# A Note on Forecasting the Historical Realized Variance of Oil-Price Movements: The Role of Gold-to-Silver and Gold-to-Platinum Price Ratios

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## Abstract

**:**

## 1. Introduction

## 2. Data and Methodologies

_{t}is the ratio of either gold-to-silver prices or gold-to-platinum prices in their natural-logarithmic form, and acts as a proxy for risk at time t, and ${\epsilon}_{t+h}$ is the disturbance term. Our benchmark model is nested in Equation (1) and obtained by setting γ = 0.

_{t}). Because platinum data were only available from 1968:01 onward, the analysis associated with the logarithm of the gold-to-platinum price ratio (GP

_{t}) was conducted over a shorter sample period beginning at that month. Our analyses ended in 2021:03, which was the last available data point for all our variables at the time of writing this paper.

## 3. Empirical Results

_{R}− MSFE

_{UR})/MSFE

_{UR}, where T is the sample size, R is the length of the in-sample, h is the forecast horizon, and MSFE

_{R}and MSFE

_{UR}are MSFEs from the restricted (benchmark) and unrestricted (with the Ratio as predictor) models, respectively. A positive and significant MSE-F statistic indicates that the unrestricted model forecasts are statistically superior to those of the restricted model. As can be seen, the relative MSFEs were less than one under both GS and GP for all five forecast horizons. This suggests that including information on the two proxies for global risks in the model produces lower forecast errors associated with RV compared to the case when the ratios are excluded. More specifically, the forecasting gains from GS were equal to 7.1713%, 8.2584%, 9.7727%, 10.2746%, and 10.2948% for h = 1, 3, 6, 9, and 12, respectively. The corresponding values for GP were: 6.9194%, 8.3239%, 9.3775%, 9.8184%, and 10.3285% for the same set of forecasting horizons. Note that the forecasting gains increased over the out-of-sample period as the horizon became longer, suggesting that as the information on global risks is incorporated into investment decisions over the horizon of one year, the accuracy of the predictions of oil-market volatility improve. This is probably because heightened risks affect the oil-market volatility via a reduction in investment and consumption, which takes time to feed into the business cycles, and hence is reflected more strongly at longer horizons involving RV.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Data plot. Note: RV is realized variance of oil returns, with $\tilde{RV}$ = ln(1 + RV); GS is the natural logarithm of gold-to-silver price ratio; GP is the natural logarithm of gold-to-platinum price ratio. Shaded regions correspond to NBER recession dates in the US.

**Figure A2.**Plot of Recursive Estimate of γ. Note: see note to Table 1. Plots include the recursive estimate of γ (blue line) along with the 95% confidence bands (red dotted lines). (

**a**) Time-varying predictability of GS. (

**b**) Time-varying predictability of GP.

**Figure A3.**Plot of relative MSFEs from the quantiles-based predictive regression. Note: relative MSFE values less than one in the above figures are indicative of better performance of the model with a predictor (GS or GP), relative to the model without it, across forecasting horizons and conditional distribution of RV. (

**a**) Forecasting performance of GS. (

**b**) Forecasting performance of GP.

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h | Coefficient γ under GS (1915:01–2021:03) | Coefficient γ under GP (1968:01–2021:03) |
---|---|---|

1 | 0.5491 [5.3552] *** | 0.1300 [1.9973] ** |

3 | 0.3662 [6.4103] *** | 0.0983 [2.5209] ** |

6 | 0.6096 [6.5661] *** | 0.1913 [2.3836] ** |

9 | 0.7195 [6.2945] *** | 0.2325 [2.2702] ** |

12 | 0.7871 [6.1143] *** | 0.2605 [2.2859] ** |

h | Relative MSFEs under GS | Relative MSFEs under GP |
---|---|---|

1 | 0.9283 [78.4893] *** | 0.9308 [40.3654] *** |

3 | 0.9174 [91.2785] *** | 0.9168 [49.1210] *** |

6 | 0.9023 [109.5039] *** | 0.9062 [55.6714] *** |

9 | 0.8973 [115.4273] *** | 0.9018 [58.2474] *** |

12 | 0.8971 [115.3361] *** | 0.8967 [61.2767] *** |

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Gupta, R.; Pierdzioch, C.; Wong, W.-K. A Note on Forecasting the Historical Realized Variance of Oil-Price Movements: The Role of Gold-to-Silver and Gold-to-Platinum Price Ratios. *Energies* **2021**, *14*, 6775.
https://doi.org/10.3390/en14206775

**AMA Style**

Gupta R, Pierdzioch C, Wong W-K. A Note on Forecasting the Historical Realized Variance of Oil-Price Movements: The Role of Gold-to-Silver and Gold-to-Platinum Price Ratios. *Energies*. 2021; 14(20):6775.
https://doi.org/10.3390/en14206775

**Chicago/Turabian Style**

Gupta, Rangan, Christian Pierdzioch, and Wing-Keung Wong. 2021. "A Note on Forecasting the Historical Realized Variance of Oil-Price Movements: The Role of Gold-to-Silver and Gold-to-Platinum Price Ratios" *Energies* 14, no. 20: 6775.
https://doi.org/10.3390/en14206775