Out-of-sample forecast evaluation [Non-nested models]
| Oil risks (brent versus WTI) | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Global | Europe | US | Asia | Solar | Wind | |||||||
| RMSE | Brent | WTI | Brent | WTI | Brent | WTI | Brent | WTI | Brent | WTI | Brent | WTI |
| h = 10 | 0.919 | 0.917 | 1.278 | 1.276 | 1.148 | 1.145 | 1.297 | 1.296 | 1.761 | 1.759 | 1.175 | 1.167 |
| h = 30 | 0.922 | 0.920 | 1.274 | 1.272 | 1.147 | 1.145 | 1.295 | 1.294 | 1.758 | 1.757 | 1.175 | 1.166 |
| h = 60 | 1.042 | 1,038 | 1.270 | 1.268 | 1.144 | 1.142 | 1.288 | 1.287 | 1.758 | 1.757 | 1.180 | 1.173 |
| h = 120 | 1.104 | 1.100 | 1.258 | 1.255 | 1.135 | 1.133 | 1.279 | 1.278 | 1.752 | 1.750 | 1.170 | 1.162 |
| MDM | Brent | WTI | Brent | WTI | Brent | WTI | Brent | WTI | Brent | WTI | Brent | WTI |
| h = 10 | −1.252 | −1.211 | −1.748** | −0.715 | −0.659 | −1.541* | ||||||
| h = 30 | −1.329* | −1.219 | −1.766** | −0.709 | −0.662 | −1.512* | ||||||
| h = 60 | −1.424* | −1.178 | −1.609* | −0.634 | −0.527 | −1.435* | ||||||
| h = 120 | −1.062 | −1.206 | −1.579* | −0.824 | −0.529 | −1.352* | ||||||
| Oil risks (brent versus WTI) | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Global | Europe | US | Asia | Solar | Wind | |||||||
| h = 10 | 0.919 | 0.917 | 1.278 | 1.276 | 1.148 | 1.145 | 1.297 | 1.296 | 1.761 | 1.759 | 1.175 | 1.167 |
| h = 30 | 0.922 | 0.920 | 1.274 | 1.272 | 1.147 | 1.145 | 1.295 | 1.294 | 1.758 | 1.757 | 1.175 | 1.166 |
| h = 60 | 1.042 | 1,038 | 1.270 | 1.268 | 1.144 | 1.142 | 1.288 | 1.287 | 1.758 | 1.757 | 1.180 | 1.173 |
| h = 120 | 1.104 | 1.100 | 1.258 | 1.255 | 1.135 | 1.133 | 1.279 | 1.278 | 1.752 | 1.750 | 1.170 | 1.162 |
| h = 10 | −1.252 | −1.211 | −1.748** | −0.715 | −0.659 | −1.541* | ||||||
| h = 30 | −1.329* | −1.219 | −1.766** | −0.709 | −0.662 | −1.512* | ||||||
| h = 60 | −1.424* | −1.178 | −1.609* | −0.634 | −0.527 | −1.435* | ||||||
| h = 120 | −1.062 | −1.206 | −1.579* | −0.824 | −0.529 | −1.352* | ||||||
| Climate risk (EER versus CPU) | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Global | Europe | US | Asia | Solar | Wind | |||||||
| RMSE | EER | CPU | EER | CPU | EER | CPU | EER | CPU | EER | CPU | EER | CPU |
| h = 1 | 4.373 | 4.387 | 4.631 | 4.681 | 3.785 | 3.727 | 6.338 | 6.417 | 8.234 | 7.778 | 5.421 | 5.335 |
| h = 2 | 4.393 | 4.394 | 4.655 | 4.662 | 3.771 | 3.725 | 6.316 | 6.396 | 8.218 | 7.746 | 5.394 | 5.355 |
| h = 3 | 5.072 | 5.057 | 4.880 | 5.056 | 4.227 | 4.372 | 6.539 | 6.801 | 8.502 | 8.190 | 5.360 | 5.304 |
| h = 4 | 5.045 | 5.030 | 4.861 | 5.054 | 4.220 | 4.352 | 6.512 | 6.797 | 8.465 | 8.162 | 5.312 | 5.257 |
| MDM | EER | CPU | EER | CPU | EER | CPU | EER | CPU | EER | CPU | EER | CPU |
| h = 1 | 0.134 | 0.470 | −0.398 | 0.444 | −1.515* | −0.213 | ||||||
| h = 2 | 0.005 | 0.057 | −0.276 | 0.386 | −1.360 | −0.056 | ||||||
| h = 3 | −0.072 | 0.505 | 0.371 | 0.603 | −0.578 | −0.043 | ||||||
| h = 4 | −0.084 | 0.121 | 0.074 | 0.143 | −0.122 | −0.395 | ||||||
| Climate risk (EER versus CPU) | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Global | Europe | US | Asia | Solar | Wind | |||||||
| h = 1 | 4.373 | 4.387 | 4.631 | 4.681 | 3.785 | 3.727 | 6.338 | 6.417 | 8.234 | 7.778 | 5.421 | 5.335 |
| h = 2 | 4.393 | 4.394 | 4.655 | 4.662 | 3.771 | 3.725 | 6.316 | 6.396 | 8.218 | 7.746 | 5.394 | 5.355 |
| h = 3 | 5.072 | 5.057 | 4.880 | 5.056 | 4.227 | 4.372 | 6.539 | 6.801 | 8.502 | 8.190 | 5.360 | 5.304 |
| h = 4 | 5.045 | 5.030 | 4.861 | 5.054 | 4.220 | 4.352 | 6.512 | 6.797 | 8.465 | 8.162 | 5.312 | 5.257 |
| h = 1 | 0.134 | 0.470 | −0.398 | 0.444 | −1.515* | −0.213 | ||||||
| h = 2 | 0.005 | 0.057 | −0.276 | 0.386 | −1.360 | −0.056 | ||||||
| h = 3 | −0.072 | 0.505 | 0.371 | 0.603 | −0.578 | −0.043 | ||||||
| h = 4 | −0.084 | 0.121 | 0.074 | 0.143 | −0.122 | −0.395 | ||||||
Note(s): This table presents the results for the forecast evaluation of the oil risk-based models where either the realized volatility of WTI or Brent price serve as the predictor in the upper panel and the climate risk-based models where either the CPU or EER serve as the predictor in the lower panel. The forecast evaluation analysis compares each of the two oil risk-based models and the two climate risk-based models. The climate risk-based models and oil risk-based models are “non-nested” since for instance the model with Brent price volatility as the predictor cannot be seen as a subset of the model with WTI price volatility. Likewise, the models with CPU and EER are also non-nested, hence the choice of MDM forecast evaluation test. Negative and statistical significance of the MDM test indicates the better performance of the preferred models over the benchmark models. In both cases, the models with WTI are specified as the preferred of the oil risk models whereas the models with CPU are specified as the preferred of the two climate risk models. “*”, “**” and “***” indicates statistical significance at the 10%, 5% and 1% significance levels
Source(s): Table by authors
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