 0.17 | 0.23 | 0.45 | 0.86 | 0.60 | 0.58 | 0.67 | 0.83 | 0.15 |
4 | 0.20 | 0.15 | 0.91 | 0.19 | 0.63 | 0.52 | 0.77 | 0.24 | 0.17 | 0.21 | 0.92 | 0.23 | 0.76 | 0.81 | 0.93 | 0.24 | 0.17 | 0.22 | 0.94 | 0.26 | 0.69 | 0.76 | 0.92 | 0.21 |
5 | 0.30 | 0.04 | 0.43 | 0.24 | 0.40 | 0.62 | 0.87 | 0.26 | 0.26 | 0.06 | 0.46 | 0.30 | 0.62 | 0.90 | 0.97 | 0.31 | 0.25 | 0.06 | 0.48 | 0.33 | 0.58 | 0.86 | 0.97 | 0.27 |
6 | 0.39 | 0.03 | 0.55 | 0.34 | 0.52 | 0.43 | 0.85 | 0.17 | 0.34 | 0.03 | 0.59 | 0.41 | 0.73 | 0.65 | 0.95 | 0.18 | 0.34 | 0.04 | 0.61 | 0.45 | 0.69 | 0.59 | 0.96 | 0.15 |
7 | 0.31 | 0.05 | 0.66 | 0.29 | 0.55 | 0.54 | 0.91 | 0.23 | 0.27 | 0.05 | 0.70 | 0.34 | 0.74 | 0.74 | 0.98 | 0.23 | 0.27 | 0.06 | 0.72 | 0.36 | 0.73 | 0.70 | 0.98 | 0.20 |
8 | 0.28 | 0.07 | 0.13 | 0.38 | 0.45 | 0.42 | 0.68 | 0.24 | 0.24 | 0.08 | 0.12 | 0.44 | 0.56 | 0.63 | 0.80 | 0.27 | 0.24 | 0.09 | 0.13 | 0.46 | 0.58 | 0.58 | 0.82 | 0.23 |
12 | 0.58 | 0.04 | 0.10 | 0.24 | 0.55 | 0.59 | 0.38 | 0.28 | 0.53 | 0.04 | 0.08 | 0.26 | 0.68 | 0.74 | 0.48 | 0.32 | 0.54 | 0.04 | 0.10 | 0.26 | 0.68 | 0.68 | 0.48 | 0.27 |
20 | 0.29 | 0.04 | 0.22 | 0.20 | 0.47 | 0.43 | 0.47 | 0.38 | 0.27 | 0.02 | 0.20 | 0.22 | 0.58 | 0.60 | 0.65 | 0.43 | 0.27 | 0.03 | 0.23 | 0.23 | 0.61 | 0.57 | 0.68 | 0.39 |
Normal Distribution | ||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
AR(1)-GARCH(1,1) | AR(1)-EGARCH(1,1) | AR(1)-APARCH(1,1) | ||||||||||||||||||||||
m | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | Kingspan | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger |
1 | 0.15 | 0.00 | 0.00 | 0.72 | 0.28 | 0.17 | 0.24 | 0.60 | 0.19 | 0.00 | 0.00 | 0.09 | 0.43 | 0.22 | 0.38 | 0.57 | 0.23 | 0.00 | 0.00 | 0.03 | 0.30 | 0.16 | 0.58 | 0.98 |
2 | 0.25 | 0.01 | 0.00 | 0.93 | 0.08 | 0.01 | 0.36 | 0.30 | 0.36 | 0.01 | 0.00 | 0.22 | 0.25 | 0.15 | 0.40 | 0.34 | 0.43 | 0.01 | 0.00 | 0.09 | 0.34 | 0.12 | 0.26 | 0.45 |
3 | 0.43 | 0.03 | 0.00 | 0.75 | 0.17 | 0.02 | 0.26 | 0.48 | 0.56 | 0.02 | 0.00 | 0.26 | 0.43 | 0.09 | 0.48 | 0.53 | 0.64 | 0.02 | 0.00 | 0.12 | 0.54 | 0.07 | 0.26 | 0.63 |
4 | 0.38 | 0.04 | 0.00 | 0.78 | 0.28 | 0.03 | 0.23 | 0.62 | 0.39 | 0.04 | 0.00 | 0.39 | 0.58 | 0.14 | 0.36 | 0.68 | 0.41 | 0.03 | 0.00 | 0.21 | 0.71 | 0.10 | 0.21 | 0.77 |
5 | 0.19 | 0.06 | 0.00 | 0.83 | 0.40 | 0.05 | 0.34 | 0.50 | 0.22 | 0.04 | 0.00 | 0.53 | 0.72 | 0.18 | 0.50 | 0.62 | 0.22 | 0.04 | 0.00 | 0.32 | 0.82 | 0.16 | 0.32 | 0.64 |
6 | 0.26 | 0.08 | 0.00 | 0.90 | 0.51 | 0.07 | 0.30 | 0.62 | 0.31 | 0.08 | 0.00 | 0.65 | 0.78 | 0.21 | 0.28 | 0.74 | 0.31 | 0.07 | 0.00 | 0.43 | 0.86 | 0.18 | 0.15 | 0.76 |
7 | 0.18 | 0.12 | 0.00 | 0.95 | 0.48 | 0.08 | 0.11 | 0.54 | 0.25 | 0.12 | 0.00 | 0.73 | 0.79 | 0.28 | 0.15 | 0.53 | 0.25 | 0.11 | 0.00 | 0.52 | 0.84 | 0.24 | 0.10 | 0.52 |
8 | 0.23 | 0.17 | 0.00 | 0.97 | 0.41 | 0.06 | 0.16 | 0.65 | 0.27 | 0.18 | 0.00 | 0.82 | 0.41 | 0.12 | 0.22 | 0.62 | 0.26 | 0.16 | 0.00 | 0.62 | 0.49 | 0.10 | 0.15 | 0.63 |
12 | 0.35 | 0.37 | 0.00 | 0.99 | 0.44 | 0.03 | 0.29 | 0.82 | 0.36 | 0.39 | 0.00 | 0.95 | 0.26 | 0.03 | 0.39 | 0.74 | 0.36 | 0.36 | 0.00 | 0.85 | 0.40 | 0.02 | 0.32 | 0.79 |
20 | 0.12 | 0.41 | 0.00 | 1.00 | 0.65 | 0.15 | 0.61 | 0.85 | 0.20 | 0.33 | 0.00 | 0.99 | 0.70 | 0.14 | 0.69 | 0.84 | 0.18 | 0.28 | 0.00 | 0.97 | 0.77 | 0.12 | 0.63 | 0.89 |
Skew-Normal Distribution | ||||||||||||||||||||||||
AR(1)-GARCH(1,1) | AR(1)-EGARCH(1,1) | AR(1)-APARCH(1,1) | ||||||||||||||||||||||
m | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | Kingspan | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger |
1 | 0.15 | 0.00 | 0.00 | 0.73 | 0.27 | 0.16 | 0.28 | 0.60 | 0.19 | 0.00 | 0.00 | 0.10 | 0.42 | 0.25 | 0.43 | 0.57 | 0.23 | 0.00 | 0.00 | 0.03 | 0.29 | 0.17 | 0.61 | 0.98 |
2 | 0.25 | 0.01 | 0.00 | 0.94 | 0.10 | 0.02 | 0.38 | 0.31 | 0.36 | 0.01 | 0.00 | 0.25 | 0.30 | 0.13 | 0.39 | 0.34 | 0.43 | 0.01 | 0.00 | 0.10 | 0.37 | 0.11 | 0.24 | 0.45 |
3 | 0.42 | 0.03 | 0.00 | 0.74 | 0.20 | 0.02 | 0.24 | 0.49 | 0.56 | 0.02 | 0.00 | 0.28 | 0.49 | 0.09 | 0.45 | 0.53 | 0.64 | 0.02 | 0.00 | 0.12 | 0.58 | 0.07 | 0.23 | 0.63 |
4 | 0.38 | 0.04 | 0.00 | 0.78 | 0.32 | 0.04 | 0.21 | 0.62 | 0.39 | 0.04 | 0.00 | 0.41 | 0.64 | 0.14 | 0.32 | 0.68 | 0.41 | 0.04 | 0.00 | 0.21 | 0.74 | 0.10 | 0.18 | 0.77 |
5 | 0.19 | 0.06 | 0.00 | 0.82 | 0.45 | 0.06 | 0.32 | 0.50 | 0.22 | 0.05 | 0.00 | 0.54 | 0.77 | 0.18 | 0.45 | 0.63 | 0.22 | 0.04 | 0.00 | 0.32 | 0.84 | 0.15 | 0.28 | 0.64 |
6 | 0.26 | 0.08 | 0.00 | 0.90 | 0.57 | 0.07 | 0.26 | 0.63 | 0.32 | 0.08 | 0.00 | 0.67 | 0.82 | 0.21 | 0.24 | 0.75 | 0.32 | 0.07 | 0.00 | 0.44 | 0.88 | 0.18 | 0.12 | 0.76 |
7 | 0.19 | 0.13 | 0.00 | 0.94 | 0.52 | 0.08 | 0.10 | 0.54 | 0.26 | 0.13 | 0.00 | 0.75 | 0.83 | 0.28 | 0.13 | 0.53 | 0.26 | 0.12 | 0.00 | 0.53 | 0.86 | 0.23 | 0.08 | 0.52 |
8 | 0.23 | 0.18 | 0.00 | 0.97 | 0.45 | 0.07 | 0.15 | 0.65 | 0.28 | 0.19 | 0.00 | 0.83 | 0.42 | 0.12 | 0.19 | 0.62 | 0.27 | 0.17 | 0.00 | 0.63 | 0.48 | 0.10 | 0.13 | 0.63 |
12 | 0.35 | 0.38 | 0.00 | 0.99 | 0.49 | 0.04 | 0.27 | 0.82 | 0.36 | 0.40 | 0.00 | 0.95 | 0.26 | 0.03 | 0.35 | 0.74 | 0.36 | 0.37 | 0.00 | 0.85 | 0.38 | 0.02 | 0.28 | 0.79 |
20 | 0.12 | 0.41 | 0.00 | 1.00 | 0.69 | 0.18 | 0.59 | 0.85 | 0.20 | 0.33 | 0.00 | 0.99 | 0.70 | 0.13 | 0.65 | 0.84 | 0.18 | 0.28 | 0.00 | 0.97 | 0.76 | 0.12 | 0.58 | 0.89 |
Student’s t Distribution | ||||||||||||||||||||||||
AR(1)-GARCH(1,1) | AR(1)-EGARCH(1,1) | AR(1)-APARCH(1,1) | ||||||||||||||||||||||
m | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | Kingspan | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger |
1 | 0.37 | 0.00 | 0.14 | 0.57 | 0.23 | 0.21 | 0.34 | 0.70 | 0.40 | 0.01 | 0.00 | 0.07 | 0.37 | 0.29 | 0.39 | 0.48 | 0.47 | 0.01 | 0.02 | 0.05 | 0.27 | 0.20 | 0.62 | 0.79 |
2 | 0.62 | 0.01 | 0.28 | 0.83 | 0.10 | 0.01 | 0.36 | 0.31 | 0.69 | 0.02 | 0.00 | 0.19 | 0.28 | 0.10 | 0.38 | 0.40 | 0.77 | 0.02 | 0.07 | 0.13 | 0.34 | 0.10 | 0.22 | 0.50 |
3 | 0.78 | 0.02 | 0.34 | 0.72 | 0.19 | 0.02 | 0.19 | 0.49 | 0.84 | 0.04 | 0.00 | 0.22 | 0.46 | 0.08 | 0.45 | 0.57 | 0.87 | 0.04 | 0.09 | 0.15 | 0.53 | 0.07 | 0.22 | 0.66 |
4 | 0.43 | 0.03 | 0.43 | 0.77 | 0.32 | 0.03 | 0.15 | 0.64 | 0.36 | 0.06 | 0.00 | 0.34 | 0.62 | 0.13 | 0.34 | 0.73 | 0.34 | 0.06 | 0.14 | 0.25 | 0.70 | 0.10 | 0.18 | 0.80 |
5 | 0.14 | 0.0 | 0.58 | 0.83 | 0.44 | 0.05 | 0.24 | 0.49 | 0.15 | 0.08 | 0.00 | 0.47 | 0.75 | 0.16 | 0.48 | 0.64 | 0.13 | 0.07 | 0.23 | 0.37 | 0.81 | 0.15 | 0.28 | 0.66 |
6 | 0.18 | 0.06 | 0.67 | 0.91 | 0.56 | 0.06 | 0.18 | 0.62 | 0.20 | 0.13 | 0.01 | 0.60 | 0.81 | 0.19 | 0.27 | 0.76 | 0.18 | 0.12 | 0.29 | 0.49 | 0.85 | 0.17 | 0.13 | 0.77 |
7 | 0.09 | 0.10 | 0.77 | 0.95 | 0.49 | 0.07 | 0.07 | 0.56 | 0.13 | 0.19 | 0.01 | 0.69 | 0.81 | 0.26 | 0.14 | 0.54 | 0.11 | 0.18 | 0.39 | 0.59 | 0.82 | 0.23 | 0.09 | 0.52 |
8 | 0.14 | 0.15 | 0.77 | 0.98 | 0.47 | 0.06 | 0.11 | 0.66 | 0.16 | 0.27 | 0.01 | 0.78 | 0.49 | 0.11 | 0.20 | 0.63 | 0.14 | 0.25 | 0.39 | 0.69 | 0.53 | 0.09 | 0.13 | 0.63 |
12 | 0.23 | 0.36 | 0.87 | 0.98 | 0.54 | 0.03 | 0.21 | 0.84 | 0.23 | 0.48 | 0.03 | 0.93 | 0.37 | 0.03 | 0.37 | 0.80 | 0.21 | 0.45 | 0.51 | 0.88 | 0.47 | 0.02 | 0.28 | 0.82 |
20 | 0.10 | 0.42 | 0.34 | 0.99 | 0.69 | 0.15 | 0.51 | 0.85 | 0.17 | 0.36 | 0.01 | 0.98 | 0.78 | 0.13 | 0.68 | 0.87 | 0.14 | 0.32 | 0.15 | 0.97 | 0.81 | 0.12 | 0.59 | 0.91 |
Skewed-t Distribution | ||||||||||||||||||||||||
AR(1)-GARCH(1,1) | AR(1)-EGARCH(1,1) | AR(1)-APARCH(1,1) | ||||||||||||||||||||||
m | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | Kingspan | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger |
1 | 0.37 | 0.00 | 0.14 | 0.57 | 0.23 | 0.21 | 0.34 | 0.70 | 0.40 | 0.01 | 0.00 | 0.07 | 0.37 | 0.29 | 0.39 | 0.48 | 0.47 | 0.01 | 0.02 | 0.05 | 0.27 | 0.20 | 0.62 | 0.79 |
2 | 0.62 | 0.01 | 0.28 | 0.83 | 0.10 | 0.01 | 0.36 | 0.31 | 0.69 | 0.02 | 0.00 | 0.19 | 0.28 | 0.10 | 0.38 | 0.40 | 0.77 | 0.02 | 0.07 | 0.13 | 0.34 | 0.10 | 0.22 | 0.50 |
3 | 0.78 | 0.02 | 0.34 | 0.72 | 0.19 | 0.02 | 0.19 | 0.49 | 0.84 | 0.04 | 0.00 | 0.22 | 0.46 | 0.08 | 0.45 | 0.57 | 0.87 | 0.04 | 0.09 | 0.15 | 0.53 | 0.07 | 0.22 | 0.66 |
4 | 0.43 | 0.03 | 0.43 | 0.77 | 0.32 | 0.03 | 0.15 | 0.64 | 0.36 | 0.06 | 0.00 | 0.34 | 0.62 | 0.13 | 0.34 | 0.73 | 0.34 | 0.06 | 0.14 | 0.25 | 0.70 | 0.10 | 0.18 | 0.80 |
5 | 0.14 | 0.05 | 0.58 | 0.83 | 0.44 | 0.05 | 0.24 | 0.49 | 0.15 | 0.08 | 0.00 | 0.47 | 0.75 | 0.16 | 0.48 | 0.64 | 0.13 | 0.07 | 0.23 | 0.37 | 0.81 | 0.15 | 0.28 | 0.66 |
6 | 0.18 | 0.06 | 0.67 | 0.91 | 0.56 | 0.06 | 0.18 | 0.62 | 0.20 | 0.13 | 0.01 | 0.60 | 0.81 | 0.19 | 0.27 | 0.76 | 0.18 | 0.12 | 0.29 | 0.49 | 0.85 | 0.17 | 0.13 | 0.77 |
7 | 0.09 | 0.10 | 0.77 | 0.95 | 0.49 | 0.07 | 0.07 | 0.56 | 0.13 | 0.19 | 0.01 | 0.69 | 0.81 | 0.26 | 0.14 | 0.54 | 0.11 | 0.18 | 0.39 | 0.59 | 0.82 | 0.23 | 0.09 | 0.52 |
8 | 0.14 | 0.15 | 0.77 | 0.98 | 0.47 | 0.06 | 0.11 | 0.66 | 0.16 | 0.27 | 0.01 | 0.78 | 0.49 | 0.11 | 0.20 | 0.63 | 0.14 | 0.25 | 0.39 | 0.69 | 0.53 | 0.09 | 0.13 | 0.63 |
12 | 0.23 | 0.36 | 0.87 | 0.98 | 0.54 | 0.03 | 0.21 | 0.84 | 0.23 | 0.48 | 0.03 | 0.93 | 0.37 | 0.03 | 0.37 | 0.80 | 0.21 | 0.45 | 0.51 | 0.88 | 0.47 | 0.02 | 0.28 | 0.82 |
20 | 0.10 | 0.42 | 0.34 | 0.99 | 0.69 | 0.15 | 0.51 | 0.85 | 0.17 | 0.36 | 0.01 | 0.98 | 0.78 | 0.13 | 0.68 | 0.87 | 0.14 | 0.32 | 0.15 | 0.97 | 0.81 | 0.12 | 0.59 | 0.91 |
GED | ||||||||||||||||||||||||
AR(1)-GARCH(1,1) | AR(1)-EGARCH(1,1) | AR(1)-APARCH(1,1) | ||||||||||||||||||||||
m | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | Kingspan | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger |
1 | 0.24 | 0.00 | 0.00 | 0.63 | 0.25 | 0.19 | 0.29 | 0.67 | 0.30 | 0.01 | 0.00 | 0.09 | 0.40 | 0.25 | 0.39 | 0.50 | 0.34 | 0.00 | 0.00 | 0.05 | 0.28 | 0.18 | 0.60 | 0.83 |
2 | 0.43 | 0.01 | 0.00 | 0.88 | 0.08 | 0.01 | 0.36 | 0.31 | 0.55 | 0.01 | 0.00 | 0.22 | 0.26 | 0.13 | 0.37 | 0.37 | 0.62 | 0.01 | 0.00 | 0.14 | 0.33 | 0.11 | 0.23 | 0.47 |
3 | 0.63 | 0.02 | 0.00 | 0.73 | 0.17 | 0.02 | 0.22 | 0.50 | 0.74 | 0.03 | 0.00 | 0.24 | 0.44 | 0.09 | 0.45 | 0.55 | 0.79 | 0.03 | 0.00 | 0.16 | 0.53 | 0.07 | 0.23 | 0.65 |
4 | 0.42 | 0.03 | 0.00 | 0.78 | 0.28 | 0.03 | 0.18 | 0.64 | 0.38 | 0.05 | 0.00 | 0.37 | 0.60 | 0.14 | 0.34 | 0.71 | 0.37 | 0.05 | 0.00 | 0.27 | 0.70 | 0.10 | 0.19 | 0.78 |
5 | 0.15 | 0.05 | 0.00 | 0.84 | 0.41 | 0.05 | 0.28 | 0.50 | 0.16 | 0.06 | 0.00 | 0.51 | 0.73 | 0.17 | 0.48 | 0.63 | 0.15 | 0.06 | 0.00 | 0.40 | 0.81 | 0.15 | 0.29 | 0.65 |
6 | 0.20 | 0.07 | 0.00 | 0.91 | 0.52 | 0.06 | 0.23 | 0.62 | 0.23 | 0.11 | 0.00 | 0.64 | 0.79 | 0.21 | 0.27 | 0.75 | 0.21 | 0.10 | 0.00 | 0.52 | 0.85 | 0.18 | 0.13 | 0.76 |
7 | 0.12 | 0.10 | 0.00 | 0.95 | 0.47 | 0.07 | 0.09 | 0.55 | 0.16 | 0.16 | 0.00 | 0.72 | 0.80 | 0.28 | 0.15 | 0.54 | 0.15 | 0.15 | 0.00 | 0.61 | 0.83 | 0.24 | 0.09 | 0.52 |
8 | 0.16 | 0.15 | 0.00 | 0.98 | 0.43 | 0.06 | 0.13 | 0.66 | 0.19 | 0.23 | 0.00 | 0.81 | 0.43 | 0.11 | 0.21 | 0.63 | 0.17 | 0.22 | 0.00 | 0.71 | 0.50 | 0.09 | 0.14 | 0.63 |
12 | 0.28 | 0.36 | 0.00 | 0.99 | 0.47 | 0.03 | 0.24 | 0.84 | 0.28 | 0.45 | 0.00 | 0.95 | 0.30 | 0.03 | 0.37 | 0.78 | 0.27 | 0.42 | 0.01 | 0.90 | 0.42 | 0.02 | 0.29 | 0.81 |
20 | 0.11 | 0.42 | 0.00 | 1.00 | 0.67 | 0.15 | 0.56 | 0.85 | 0.18 | 0.35 | 0.00 | 0.99 | 0.73 | 0.13 | 0.69 | 0.86 | 0.16 | 0.31 | 0.00 | 0.98 | 0.78 | 0.11 | 0.60 | 0.90 |
SGED | ||||||||||||||||||||||||
AR(1)-GARCH(1,1) | AR(1)-EGARCH(1,1) | AR(1)-APARCH(1,1) | ||||||||||||||||||||||
m | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | Kingspan | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger | Epistar | King span | Boralex | Nibe | Exxon Mobil | Chevron | Total S.A | Schlum berger |
1 | 0.24 | 0.00 | 0.00 | 0.64 | 0.26 | 0.18 | 0.34 | 0.67 | 0.30 | 0.01 | 0.00 | 0.10 | 0.42 | 0.27 | 0.44 | 0.49 | 0.34 | 0.00 | 0.00 | 0.05 | 0.29 | 0.18 | 0.65 | 0.82 |
2 | 0.43 | 0.01 | 0.00 | 0.88 | 0.10 | 0.01 | 0.38 | 0.31 | 0.55 | 0.01 | 0.00 | 0.23 | 0.31 | 0.11 | 0.38 | 0.37 | 0.61 | 0.01 | 0.00 | 0.15 | 0.38 | 0.10 | 0.22 | 0.47 |
3 | 0.63 | 0.02 | 0.00 | 0.73 | 0.20 | 0.02 | 0.21 | 0.50 | 0.75 | 0.03 | 0.00 | 0.26 | 0.51 | 0.09 | 0.43 | 0.55 | 0.79 | 0.03 | 0.00 | 0.17 | 0.58 | 0.07 | 0.20 | 0.64 |
4 | 0.43 | 0.03 | 0.00 | 0.78 | 0.32 | 0.03 | 0.16 | 0.64 | 0.38 | 0.05 | 0.00 | 0.39 | 0.66 | 0.14 | 0.31 | 0.71 | 0.37 | 0.05 | 0.00 | 0.28 | 0.74 | 0.10 | 0.16 | 0.78 |
5 | 0.16 | 0.05 | 0.00 | 0.83 | 0.45 | 0.05 | 0.26 | 0.49 | 0.16 | 0.06 | 0.00 | 0.52 | 0.79 | 0.17 | 0.44 | 0.63 | 0.15 | 0.06 | 0.00 | 0.40 | 0.85 | 0.15 | 0.25 | 0.65 |
6 | 0.21 | 0.07 | 0.00 | 0.91 | 0.57 | 0.07 | 0.20 | 0.62 | 0.23 | 0.11 | 0.00 | 0.65 | 0.84 | 0.20 | 0.23 | 0.75 | 0.22 | 0.10 | 0.00 | 0.53 | 0.88 | 0.18 | 0.11 | 0.76 |
7 | 0.12 | 0.11 | 0.00 | 0.95 | 0.51 | 0.07 | 0.08 | 0.55 | 0.16 | 0.16 | 0.00 | 0.74 | 0.84 | 0.27 | 0.12 | 0.54 | 0.15 | 0.15 | 0.00 | 0.62 | 0.86 | 0.23 | 0.07 | 0.52 |
8 | 0.17 | 0.16 | 0.00 | 0.97 | 0.46 | 0.06 | 0.12 | 0.66 | 0.19 | 0.23 | 0.00 | 0.82 | 0.46 | 0.11 | 0.18 | 0.63 | 0.18 | 0.22 | 0.00 | 0.72 | 0.51 | 0.09 | 0.11 | 0.63 |
12 | 0.29 | 0.37 | 0.00 | 0.99 | 0.52 | 0.04 | 0.23 | 0.84 | 0.28 | 0.46 | 0.00 | 0.95 | 0.30 | 0.03 | 0.33 | 0.78 | 0.27 | 0.43 | 0.01 | 0.90 | 0.42 | 0.02 | 0.25 | 0.80 |
20 | 0.12 | 0.42 | 0.00 | 1.00 | 0.70 | 0.17 | 0.53 | 0.85 | 0.19 | 0.36 | 0.00 | 0.99 | 0.74 | 0.12 | 0.64 | 0.86 | 0.16 | 0.31 | 0.00 | 0.98 | 0.79 | 0.12 | 0.55 | 0.90 |
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Panel A: Normal, Skew-Normal, t-Student and Skew t | Panel B: GED and SGED | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Test Z1 | Skew Parameter (λ,ξ) | Skew Parameter (ζ) | |||||||||||
Degrees of freedom (ν) | 0.6 | 0.8 | 0.9 | 1 | 1.1 | 1.2 | Shape parameter (η) | 0.6 | 0.8 | 0.9 | 1 | 1.1 | 1.2 |
3 | −0.13 | −0.13 | −0.14 | −0.14 | −0.14 | −0.14 | 1 | −0.06 | −0.06 | −0.06 | −0.06 | −0.05 | −0.05 |
5 | −0.07 | −0.07 | −0.07 | −0.08 | −0.07 | −0.08 | 1.2 | −0.05 | −0.05 | −0.05 | −0.05 | −0.05 | −0.05 |
7 | −0.05 | −0.06 | −0.06 | −0.06 | −0.06 | −0.06 | 1.4 | −0.05 | −0.05 | −0.04 | −0.04 | −0.04 | −0.04 |
10 | −0.05 | −0.05 | −0.05 | −0.05 | −0.05 | −0.05 | 1.6 | −0.04 | −0.04 | −0.04 | −0.04 | −0.04 | −0.04 |
Skew−Normal | −0.03 | −0.03 | −0.03 | −0.03 | −0.03 | −0.03 | 1.8 | −0.04 | −0.04 | −0.04 | −0.03 | −0.03 | −0.03 |
Test Z2 | Skew Parameter (λ,ξ) | Skew Parameter (ζ) | |||||||||||
Degrees of freedom (ν) | 0.6 | 0.8 | 0.9 | 1 | 1.1 | 1.2 | Shape parameter (η) | 0.6 | 0.8 | 0.9 | 1 | 1.1 | 1.2 |
3 | −0.25 | −0.26 | −0.26 | −0.26 | −0.26 | −0.26 | 1 | −0.22 | −0.22 | −0.22 | −0.22 | −0.22 | −0.22 |
5 | −0.22 | −0.23 | −0.22 | −0.23 | −0.23 | −0.22 | 1.2 | −0.22 | −0.22 | −0.22 | −0.22 | −0.21 | −0.22 |
7 | −0.22 | −0.21 | −0.22 | −0.22 | −0.23 | −0.22 | 1.4 | −0.22 | −0.22 | −0.22 | −0.22 | −0.22 | −0.21 |
10 | −0.22 | −0.22 | −0.22 | −0.22 | −0.22 | −0.22 | 1.6 | −0.22 | −0.22 | −0.21 | −0.22 | −0.22 | −0.22 |
Skew−Normal | −0.21 | −0.21 | −0.21 | −0.21 | −0.21 | −0.21 | 1.8 | −0.22 | −0.22 | −0.22 | −0.21 | −0.22 | −0.22 |
Test ZES | Skew Parameter (λ,ξ) | Skew Parameter (ζ) | |||||||||||
Degrees of freedom (ν) | 0.6 | 0.8 | 0.9 | 1 | 1.1 | 1.2 | Shape parameter (η) | 0.6 | 0.8 | 0.9 | 1 | 1.1 | 1.2 |
3 | −0.50 | −0.51 | −0.52 | −0.52 | −0.52 | −0.52 | 1 | −0.34 | −0.33 | −0.33 | −0.32 | −0.31 | −0.30 |
5 | −0.34 | −0.35 | −0.35 | −0.36 | −0.36 | −0.37 | 1.2 | −0.31 | −0.30 | −0.29 | −0.29 | −0.28 | −0.27 |
7 | −0.29 | −0.30 | −0.30 | −0.30 | −0.31 | −0.31 | 1.4 | −0.28 | −0.28 | −0.27 | −0.26 | −0.25 | −0.24 |
10 | −0.25 | −0.26 | −0.27 | −0.27 | −0.27 | −0.28 | 1.6 | −0.25 | −0.25 | −0.25 | −0.24 | −0.23 | −0.22 |
Skew−Normal | −0.19 | −0.20 | −0.20 | −0.20 | −0.21 | −0.21 | 1.8 | −0.25 | −0.23 | −0.23 | −0.22 | −0.21 | −0.21 |
Total Period (January 2005–December 2016) | |||||||||
---|---|---|---|---|---|---|---|---|---|
Stock | Type | Mean | Median | Std. Dev. | Excess Kurtosis | Skewness | Min | Max | Obs |
Epistar | Renewable | −0.0001 | 0.0007 | 0.030 (47.62%) | 3.494 | −0.014 | −0.109 | 0.098 | 2900 |
Kingspan | Renewable | 0.0003 | 0.0008 | 0.027 (42.86%) | 11.997 | −0.546 | −0.254 | 0.179 | 2900 |
Boralex | Renewable | 0.0004 | 0.0004 | 0.023 (36.51%) | 13.677 | 0.062 | −0.195 | 0.220 | 2900 |
Nibe | Renewable | 0.0005 | 0.0002 | 0.024 (38.10%) | 12.231 | −0.119 | −0.255 | 0.224 | 2900 |
Exxon Mobil | Traditional | 0.0002 | 0.0003 | 0.016 (25.40%) | 16.283 | 0.028 | −0.150 | 0.159 | 2900 |
Chevron | Traditional | 0.0003 | 0.0008 | 0.017 (26.99%) | 15.495 | 0.086 | −0.133 | 0.189 | 2900 |
Total S.A. | Traditional | 0.0000 | 0.0004 | 0.019 (30.16%) | 10.130 | 0.184 | −0.113 | 0.162 | 2900 |
Schlumberger | Traditional | 0.0003 | 0.0002 | 0.023 (36.51%) | 10.806 | −0.533 | −0.203 | 0.139 | 2900 |
Annual volatility is presented in parentheses. |
AR(1)-GARCH(1,1) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Normal | Skew-Normal | t-Student | Skew-t | GED | SGED | |||||||||||||
v | Kupiec Test | Ind. Test | v | Kupiec Test | Ind. Test | v | Kupiec Test | Ind. Test | v | Kupiec Test | Ind. Test | v | Kupiec Test | Ind. Test | v | Kupiec Test | Ind. Test | |
Epistar | 36 | 4.57 (0.03) | 4.92 (0.09) | 36 | 5.25 (0.02) | 5.58 (0.06) | 24 | 0.02 (0.89) | 1.45 (0.48) | 27 | 0.21 (0.65) | 1.28 (0.53) | 25 | 0.04 (0.84) | 1.30 (0.52) | 28 | 0.64 (0.42) | 1.56 (0.46) |
Kingspan | 39 | 7.10 (0.01) | 9.14 (0.01) | 44 | 13.51 (0.00) | 14.82 (0.00) | 20 | 0.97 (0.32) | 7.70 (0.02) | 27 | 0.21 (0.65) | 4.68 (0.10) | 25 | 0.04 (0.84) | 4.97 (0.08) | 24 | 0.00 (1.00) | 5.23 (0.07) |
Boralex | 43 | 11.20 (0.00) | 12.70 (0.00) | 48 | 18.79 (0.00) | 19.69 (0.00) | 23 | 0.12 (0.73) | 1.65 (0.48) | 26 | 0.07 (0.80) | 1.25 (0.54) | 24 | 0.00 (1.00) | 1.38 (0.50) | 27 | 0.36 (0.55) | 1.39 (0.50) |
Nibe | 31 | 1.50 (0.22) | 5.00 (0.08) | 38 | 7.01 (0.01) | 9.12 (0.01) | 17 | 2.73 (0.10) | 5.35 (0.07) | 27 | 0.21 (0.65) | 4.68 (0.10) | 21 | 0.40 (0.53) | 6.64 (0.05) | 27 | 0.36 (0.55) | 4.73 (0.09) |
Exxon Mobil | 49 | 18.75 (0.00) | 14.48 (0.00) | 45 | 14.76 (0.00) | 16.48 (0.00) | 39 | 7.10 (0.01) | 9.14 (0.01) | 28 | 0.42 (0.51) | 4.63 (0.10) | 40 | 8.97 (0.00) | 10.33 (0.01) | 36 | 5.25 (0.02) | 6.35 (0.04) |
Chevron | 46 | 14.78 (0.00) | 15.92 (0.00) | 34 | 3.73 (0.05) | 4.70 (0.10) | 31 | 1.50 (0.22) | 5.00 (0.08) | 17 | 2.73 (0.10) | 5.35 (0.07) | 40 | 8.97 (0.00) | 10.33 (0.01) | 27 | 0.36 (0.55) | 0.98 (0.61) |
Total S.A. | 45 | 13.54 (0.00) | 13.58 (0.00) | 41 | 10.03 (0.00) | 10.15 (0.01) | 27 | 0.21 (0.65) | 4.68 (0.10) | 19 | 1.45 (0.23) | 4.36 (0.08) | 33 | 3.05 (0.08) | 3.56 (0.17) | 28 | 0.64 (0.42) | 1.56 (0.46) |
Schlumberger | 39 | 7.10 (0.01) | 7.31 (0.03) | 39 | 7.96 (0.00) | 9.25 (0.01) | 23 | 0.12 (0.73) | 1.65 (0.48) | 26 | 0.07 (0.80) | 1.25 (0.54) | 31 | 1.89 (0.17) | 2.70 (0.26) | 30 | 1.40 (0.24) | 2.16 (0.34) |
AR(1)-EGARCH(1,1) | ||||||||||||||||||
Normal | Skew-Normal | t-Student | Skew-t | GED | SGED | |||||||||||||
v | Kupiec Test | Ind. Test | v | Kupiec Test | Ind. Test | v | Kupiec Test | Ind. Test | v | Kupiec Test | Ind. Test | v | Kupiec Test | Ind. Test | v | Kupiec Test | Ind. Test | |
Epistar | 45 | 13.54 (0.00) | 14.81 (0.00) | 42 | 11.14 (0.00) | 12.70 (0.00) | 32 | 1.99 (0.16) | 5.27 (0.07) | 38 | 6.20 (0.01) | 8.40 (0.02) | 33 | 3.05 (0.08) | 6.04 (0.05) | 36 | 5.25 (0.02) | 7.69 (0.02) |
Kingspan | 43 | 11.20 (0.00) | 15.27 (0.00) | 44 | 13.51 (0.00) | 14.82 (0.00) | 22 | 0.31 (0.58) | 6.30 (0.04) | 29 | 0.71 (0.40) | 8.96 (0.01) | 21 | 0.40 (0.53) | 2.22 (0.33) | 27 | 0.36 (0.55) | 4.73 (0.09) |
Boralex | 52 | 23.11 (0.00) | 23.74 (0.00) | 50 | 21.68 (0.00) | 21.68 (0.00) | 27 | 0.42 (0.51) | 4.63 (0.10) | 26 | 0.07 (0.80) | 1.25 (0.54) | 28 | 0.64 (0.42) | 1.56 (0.46) | 31 | 1.89 (0.17) | 2.54 (0.28) |
Nibe | 30 | 1.07 (0.30) | 8.93 (0.01) | 36 | 5.25 (0.02) | 7.69 (0.02) | 21 | 0.59 (0.44) | 6.94 (0.03) | 27 | 0.21 (0.65) | 9.28 (0.01) | 21 | 0.40 (0.53) | 2.22 (0.33) | 26 | 0.16 (0.69) | 4.80 (0.09) |
Exxon Mobil | 58 | 32.85 (0.00) | 36.45 (0.00) | 42 | 11.14 (0.00) | 12.64 (0.00) | 46 | 14.78 (0.00) | 15.94 (0.00) | 32 | 1.99 (0.16) | 2.60 (0.27) | 42 | 11.14 (0.00) | 12.64 (0.00) | 37 | 6.10 (0.01) | 7.26 (0.03) |
Chevron | 54 | 26.20 (0.00) | 28.29 (0.00) | 40 | 8.97 (0.00) | 10.33 (0.01) | 49 | 18.75 (0.00) | 21.64 (0.00) | 22 | 0.31 (0.58) | 6.30 (0.04) | 47 | 17.40 (0.00) | 19.28 (0.00) | 37 | 6.10 (0.01) | 7.26 (0.03) |
Total S.A. | 49 | 18.75 (0.88) | 18.75 (0.00) | 40 | 8.97 (0.00) | 9.12 (0.01) | 38 | 6.20 (0.01) | 6.45 (0.04) | 28 | 0.42 (0.51) | 4.63 (0.10) | 39 | 7.96 (0.00) | 8.15 (0.02) | 33 | 3.05 (0.08) | 3.97 (0.14) |
Schlumberger | 38 | 6.20 (0.01) | 8.40 (0.00) | 38 | 7.01 (0.01) | 8.23 (0.01) | 29 | 0.71 (0.40) | 1.58 (0.45) | 28 | 0.42 (0.51) | 4.63 (0.10) | 29 | 0.99 (0.32) | 1.70 (0.43) | 27 | 0.36 (0.55) | 0.98 (0.61) |
AR(1)-APARCH(1,1) | ||||||||||||||||||
Normal | Skew-Normal | t-Student | Skew-t | GED | SGED | |||||||||||||
v | Kupiec Test | Ind. Test | v | Kupiec Test | Ind. Test | v | Kupiec Test | Ind. Test | v | Kupiec Test | Ind. Test | v | Kupiec Test | Ind. Test | v | Kupiec Test | Ind. Test | |
Epistar | 55 | 27.81 (0.00) | 29.76 (0.00) | 44 | 12.20 (0.00) | 12.44 (0.00) | 38 | 6.20 (0.01) | 8.40 (0.02) | 42 | 10.10 (0.00) | 14.40 (0.00) | 33 | 3.05 (0.08) | 6.04 (0.05) | 28 | 0.64 (0.42) | 1.56 (0.46) |
Kingspan | 43 | 11.20 (0.00) | 11.29 (0.00) | 41 | 9.05 (0.00) | 9.31 (0.00) | 21 | 0.59 (0.44) | 2.46 (0.29) | 28 | 0.42 (0.51) | 4.63 (0.10) | 27 | 0.36 (0.55) | 4.73 (0.09) | 24 | 0.02 (0.89) | 0.00 (0.99) |
Boralex | 40 | 8.05 (0.00) | 8.22 (0.02) | 45 | 11.20 (0.00) | 13.13 (0.00) | 22 | 0.31 (0.58) | 6.30 (0.04) | 24 | 0.02 (0.89) | 0.00 (0.99) | 24 | 0.02 (0.89) | 0.00 (0.99) | 24 | 0.02 (0.89) | 0.00 (0.99) |
Nibe | 29 | 0.71 (0.40) | 4.67 (0.10) | 32 | 1.99 (0.16) | 5.51 (0.08) | 25 | 0.00 (0.95) | 1.30 (0.52) | 39 | 7.10 (0.01) | 15.92 (0.00) | 22 | 0.31 (0.58) | 4.63 (0.10) | 28 | 0.64 (0.42) | 4.73 (0.09) |
Exxon Mobil | 56 | 29.45 (0.00) | 30.23 (0.00) | 43 | 11.20 (0.00) | 12.41 (0.00) | 46 | 14.78 (0.00) | 16.82 (0.00) | 28 | 0.42 (0.51) | 4.63 (0.10) | 42 | 11.14 (0.00) | 12.64 (0.00) | 44 | 13.51 (0.00) | 14.82 (0.00) |
Chevron | 50 | 20.16 (0.00) | 20.16 (0.00) | 46 | 14.78 (0.00) | 16.01 (0.00) | 38 | 6.20 (0.01) | 6.45 (0.04) | 20 | 0.97 (0.32) | 3.56 (0.08) | 44 | 13.51 (0.00) | 14.82 (0.00) | 47 | 17.40 (0.00) | 19.28 (0.00) |
Total S.A. | 51 | 21.61 (0.00) | 22.32 (0.00) | 40 | 8.97 (0.00) | 11.46 (0.01) | 33 | 2.54 (0.11) | 5.52 (0.05) | 25 | 0.00 (0.95) | 1.23 (0.59) | 38 | 6.20 (0.01) | 8.40 (0.02) | 37 | 6.10 (0.01) | 7.26 (0.03) |
Schlumberger | 41 | 9.05 (0.00) | 9.31 (0.00) | 39 | 7.10 (0.01) | 8.35 (0.00) | 25 | 0.00 (0.95) | 1.23 (0.59) | 26 | 0.07 (0.80) | 1.25 (0.54) | 28 | 0.42 (0.51) | 4.63 (0.10) | 27 | 0.21 (0.65) | 2.60 (0.27) |
AR(1)-GARCH(1,1) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Normal | Skew-Normal | t-Student | Skew-t | GED | SGED | |||||||||||||
v | Kupiec Test | Ind. Test | v | Kupiec Test | Ind. Test | v | Kupiec Test | Ind. Test | v | Kupiec Test | Ind. Test | v | Kupiec Test | Ind. Test | v | Kupiec Test | Ind. Test | |
Epistar | 81 | 5.60 (0.02) | 8.98 (0.01) | 79 | 5.62 (0.02) | 9.16 (0.01) | 66 | 0.29 (0.59) | 1.05 (0.58) | 77 | 3.57 (0.06) | 7.73 (0.02) | 74 | 3.12 (0.08) | 4.26 (0.12) | 78 | 5.07 (0.02) | 7.09 (0.03) |
Kingspan | 73 | 1.98 (0.16) | 3.33 (0.19) | 84 | 8.77 (0.00) | 10.07 (0.01) | 61 | 0.01 (0.92) | 1.23 (0.54) | 67 | 0.44 (0.51) | 1.13 (0.57) | 61 | 0.02 (0.90) | 1.15 (0.56) | 64 | 0.27 (0.60) | 2.67 (0.26) |
Boralex | 74 | 2.34 (0.13) | 7.13 (0.03) | 74 | 3.12 (0.08) | 10.02 (0.01) | 62 | 0.00 (0.98) | 1.12 (0.57) | 63 | 0.02 (0.87) | 1.05 (0.59) | 53 | 0.87 (0.35) | 1.38 (0.50) | 55 | 0.44 (0.51) | 0.83 (0.66) |
Nibe | 61 | 0.01 (0.92) | 0.16 (0.92) | 67 | 0.81 (0.37) | 1.42 (0.49) | 57 | 0.39 (0.53) | 0.71 (0.70) | 78 | 4.04 (0.05) | 6.22 (0.04) | 51 | 1.46 (0.23) | 2.11 (0.35) | 63 | 0.15 (0.70) | 0.22 (0.89) |
Exxon Mobil | 91 | 12.41 (0.00) | 13.17 (0.00) | 79 | 5.62 (0.02) | 6.32 (0.04) | 81 | 5.60 (0.02) | 5.79 (0.06) | 64 | 0.08 (0.78) | 0.15 (0.93) | 79 | 5.62 (0.02) | 5.68 (0.06) | 72 | 2.32 (0.13) | 2.33 (0.31) |
Chevron | 87 | 9.39 (0.00) | 9.84 (0.01) | 70 | 1.62 (0.20) | 2.31 (0.31) | 79 | 4.53 (0.03) | 4.66 (0.10) | 43 | 6.54 (0.01) | 6.62 (0.04) | 85 | 9.48 (0.00) | 9.89 (0.01) | 64 | 0.27 (0.60) | 0.63 (0.73) |
Total S.A. | 80 | 5.05 (0.02) | 6.40 (0.04) | 78 | 5.07 (0.02) | 6.34 (0.04) | 72 | 1.65 (0.20) | 2.40 (0.30) | 52 | 1.68 (0.20) | 1.68 (0.43) | 72 | 2.32 (0.13) | 3.14 (0.21) | 66 | 0.60 (0.44) | 1.06 (0.59) |
Schlumberger | 66 |