# El Niño, La Niña, and the Forecastability of the Realized Variance of Heating Oil Price Movements

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## Abstract

**:**

## 1. Introduction

## 2. Data

## 3. The HAR–RV Model

## 4. Empirical Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Code Availability

## Appendix A

Heating Oil Returns | Heating Oil Volatility (Squared Returns) | |||||||
---|---|---|---|---|---|---|---|---|

Spot | Futures | Spot | Futures | |||||

Quantile | El Niño | La Niña | El Niño | La Niña | El Niño | La Niña | El Niño | La Niña |

0.05 | 1.89 * | 1.98 ** | 2.00 ** | 2.29 ** | 1.70 * | 1.84 * | 2.21 ** | 2.24 ** |

0.10 | 2.71 *** | 2.61 *** | 3.40 *** | 3.23 *** | 2.63 *** | 2.58 *** | 3.26 *** | 3.07 *** |

0.15 | 3.82 *** | 3.51 *** | 4.32 *** | 4.33 *** | 3.57 *** | 3.40 *** | 4.07 *** | 4.08 *** |

0.20 | 4.44 *** | 4.35 *** | 4.78 *** | 4.86 *** | 4.08 *** | 3.91 *** | 4.81 *** | 5.10 *** |

0.25 | 4.66 *** | 4.41 *** | 5.77 *** | 5.39 *** | 4.67 *** | 4.51 *** | 5.36 *** | 5.11 *** |

0.30 | 4.93 *** | 5.08 *** | 5.80 *** | 5.50 *** | 4.79 *** | 4.84 *** | 5.75 *** | 5.95 *** |

0.35 | 5.19 *** | 5.21 *** | 5.86 *** | 5.90 *** | 5.08 *** | 5.39 *** | 6.10 *** | 6.19 *** |

0.40 | 5.22 *** | 5.22 *** | 5.86 *** | 6.03 *** | 5.26 *** | 5.34 *** | 5.95 *** | 6.01 *** |

0.45 | 5.26 *** | 5.28 *** | 5.91 *** | 5.84 *** | 5.38 *** | 5.39 *** | 5.84 *** | 6.03 *** |

0.50 | 5.53 *** | 5.40 *** | 5.98 *** | 5.90 *** | 5.38 *** | 5.31 *** | 5.93 *** | 5.81 *** |

0.55 | 5.09 *** | 5.25 *** | 5.91 *** | 5.62 *** | 5.09 *** | 5.09 *** | 5.87 *** | 5.73 *** |

0.60 | 4.86 *** | 5.03 *** | 5.59 *** | 5.43 *** | 4.91 *** | 4.88 *** | 5.50 *** | 5.34 *** |

0.65 | 4.71 *** | 4.87 *** | 5.16 *** | 5.31 *** | 4.66 *** | 4.86 *** | 5.48 *** | 5.30 *** |

0.70 | 4.15 *** | 4.45 *** | 4.86 *** | 5.22 *** | 4.26 *** | 4.64 *** | 5.12 *** | 5.13 *** |

0.75 | 3.96 *** | 4.17 *** | 4.57 *** | 4.90 *** | 4.00 *** | 4.17 *** | 4.66 *** | 5.10 *** |

0.80 | 3.59 *** | 3.72 *** | 4.28 *** | 4.45 *** | 3.48 *** | 3.76 *** | 4.14 *** | 4.23 *** |

0.85 | 3.09 *** | 3.42 *** | 3.55 *** | 3.57 *** | 3.02 *** | 3.32 *** | 3.61 *** | 3.66 *** |

0.90 | 2.79 *** | 2.87 *** | 2.85 *** | 3.09 *** | 2.69 *** | 2.87 *** | 3.13 *** | 3.21 *** |

0.95 | 2.22 ** | 1.98 ** | 2.24 ** | 2.25 ** | 2.06 ** | 2.03 ** | 2.10 ** | 2.12 ** |

**Figure A1.**Results for the HARQ-RV Model (Futures; Lin-Lin Loss Function). Note: This figure reports the out-of-sample relative loss criterion for a lin-lin loss function (L1) and an extended HARQ-RV models that features either El Niño or La Niña phases as an additional predictor. The baseline model is the benchmark HARQ-RV model. White spaces indicate areas where the out-of-sample relative loss criterion takes on negative values (the baseline model performs better than the extended model). The rolling-estimation window is varied from 48, 49, 50, … to 120 observations. The results are based on the SOI data. The parameter h denotes the forecast horizon (in months).

**Figure A2.**Results for the HARQ-RV Model (Futures; Quad-Quad Loss Function). Note: This figure reports the out-of-sample relative loss criterion for a quad-quad loss function (L2) and an extended HARQ-RV models that features either El Niño or La Niña phases as an additional predictor. The baseline model is the benchmark HARQ-RV model. White spaces indicate areas where the out-of-sample relative loss criterion takes on negative values (the baseline model performs better than the extended model). The rolling-estimation window is varied from 48, 49, 50, … to 120 observations. The results are based on the SOI data. The parameter h denotes the forecast horizon (in months).

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**Figure 1.**The Spot and Futures Data. Note: The figure shows the daily spot und futures price data (in US dollars per gallon) used to construct the monthly realized variance of movements of the price of heating oil.

**Figure 3.**Results for the HARQ–RV Model (Spot; Lin–Lin Loss Function). Note: This figure reports the out-of-sample relative loss criterion for a lin–lin loss function (L1) and an extended HARQ–RV models that features either El Niño or La Niña phases as an additional predictor. The baseline model is the benchmark HARQ–RV model. White spaces indicate areas where the out-of-sample relative loss criterion takes on negative values (the baseline model performs better than the extended model). The rolling estimation window is varied from 48, 49, 50, … to 120 observations. The results are based on the EQSOI data. The parameter h denotes the forecast horizon (in months).

**Figure 4.**Results for the HARQ–RV Model (Spot; Quad–Quad Loss Function). Note: This figure reports the out-of-sample relative loss criterion for a quad-quad loss function (L2) and an extended HARQ–RV models that features either El Niño or La Niña phases as an additional predictor. The baseline model is the benchmark HARQ–RV model. White spaces indicate areas where the out-of-sample relative loss criterion takes on negative values (the baseline model performs better than the extended model). The rolling estimation window is varied from 48, 49, 50, … to 120 observations. The results are based on the EQSOI data. The parameter h denotes the forecast horizon (in months).

Statistic | Spot | Futures |
---|---|---|

Mean | 0.0002 | 0.0002 |

Standard deviation | 0.0246 | 0.0229 |

Skewness | −1.4094 | −1.1954 |

Kurtosis | 37.1312 | 21.3331 |

AR(1) | 0.0002 | −0.0236 |

Panel A: Spot RV (El Niño) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.1766 | 0.1141 | 0.1336 | 0.0135 | 0.4691 | 0.1135 | 0.1155 |

Window length = 60 | 0.0993 | 0.0354 | 0.0606 | 0.0319 | 0.0219 | 0.1080 | 0.2243 |

Window length = 72 | 0.0797 | 0.0462 | 0.0585 | 0.0376 | 0.0772 | 0.4138 | 0.7867 |

Window length = 96 | 0.1459 | 0.0943 | 0.0916 | 0.0875 | 0.1299 | 0.7561 | 0.8137 |

Window length = 120 | 0.1027 | 0.0960 | 0.1349 | 0.1423 | 0.1578 | 0.6694 | 0.7623 |

Panel B: Spot RV (La Niña) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.0355 | 0.0078 | 0.0374 | 0.0180 | 0.3356 | 0.6720 | 0.0502 |

Window length = 60 | 0.0405 | 0.0581 | 0.0284 | 0.0096 | 0.0008 | 0.0107 | 0.0013 |

Window length = 72 | 0.0813 | 0.0904 | 0.0606 | 0.0290 | 0.0054 | 0.0020 | 0.0020 |

Window length = 96 | 0.1410 | 0.1247 | 0.1048 | 0.0536 | 0.0394 | 0.0299 | 0.0172 |

Window length = 120 | 0.1553 | 0.1632 | 0.1706 | 0.1034 | 0.0822 | 0.1033 | 0.0734 |

Panel C: Spot RV (El Niño and La Niña) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.0191 | 0.0017 | 0.0099 | 0.0074 | 0.4377 | 0.0695 | 0.0368 |

Window length = 60 | 0.0288 | 0.0457 | 0.0102 | 0.0046 | 0.0009 | 0.0397 | 0.0186 |

Window length = 72 | 0.0650 | 0.0729 | 0.0335 | 0.0206 | 0.0050 | 0.0177 | 0.0065 |

Window length = 96 | 0.1312 | 0.1145 | 0.0837 | 0.0487 | 0.0392 | 0.0052 | 0.0040 |

Window length = 120 | 0.1369 | 0.1375 | 0.1342 | 0.0931 | 0.0740 | 0.0298 | 0.0274 |

Panel D: Futures RV (El Niño) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.0221 | 0.0069 | 0.0159 | 0.0277 | 0.0232 | 0.0448 | 0.0685 |

Window length = 60 | 0.0459 | 0.0123 | 0.0222 | 0.0545 | 0.0683 | 0.0584 | 0.0658 |

Window length = 72 | 0.2770 | 0.0685 | 0.1112 | 0.1005 | 0.2046 | 0.5192 | 0.7192 |

Window length = 96 | 0.4088 | 0.0964 | 0.1847 | 0.3417 | 0.6243 | 0.9867 | 0.9144 |

Window length = 120 | 0.3303 | 0.0517 | 0.0616 | 0.0122 | 0.0024 | 0.3246 | 0.4821 |

Panel E: Futures RV (La Niña) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.1697 | 0.0652 | 0.1175 | 0.3629 | 0.0340 | 0.0737 | 0.0333 |

Window length = 60 | 0.0167 | 0.0266 | 0.0168 | 0.0321 | 0.0024 | 0.0239 | 0.0072 |

Window length = 72 | 0.2276 | 0.0947 | 0.0545 | 0.0398 | 0.0039 | 0.0022 | 0.0015 |

Window length = 96 | 0.1098 | 0.0800 | 0.0501 | 0.0717 | 0.1550 | 0.2296 | 0.0582 |

Window length = 120 | 0.1188 | 0.1280 | 0.0809 | 0.0655 | 0.0411 | 0.0700 | 0.0647 |

Panel F: Futures RV (El Niño and La Niña) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

tabularnewline Window length = 48 | 0.0096 | 0.0008 | 0.0024 | 0.0346 | 0.0091 | 0.0245 | 0.0228 |

Window length = 60 | 0.0119 | 0.0060 | 0.0114 | 0.0419 | 0.0155 | 0.0106 | 0.0032 |

Window length = 72 | 0.1960 | 0.0479 | 0.0613 | 0.0299 | 0.0022 | 0.0016 | 0.0021 |

Window length = 96 | 0.1563 | 0.0472 | 0.0487 | 0.0365 | 0.1722 | 0.2836 | 0.0678 |

Window length = 120 | 0.1839 | 0.0555 | 0.0558 | 0.0175 | 0.0200 | 0.0558 | 0.0383 |

Panel A: Spot RV (El Niño) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.0304 | 0.0238 | 0.0682 | 0.1023 | 0.0544 | 0.1206 | 0.1089 |

Window length = 60 | 0.1012 | 0.0267 | 0.0837 | 0.1018 | 0.0648 | 0.0804 | 0.1197 |

Window length = 72 | 0.0803 | 0.0304 | 0.0780 | 0.0976 | 0.1459 | 0.3367 | 0.5523 |

Window length = 96 | 0.0703 | 0.0373 | 0.0717 | 0.1230 | 0.1610 | 0.6337 | 0.6159 |

Window length = 120 | 0.0606 | 0.0432 | 0.0673 | 0.0956 | 0.1230 | 0.8169 | 0.8414 |

Panel B: Spot RV (La Niña) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.0320 | 0.0281 | 0.0073 | 0.0089 | 0.0095 | 0.0692 | 0.0320 |

Window length = 60 | 0.0131 | 0.0300 | 0.0126 | 0.0045 | 0.0002 | 0.0160 | 0.0050 |

Window length = 72 | 0.0568 | 0.0740 | 0.0551 | 0.0103 | 0.0001 | 0.0020 | 0.0011 |

Window length = 96 | 0.1485 | 0.1622 | 0.1374 | 0.0354 | 0.0188 | 0.0199 | 0.0107 |

Window length = 120 | 0.1913 | 0.1931 | 0.2123 | 0.1376 | 0.1327 | 0.1325 | 0.0926 |

Panel C: Spot RV (El Niño and La Niña) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.0112 | 0.0079 | 0.0061 | 0.0038 | 0.0299 | 0.0443 | 0.0160 |

Window length = 60 | 0.0071 | 0.0139 | 0.0070 | 0.0128 | 0.0119 | 0.0146 | 0.0177 |

Window length = 72 | 0.0327 | 0.0403 | 0.0235 | 0.0057 | 0.0011 | 0.0113 | 0.0119 |

Window length = 96 | 0.1179 | 0.1284 | 0.0959 | 0.0249 | 0.0188 | 0.0223 | 0.0129 |

Window length = 120 | 0.1702 | 0.1438 | 0.1346 | 0.1113 | 0.1212 | 0.0938 | 0.0600 |

Panel D: Futures RV (El Niño) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.0980 | 0.0106 | 0.0207 | 0.0503 | 0.0400 | 0.0463 | 0.0825 |

Window length = 60 | 0.1202 | 0.0033 | 0.0256 | 0.0819 | 0.0926 | 0.0887 | 0.1176 |

Window length = 72 | 0.1844 | 0.0219 | 0.0589 | 0.0471 | 0.1017 | 0.3484 | 0.5596 |

Window length = 96 | 0.2597 | 0.0470 | 0.1493 | 0.2718 | 0.3910 | 0.8508 | 0.6995 |

Window length = 120 | 0.3717 | 0.0831 | 0.0858 | 0.0601 | 0.0327 | 0.5982 | 0.6202 |

Panel E: Futures RV (La Niña) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.0241 | 0.0187 | 0.0279 | 0.0936 | 0.0190 | 0.0655 | 0.0203 |

Window length = 60 | 0.0086 | 0.0208 | 0.0210 | 0.0144 | 0.0027 | 0.0264 | 0.0079 |

Window length = 72 | 0.0913 | 0.0670 | 0.0728 | 0.0269 | 0.0048 | 0.0200 | 0.0191 |

Window length = 96 | 0.0665 | 0.0748 | 0.0774 | 0.0743 | 0.0769 | 0.0958 | 0.0561 |

Window length = 120 | 0.1264 | 0.1566 | 0.1785 | 0.0965 | 0.0917 | 0.1095 | 0.0891 |

Panel F: Futures RV (El Niño and La Niña) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.0295 | 0.0021 | 0.0043 | 0.0224 | 0.0181 | 0.0194 | 0.0095 |

Window length = 60 | 0.0161 | 0.0039 | 0.0069 | 0.0206 | 0.0233 | 0.0131 | 0.0080 |

Window length = 72 | 0.0787 | 0.0252 | 0.0284 | 0.0067 | 0.0063 | 0.0310 | 0.0379 |

Window length = 96 | 0.0944 | 0.0399 | 0.0590 | 0.0478 | 0.0857 | 0.1089 | 0.0552 |

Window length = 120 | 0.1770 | 0.0821 | 0.1001 | 0.0670 | 0.0874 | 0.0932 | 0.0593 |

Panel A: Spot RV (El Niño) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.1606 | 0.0285 | 0.0333 | 0.0122 | 0.5127 | 0.0322 | 0.0797 |

Window length = 60 | 0.0204 | 0.0010 | 0.0008 | 0.0021 | 0.0056 | 0.1035 | 0.3536 |

Window length = 72 | 0.0543 | 0.0156 | 0.0051 | 0.0096 | 0.0049 | 0.2092 | 0.1960 |

Window length = 96 | 0.1470 | 0.0958 | 0.0437 | 0.0520 | 0.0849 | 0.9016 | 0.2992 |

Window length = 120 | 0.1672 | 0.1758 | 0.1509 | 0.1140 | 0.2000 | 0.9645 | 0.7523 |

Panel B: Spot RV (La Niña) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.0675 | 0.0549 | 0.1364 | 0.0119 | 0.1180 | 0.3431 | 0.0071 |

Window length = 60 | 0.0105 | 0.0216 | 0.0041 | 0.0032 | 0.0022 | 0.0001 | 0.0004 |

Window length = 72 | 0.0638 | 0.0436 | 0.0343 | 0.0316 | 0.0098 | 0.0002 | 0.0051 |

Window length = 96 | 0.1169 | 0.0981 | 0.0692 | 0.0588 | 0.0450 | 0.0299 | 0.0276 |

Window length = 120 | 0.0656 | 0.1245 | 0.1047 | 0.0400 | 0.0344 | 0.0409 | 0.0232 |

Panel C: Spot RV (El Niño and La Niña) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.2468 | 0.0192 | 0.0743 | 0.0182 | 0.1948 | 0.0011 | 0.0038 |

Window length = 60 | 0.0122 | 0.0106 | 0.0009 | 0.0032 | 0.0011 | 0.0004 | 0.0003 |

Window length = 72 | 0.0545 | 0.0303 | 0.0074 | 0.0156 | 0.0052 | 0.0001 | 0.0016 |

Window length = 96 | 0.1256 | 0.0951 | 0.0608 | 0.0538 | 0.0426 | 0.0194 | 0.0227 |

Window length = 120 | 0.1051 | 0.1241 | 0.0890 | 0.0628 | 0.0356 | 0.0147 | 0.0193 |

Panel D: Futures RV (El Niño) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.1421 | 0.0776 | 0.0139 | 0.0011 | 0.0238 | 0.0411 | 0.0397 |

Window length = 60 | 0.0677 | 0.0075 | 0.0009 | 0.0013 | 0.0115 | 0.0147 | 0.0162 |

Window length = 72 | 0.1734 | 0.0596 | 0.0078 | 0.0053 | 0.0188 | 0.0244 | 0.0272 |

Window length = 96 | 0.2947 | 0.1487 | 0.0414 | 0.1266 | 0.6690 | 0.9802 | 0.7344 |

Window length = 120 | 0.1104 | 0.0412 | 0.0062 | 0.0052 | 0.0003 | 0.1895 | 0.3012 |

Panel E: Futures RV (La Niña) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.4347 | 0.0727 | 0.2163 | 0.3099 | 0.0625 | 0.1152 | 0.0574 |

Window length = 60 | 0.0861 | 0.0056 | 0.0095 | 0.0028 | 0.0070 | 0.0143 | 0.0035 |

Window length = 72 | 0.2762 | 0.0896 | 0.0600 | 0.0279 | 0.0089 | 0.0046 | 0.0013 |

Window length = 96 | 0.0469 | 0.0359 | 0.0665 | 0.0652 | 0.1159 | 0.0520 | 0.0087 |

Window length = 120 | 0.0569 | 0.0648 | 0.0742 | 0.0467 | 0.0120 | 0.0208 | 0.0164 |

Panel F: Futures RV (El Niño and La Niña) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.2481 | 0.1042 | 0.0253 | 0.0275 | 0.0129 | 0.0205 | 0.0102 |

Window length = 60 | 0.0289 | 0.0012 | 0.0005 | 0.0006 | 0.0028 | 0.0036 | 0.0017 |

Window length = 72 | 0.1368 | 0.0348 | 0.0034 | 0.0040 | 0.0037 | 0.0015 | 0.0005 |

Window length = 96 | 0.0787 | 0.0351 | 0.0243 | 0.0627 | 0.2061 | 0.1375 | 0.0198 |

Window length = 120 | 0.0986 | 0.0453 | 0.0106 | 0.0113 | 0.0083 | 0.0251 | 0.0204 |

Panel A: EQSOI | |||

results.table | El Niño | La Niña | Both |

RMSFE / Spot | 0.9954 | 1.0137 | 1.0124 |

RMSFE / Futures | 1.0012 | 1.0364 | 1.0284 |

MAFE / Spot | 1.0057 | 1.0524 | 1.0680 |

MAFE / Futures | 1.0070 | 1.0392 | 1.0411 |

Panel B: SOI | |||

results.table | El Niño | La Niña | Both |

RMSFE / Spot | 1.0026 | 1.0474 | 1.0420 |

RMSFE / Futures | 1.0130 | 1.0396 | 1.0333 |

MAFE / Spot | 1.0080 | 1.0621 | 1.0638 |

MAFE / Futures | 1.0178 | 1.0388 | 1.0384 |

Panel A: Futures Upside RV (El Niño) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.0802 | 0.0083 | 0.0436 | 0.0651 | 0.0199 | 0.0351 | 0.0661 |

Window length = 60 | 0.2215 | 0.0261 | 0.0388 | 0.0385 | 0.0540 | 0.0393 | 0.0463 |

Window length = 72 | 0.2874 | 0.0776 | 0.0740 | 0.0650 | 0.0872 | 0.3049 | 0.5776 |

Window length = 96 | 0.6678 | 0.0958 | 0.2408 | 0.3105 | 0.3256 | 0.8476 | 0.7553 |

Window length = 120 | 0.4435 | 0.0650 | 0.1044 | 0.1062 | 0.0232 | 0.6889 | 0.6491 |

Panel B: Futures Upside RV (La Niña) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.1360 | 0.0536 | 0.1111 | 0.1723 | 0.0265 | 0.0649 | 0.0304 |

Window length = 60 | 0.0655 | 0.0114 | 0.0059 | 0.0055 | 0.0026 | 0.0142 | 0.0020 |

Window length = 72 | 0.2895 | 0.0650 | 0.0326 | 0.0231 | 0.0081 | 0.0339 | 0.0170 |

Window length = 96 | 0.1860 | 0.0451 | 0.0337 | 0.0583 | 0.1715 | 0.1808 | 0.0711 |

Window length = 120 | 0.1357 | 0.1055 | 0.0864 | 0.1136 | 0.1010 | 0.1301 | 0.0827 |

Panel C: Futures Upside RV (El Niño and La Niña) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.0533 | 0.0032 | 0.0102 | 0.0393 | 0.0106 | 0.0134 | 0.0128 |

Window length = 60 | 0.1807 | 0.0060 | 0.0114 | 0.0171 | 0.0201 | 0.0063 | 0.0016 |

Window length = 72 | 0.2214 | 0.0263 | 0.0364 | 0.0186 | 0.0066 | 0.0472 | 0.0292 |

Window length = 96 | 0.2847 | 0.0135 | 0.0326 | 0.0229 | 0.1442 | 0.1936 | 0.0782 |

Window length = 120 | 0.3162 | 0.0477 | 0.0733 | 0.0343 | 0.0821 | 0.1282 | 0.0658 |

Panel D: Futures Downside RV (El Niño) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.2710 | 0.0041 | 0.0225 | 0.0106 | 0.0086 | 0.0434 | 0.0574 |

Window length = 60 | 0.0560 | 0.0106 | 0.0298 | 0.0224 | 0.0411 | 0.0454 | 0.0393 |

Window length = 72 | 0.2463 | 0.1200 | 0.2237 | 0.2001 | 0.3406 | 0.6335 | 0.7758 |

Window length = 96 | 0.2147 | 0.1212 | 0.2447 | 0.3576 | 0.5843 | 0.9916 | 0.9729 |

Window length = 120 | 0.1684 | 0.0538 | 0.0585 | 0.0428 | 0.1032 | 0.0623 | 0.3510 |

Panel E: Futures Downside RV (La Niña) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.2406 | 0.1667 | 0.2421 | 0.4474 | 0.0424 | 0.0513 | 0.0483 |

Window length = 60 | 0.0164 | 0.0844 | 0.0665 | 0.0249 | 0.0008 | 0.0055 | 0.0027 |

Window length = 72 | 0.2914 | 0.1460 | 0.1349 | 0.0762 | 0.0065 | 0.0006 | 0.0004 |

Window length = 96 | 0.0882 | 0.1237 | 0.1200 | 0.0665 | 0.1919 | 0.3756 | 0.1083 |

Window length = 120 | 0.1228 | 0.1277 | 0.1302 | 0.0547 | 0.0141 | 0.0258 | 0.0377 |

Panel F: Futures Downside RV (El Niño and La Niña) | |||||||

Forecast horizon | h = 1 | h = 3 | h = 6 | h = 12 | h = 24 | h = 36 | h = 48 |

Window length = 48 | 0.1381 | 0.0011 | 0.0101 | 0.0317 | 0.0019 | 0.0203 | 0.0201 |

Window length = 60 | 0.0170 | 0.0359 | 0.0430 | 0.0298 | 0.0035 | 0.0041 | 0.0013 |

Window length = 72 | 0.3039 | 0.1486 | 0.1882 | 0.0822 | 0.0046 | 0.0001 | 0.0002 |

Window length = 96 | 0.1072 | 0.0984 | 0.1174 | 0.0554 | 0.2025 | 0.4249 | 0.1153 |

Window length = 120 | 0.1366 | 0.0746 | 0.0512 | 0.0230 | 0.0147 | 0.0111 | 0.0199 |

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## Share and Cite

**MDPI and ACS Style**

Balcilar, M.; Bouri, E.; Gupta, R.; Pierdzioch, C.
El Niño, La Niña, and the Forecastability of the Realized Variance of Heating Oil Price Movements. *Sustainability* **2021**, *13*, 7987.
https://doi.org/10.3390/su13147987

**AMA Style**

Balcilar M, Bouri E, Gupta R, Pierdzioch C.
El Niño, La Niña, and the Forecastability of the Realized Variance of Heating Oil Price Movements. *Sustainability*. 2021; 13(14):7987.
https://doi.org/10.3390/su13147987

**Chicago/Turabian Style**

Balcilar, Mehmet, Elie Bouri, Rangan Gupta, and Christian Pierdzioch.
2021. "El Niño, La Niña, and the Forecastability of the Realized Variance of Heating Oil Price Movements" *Sustainability* 13, no. 14: 7987.
https://doi.org/10.3390/su13147987