The real (inflation-adjusted) price of crude oil is a key variable in the macroeconomic projections generated by central banks, private sector forecasters, and international organisations (IMF 2005, 2007). The recent cutback in Libyan oil production, widespread political unrest in the Middle East, and ongoing concerns about the state of the global recovery from the financial crisis have sharpened awareness of the uncertainty about the future path of the real price of crude oil. It seems surprising that, to date, no studies have systematically investigated how best to forecast the real price of oil in real time.

One reason is perhaps that there has been no readily available real-time database for the relevant economic variables. Although it is common to assess the out-of-sample accuracy of competing forecasting models based on ex-post revised data, such comparisons can be misleading. Ex-post revised data are not available to forecasters at the time their forecasts are generated. Instead, real-life forecasters have to work with the latest vintage of data known at the time. The use of successive vintages of real-time data in forecasting raises two distinct complications.

- First, even preliminary data often become available only with a lag. For example, it may take months for the first estimate of this month’s global oil production to be released.
- Second, the initial data releases are continuously revised. It takes successive data revisions until we know, to the best of our ability, the true level of oil production in the current month. Little is known about the nature of these revisions in oil market data or about how data revisions and delays in data availability affect the out-of-sample accuracy of oil price forecasts.

In recent research with Christiane Baumeister (Baumeister and Kilian 2011), we aim to address this problem. We construct a comprehensive monthly real-time data set consisting of vintages for January 1991 through December 2010, each covering data extending back to January 1973. Backcasting and nowcasting methods are used to fill gaps in the real-time data sets. This database allows the construction of real-time forecasts of the real price of oil from a variety of models.

Perhaps surprisingly, it can be shown that suitably constructed model-based real-time forecasts of the real price of oil are more accurate than the no-change forecast at horizons up to one year. This result holds both for the US refiners’ acquisition cost for crude oil imports, which may be viewed as a proxy for the price of oil in global markets, and for the West Texas Intermediate price that receives most attention in the media. (The price of Brent crude oil is not available for a long enough time span to allow a similar analysis). These results are based on a forecast evaluation window covering January 1992 through June 2010. This window includes recent periods of turmoil in oil markets and provides a challenging test of the forecasting ability of alternative forecasting models. The evaluation criteria are the recursive mean-squared prediction error of the forecasts and their directional accuracy.

In particular, it can be shown that recursive forecasts from vector autoregressive models motivated by the economic analysis of global oil markets in our research tend to have lower mean-squared prediction errors at short horizons than forecasts based on oil futures prices, forecasts based on autoregressive and autoregressive-moving average models, and the no-change forecast (see also Kilian and Murphy 2010). These models include data on global oil production, global real activity, the real price of oil and the change in global crude oil inventories. Real-time recursive mean-squared prediction error reductions may be as high as 25% one month ahead and 24% three months ahead. This result is in striking contrast to related results in the literature on forecasting real exchange rates or real stock returns, where it has proved very difficult to improve on the no-change forecast benchmark. The same models also have consistently and often significantly higher directional accuracy with success ratios as high as 65% in real time in some cases. Such success ratios are high by the standards of the empirical finance literature. In contrast, more conventional forecasting methods based on oil futures prices do not produce significant mean-squared prediction error reductions and have lower directional accuracy than suitably chosen vector autoregressive models. Likewise, vector autoregressive models have advantages over models based on non-oil industrial commodity prices alone.

Figure 1 illustrates the implementation of real-time forecasts in practice. The upper panel of Figure 1 shows the real-time forecast of the real US refiners’ acquisition cost of crude oil imports as of December 2010, well before the outbreak of the Libyan crisis in mid-February 2011. The nowcast of the real price of oil for 2010.12 is $97. The real-time model forecast indicates an initial increase in the real price of oil to $105 after one quarter, followed by a decline to between $75 and $83 in the second year. By contrast, the real-time forecast based on oil futures prices indicates a gradual decline from $97 to $90 after two years, while the no-change forecast suggests a constant price of $97. Based on our evidence, the vector autoregressive real-time forecast is the most reliable forecast overall in terms of mean-squared prediction errors and directional accuracy among these three forecasts, at least in the short run.

**Figure 1. **Baseline real-time forecast of real refiners’ acquisition cost as of 2010.12 and risk analysis

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*Notes: The alternative forecasting scenarios in panel (b) are discussed in detail in the discussion paper. The vertical line indicates the last nowcast and corresponds to December 2010. Source: Baumeister and Kilian (2011).*

An important limitation of standard reduced-form forecasting models from a policy point of view is that they provide no insight into what is driving the forecast and do not allow the policymaker to explore alternative hypothetical forecast scenarios. Policymakers not only expect oil price forecasts to be interpretable in light of an economic model, but they also want to be in a position to evaluate the risks associated with the baseline forecast based on an analysis of how this forecast changes with changes in the economic environment. This task requires additional econometric tools.

A natural approach is to build on the vector autoregressive forecasting approach. It can be shown that – with the additional identifying assumptions proposed in Kilian and Murphy (2010) – the structural moving average representation of the forecasting model may be used not only to forecast the real price of oil out-of-sample, but also to construct real-time conditional projections of how the oil price forecast would deviate from the unconditional forecast benchmark under hypothetical scenarios about future oil demand and oil supply conditions. Using this new econometric tool, it can be demonstrated, for example, that an unexpected full recovery of the world economy would raise the real price of oil by an additional 50% after a year and a half. On the other hand, a surge in speculative demand driven by civil unrest in the Middle East would increase the real price of oil by 20% after about one year, if the shift in speculative demand is comparable to that during the Iranian crisis of 1979.

The lower panel of Figure 1 shows the baseline forecast as of December 2010 implied by the Kilian-Murphy (2010) model as well as a wide range of alternative forecasting scenarios. It illustrates that the real price of oil may rise as high as $148 after one quarter or fall as low as $100, depending on the scenario. After one year, the range is between $76 and $131; at the two-year horizon between $66 and $115. For example, a complete shutdown of Libyan oil production in January 2011 (all else equal) would have been expected to drive the real price of oil as high as $115 in early 2011. These results, while necessarily tentative, illustrate how structural models of oil markets may be used to assess risks in oil price forecasts and to investigate the sensitivity of reduced-form forecasts to specific economic events.

Conditional projections, of course, are only as good as the underlying structural models. Figure 1 highlights the importance of refining these models and of improving structural forecasting methods. Clearly, forecast scenarios could alternatively be constructed from dynamic stochastic general equilibrium models, provided that these models incorporate suitable structural oil-market models. One reason for focusing on the model in Kilian and Murphy (2010) instead is that currently available dynamic stochastic general equilibrium models are still too simplistic when it comes to modelling the global oil market to be useful for policy analysis. In particular, modelling the global demand for industrial commodities (as opposed to measures of value added or productivity) has proved challenging. As these models become more sophisticated, we would expect this situation to change, however. Whether the additional model structure required in specifying a dynamic stochastic general equilibrium model compared with a structural vector autoregressive model on balance will help improve out-of-sample forecast accuracy remains an open question.

# References

Baumeister, C and L Kilian (2011), “Real-Time Forecasts of the Real Price of Oil [1]”, CEPR DP 8414.

International Monetary Fund (2005), *World Economic Outlook*.

International Monetary Fund (2007), *World Economic Outlook*.

Kilian, L and DP Murphy (2010), “The Role of Inventories and Speculative Trading in the Global Market for Crude Oil [2]”.