Petroleum products such as gasoline and heating oil are produced by refining crude oil. Many oil market analysts believe that the prices for these petroleum products contain useful information about the future evolution of the price of crude oil. In particular, changes in the product price spread – defined as the extent to which today’s price of gasoline or heating oil deviates from today’s price of crude oil – is widely viewed as a predictor of changes in the price of crude oil. For example, in April 2013 Goldman Sachs cut its oil price forecast citing significant downward pressure on product price spreads, which it interpreted as an indication of reduced final demand for products. Likewise, in 2011 energy consultant Kent Moors predicted higher oil prices based on widening gasoline and heating oil-price spreads.

Although energy economists have made great strides in recent years in forecasting the price of oil at short horizons, the forecasting ability of product spreads has never been formally analysed to date. Our recent work asks whether academic economists have missed something about forecasting oil prices that oil industry analysts know. The answer is that they have, but so have practitioners. Based on a rigorous real-time out-of-sample evaluation of numerous oil price forecasting models, we find that not all product spread forecasting models are useful in practice. Some forecasting models used by oil market analysts lack a solid foundation, but there are alternative product price spread models that greatly improve our ability to forecast the real price of oil. We develop forecasting models based on the gasoline-price spread that are systematically more accurate in real time compared with conventional no-change forecasts. Such models work particularly well at forecast horizons between one and two years, far beyond the short horizons for which earlier oil-price forecasting models based on economic fundamentals have been shown to work well. We obtain even more accurate results with a model that allows the predictive power of gasoline price spreads and heating oil spreads to evolve over time.

# Predicting with spreads

Our study is based on the proposition that that the price of crude oil can be expressed as a weighted average of product prices. This proposition has a long tradition in energy economics. For example, oil analyst Philip K. Verleger popularized the idea that the demand for crude oil ultimately derives from the demand for refined products, with refiners buying crude oil only if they can generate a profit at prevailing product prices. Our forecast analysis does not depend on this economic interpretation; all that is required to motivate the forecasting models in question is that the price of oil and the product prices share a common trend.

The study considers four basic forecasting models based on spreads with futures prices as well as spot prices for gasoline and heating oil:

- Models of individual product spreads such as the gasoline-price spread or the heating oil price spread.
- Models based on weighted product spreads.
- Models based on the crack spread, and
- Equal-weighted forecast combinations of gasoline spread and heating oil-spread models.

The evaluation period extends from early 1992 until September 2012. The study evaluates the out-of-sample accuracy of each of the forecasting models in terms of the recursive mean-squared prediction error (MSPE) relative to the no-change forecast and based on their ability to predict the direction of change in the real price of oil.

We find that not all product spread models are useful for out-of-sample forecasting, but some models perform well. The best single-spread forecasting model is a model based on the gasoline spot spread alone which yields MSPE reductions as large as 15% and directional accuracy as high as 63% at the two-year horizon. Heating oil spot spreads are far less accurate predictors than gasoline spot spreads. Weighted product spread models are never more accurate than gasoline spread models. Perhaps surprisingly, there is no evidence of forecasting models based on the commonly cited 3:2:1 crack spread having out-of-sample forecasting ability. We show that imposing parameter restrictions may greatly improve the forecast accuracy of spread models, regardless of the specification. For the preferred model based on the gasoline spread, a specification that sets the intercept to zero tends to generate the largest and most statistically significant MSPE reductions relative to the no-change forecast.

# Robustness concerns

The simplicity of product-spread forecasting models is appealing, yet there are reasons to be wary. From an economic point of view there is no reason to expect any one product spread to be a good predictor throughout the sample. One concern is that the global price of crude oil is likely to be determined by the refined product that is in highest demand. As discussed in Verleger (2011) this product had traditionally been gasoline, and the marginal market for gasoline production had been the US. As of late this product has been diesel fuel (which is almost interchangeable with heating oil), with Europe becoming the marginal market. To the extent that products are produced in roughly fixed proportions, this means that one refined product in one part of the world may have disproportionate predictive power for the price of oil. The predictive relationship is further complicated by the fact that different refiners use different grades of crude oil inputs, which in turn are associated with different proportions of refined product outputs, making it more difficult to predict which market will tighten and which will suffer from a glut in response to rising demand for, say, diesel fuel.

Although trade in petroleum products over time may alleviate the resulting market imbalances, there is reason to believe that the predictive relationships that industry analysts appeal to are not stable even in the absence of complicating factors such as:

- Oil-supply shocks.
- Changes in environmental regulations.
- Local capacity constraints in refining and unexpected refinery outages, or
- Other market turmoil.

And the predictive relationships are certainly unstable in the presence of these market forces. To account for this possibility, our study also explores the usefulness of time-varying parameter (TVP) forecasting models for linear combinations of the gasoline and heating oil price spreads. It is shown that suitably restricted TVP forecasting models that allow the marginal product market to change over time yield further improvements in out-of-sample forecast accuracy. The TVP model is more accurate than the no-change forecast at all forecast horizons up to two years. In fact, the study documents MSPE reductions as high as 20% and directional accuracy as high as 66%, making this specification overall the most useful forecasting approach.

The results of this study should be of particular interest to policymakers and financial analysts, in that to date no other forecasting method has been able to beat the no-change forecast of the real price of oil at horizons between one and two years. Models based on economic fundamentals such as global real economic activity, crude oil inventories and world oil production have been shown to be most accurate at horizons up to three months, but increasingly less accurate at longer horizons. This suggests that product-spread models are a good complement to fundamentals-based models of the global oil market to obtain the most accurate forecast of the price of oil at horizons up to two years.

# References

Baumeister, C and L Kilian (2012), “Real-Time Forecasts of the Real Price of Oil,” *Journal of Business and Economic Statistics*, 30, 326-336.

Baumeister C, L Kilian, and X Zhou (2013), “Are Product Spreads Useful for Forecasting? An Empirical Evaluation of the Verleger Hypothesis,” CEPR DP 9572.

Moors, K (2011), “Crack Spreads, Oil Futures and $5 Gasoline [2]”, *The Oil and Energy Investor*, January 7.

Strumpf, D (2013), “Goldman Cuts the Near-Term Brent Crude Forecast to $100 a Barrel,” *The Wall Street Journal*, April 23.

Verleger, P K (1982), “The Determinants of Official OPEC Crude Oil Prices”, *Review of Economics and Statistics*, 64, 177-183.

Verleger, P K (2011), “The Margin, Currency, and the Price of Oil,” *Business Economics*, 46, 71-82.