test for forecast accuracy developed by Diebold and Mariano (1995) and the test for directional forecast accuracy developed by Pesaran and Timmermann (2009).<sup>2</sup> The paper documents three main findings. First, all approaches other than the BVAR (and, for copper and lead, consensus forecasts) did well in terms of directional accuracy, at least at horizons of less than one year. Forecast biases typically did not differ significantly across models for most forecast horizons and commodities. However, forecast precision, as captured in root mean squared errors, differed significantly.

Second, futures prices or bivariate correlations performed well at short horizons for most commodities. Consensus forecasts and a macroeconometric model ( _Oxford Economic Model_ ) were preferred at long horizons.

Third, the reduced form BVAR model had significantly poorer forecast performance than all other approaches, both in terms of bias and precision, for all commodities and all horizons.<sup>3</sup> Also, the strength of BVAR models lies not only in forecast performance, but in scenario analysis: Bayesian vector autoregressive (BVAR) models are an important approach that allows a straightforward translation of global output growth forecasts into industrial commodity price forecasts.

Section 2 reviews the extensive literature on commodity price forecasting. Section 3 presents the six models selected for forecasting the seven industrial commodity prices. Section 4 discusses these models’ forecast performance. Section 5 summarizes the main findings and highlights the uncertainty in commodity price forecasts.

# **2. Literature review**

The empirical literature on commodity price forecasting distinguishes between quantitative methods and qualitative methods. The most common quantitative methods used in the forecasting literature include financial models, Bayesian time series models, univariate time series models, and non-standard methods such as Artificial Neural Networks (ANN) and Support Vector Machines (SVM). Qualitative approaches include methods such as belief networks, the Delphi procedure, fuzzy logic and expert systems, and text mining techniques (Behmiri and Manso 2013; Drachal 2016; Frey et al. 2009). This review of the commodity price forecasting literature focuses on quantitative methods for crude oil and metal commodity prices ( **Table 1** ).

## **2.1. Crude oil price forecasting**

The review of the literature on crude oil price forecasting draws on 40 studies in peer-reviewed journals, most of which examine West Texas Intermediate (WTI) prices and five of which examine

> 2 Diebold (2015), in a review of the use of the test of Diebold and Mariano (1995) argue that sometimes simpler approaches remain appropriate. Here, therefore, we have used both the comparisons of bias and root mean squared errors and the formal tests of Diebold and Mariano (1995) and Pesaran and Timmerman (2009).

> **3** There are caveats. First, the sample size of the BVAR is much smaller than the other approaches due to data availability. The BVAR in this paper uses the quarterly average of monthly data while the other methods use monthly data. Second, the BVAR predicts real prices, then inflates real values to nominal prices by actual inflation rates.

3