Commodities Price Data (Pink Sheet). The price for oil is the unweighted average of the Brent, West Texas Intermediate, and Dubai oil prices. Monthly data from January 1995 to December 2014 are used for the training sample, the model is updated based on expanding scheme, and data from 2015Q1 to 2022Q1 are used as the testing period.

# **4. Forecast performance**

The six models are compared in terms of their bias and precision.<sup>18</sup> The forecast of each model is compared against all other approaches in the model suite, rather than a single benchmark ( **Figure 3** ).<sup>19</sup> The mean error (bias) is defined as the difference between the actual price and the price forecast one to eight quarters ahead for each of the seven industrial commodities. Precision is captured by the root mean squared error (RMSE). Model comparisons are tested for statistical significance in a t-test (for absolute bias) or an F-test (for RMSE) or in the significance of the Diebold-Mariano statistic. Futures prices are only available up to one year ahead with reasonable liquidity, hence longer forecast horizons are not considered here for futures prices.<sup>20</sup> Bivariate correlations are only significant for horizons up to one year ahead; hence, forecasts from bivariate correlations are dropped for horizons beyond one year. OEM forecasts are only available on a semi-annual basis and the statistical tests are adjusted for the fewer degrees of freedom.

## **4.1 Oil prices**

None of the oil price forecasts generated by any of the six methodologies had a statistically significant bias ( **Table 3.A** ). However, the RMSEs were sizable for several approaches and have tended to be larger at longer horizons (except for OEM-based forecasts, **Table 3.B** ). At horizons up to one year, all approaches except the BVAR predicted the direction of forecast changes accurately; at horizons over one year, only consensus forecasts and the OEM did so ( **Tables 3.CD** ).

At the one- to four-quarter horizons, futures prices had particularly small RMSEs that were either significantly smaller than those of most other approaches or no larger ( **Tables 4.A-B** ). Similarly, the Diebold-Mariano test suggests significantly better or no worse forecast accuracy of futures prices than all other approaches ( **Figure 3** ). At longer horizons, both OEM-based forecasts had smaller biases, lower RMSEs and better forecast accuracy than other forecasting approaches. At all horizons, BVAR-based forecasts and bivariate correlations generally performed more poorly than one or more of the other approaches, despite being unbiased.

> 18 The sample period used to compute forecast and forecast errors was restricted to 2015-2022 to ensure sufficient observations for estimation.

> 19 The evaluation period for our model suite is 2015-2022. Other studies have compared forecast performance for longer periods for several commodities, particularly for futures prices, for example Reeve and Vigfusson (2011) and Bowman and Husain (2004).

> 20 A comparison of the forecast accuracy of futures prices against other methods using the Diebold-Mariano statistic and RMSEs for time horizons beyond one year showed that futures performed better than other methods in some cases. However, we opted to exclude forecast comparisons with futures prices beyond one year from the forecast evaluation exercise over concerns about their overall robustness. Futures contracts for distant delivery months tend to have low trading volumes and liquidity. This lack of activity can reduce price discovery, leading to less reliable forecasts and a potentially biased comparison of futures prices with other models.

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