The purpose of this chapter is to present an overview of different models used in this work to
predict crude oil prices. While there have been numerous studies^{5}that deal with forecasting the
price of oil in general, this study will focus on econometric methods and their predictive power
based on time series regression and alternative methods based on oil futures prices, crude oil
inventories, non-oil industrial raw materials and oil sensitive stocks.

**2.2.1** **No-change Benchmark**

The random walk without drift is the conventional benchmark in the literature on forecasting asset prices (Alquist et al. 2013). This refers to the idea, that the best forecast for tomorrow is the price of today. Therefore, anhstep ahead forecast is set equal to the oil price today:

Y_{t}^{f}_{+}_{h}_{|}_{t}=Yt, (1)

whereY_{t}^{f}_{+}_{h}_{|}_{t}denotes theh-period forecast of the oil price andYt refers to the actual real price
of oil. The performance of other models is typically measured relative to this benchmark since
a better forecasting performance indicates that the oil price can be predicted at least to some
extent. This model will be referred to as the ‘RW’.

**2.2.2** **AR and ARMA**

Autoregressive (AR) and autoregressive moving average (ARMA) processes are two other widely used methods for generating forecasts from time series. Baumeister and Kilian (2012) and Alquist et al. (2013) provide evidence that real oil price forecasts constructed from these models can be more accurate than a no-change benchmark for horizons up to one year eval-uated based on the MSPE and their directional accuracy. Moreover, their results are robust whether the WTI or the RAC is used as the real price of oil in question. As the performance of these two models are very similar, only the results for an ARMA(1,1) model based on the log oil price will be examined in more detail. Additional information about the forecasting performance of the AR model can be found in the supplementary material section.

**2.2.3** **Futures**

Another widely used method is to generate forecasts based on futures prices. This follows the
idea that futures contracts might include market expectations about the shift in oil prices. This
approach has the advantage that it is relatively simple to generate and easy to communicate to
the public (Manescu and van Robays 2016). One can easily generate anh-step forecast for the
nominal price of oil by using a futures contract with maturityh. There are several different
vari-ations and modificvari-ations discussed in the literature.^{6}Following the suggestion by Baumeister
and Kilian (2012, 2014), the forecast for the real price of oil will be generated by subtracting the
expected inflation:

Y_{t}^{f}_{+}_{h}_{|}_{t}=Yt(1+ f_{t}^{h}−st−E(*π*^{h}_{t})), (2)
whereY_{t} is the current level of the real price of oil, f_{t}^{h} is the log of current oil futures price
with maturityh,stis the corresponding log of the spot price andE(*π*^{h}_{t})the expected inflation
rate over the nexth periods. This was done by using the monthly average growth rate of the
US Consumer Price Index (CPI) up to timet multiplied byh. This approach could be refined

5 The interested reader may find a comprehensive overview of various forecasting techniques in Frey et al. (2009), Bashiri Behmiri and Pires Manso (2013) and Gabralla and Abraham (2013).

6 See for example Alquist et al. (2013) who describe several variations of this basic model.

further, but as argued by Baumeister and Kilian (2012, 2014), the deviations are negligible given that the variations of the nominal oil price typically dominate the magnitude of the inflation rate over the horizon of interest.

Although there exists evidence that futures prices are not particularly accurate when it comes to forecasting the oil price (e.g. Alquist and Kilian (2010), Baumeister and Kilian (2012), and Reeve and Vigfusson (2011)), it is still a widely used baseline forecast of central banks (Baumeister and Kilian 2012). Furthermore, when using the Brent oil price as a benchmark, the results of Manescu and van Robays (2016) show slight improvements between 3 and 8 quar-ters ahead forecasts for the time period between 1995Q1 and 2015Q2. However, the results of Baumeister and Kilian (2014) indicate no improvement for up to 4 quarter ahead forecasts for the evaluation period between 1992.01 and 2012.09. This model will be referred to as the

‘Futures’ model.

**2.2.4** **Forecasts based on Crude Oil Inventories**

The fourth class of models considered in this study is based on the theory developed in Alquist and Kilian (2010). A shift in expectations about the real price of oil, ceteris paribus, is reflected in changes in expectations of crude oil inventories. This model has been discussed in Baumeister et al. (2015, 2014) and can be represented as:

Y_{t}^{f}_{+}_{h}_{|}_{t} =Yt(1+*β∆inv*b ^{h}_{t}), (3)
where ∆inv^{h}_{t} reflects the percentage change in US crude oil inventories over the preceding h
months and b*β* is a regression parameter that is obtained by regressing the cumulative
per-centage changes in the real price of oil on the lagged cumulative perper-centage change in US
inventories without intercept. Especially, using forecasting horizons of more than 14 months,
this approach has been useful in a forecasting combination as it lowers the MSPE as shown in
Baumeister and Kilian (2014). Additionally, Baumeister et al. (2015) find MSPE reduction up
to 30% as compared to a no-change benchmark between 1992.01 and 2012.09 for monthly data
using a MIDAS approach. Results for this classic approach can be found in the supplementary
material section. However, this work proposes a new variation of this model by using
Organ-isation for Economic Co-operation and Development (OECD) crude oil inventories as there is
reason to believe that the US inventories might not be representative for the Brent crude oil
price. While there do not exist monthly crude oil inventories data for this model directly, it
has been modeled by multiplying US crude oil inventories with the ratio of OECD petroleum
stocks over US petroleum stocks. This new approach outperforms the classic model that uses
the US inventories. This model will be referred to as the ‘Inventories OECD’ model.

**2.2.5** **VAR Model of the Global Oil Market**

The fifth class of models considered is the Vector Autoregressive (VAR) model of the global oil markets which has been extensively studied over the past several years. According to Baumeis-ter and Kilian (2014), this can be illustrated as a reduced form representation:

B(L)Y_{t} =c+*e*_{t}, (4)

whereYt is a vector of four variables which include the percentage change in global crude oil
production, a measure of global real activity, the log of RAC for crude oil imports deflated by
the log of the US CPI, and the change in global crude oil inventories. Furthermore,B(L)denotes
the autoregressive lag order polynomial,ca vector of constants, and *e*t represents a vector of
white noise error terms. Only a few works have examined the forecasting ability of this VAR
approach for Brent. Baumeister and Kilian (2014) have done this indirectly by modeling the

spread between Brent and RAC as a random walk and Manescu and van Robays (2016) have modeled the forecasts of Brent directly. However, both methods offer only relatively small or no gains in terms of forecast accuracy as compared to a no-change forecast using quarterly projections.

There exist two different measures for the global real activity that are discussed in the liter-ature so far. Commonly, the "Shipping Index"developed by Kilian (2009), which is constructed from data on global dry cargo ocean shipping freight rates, is used for this purpose. Alterna-tively, one could use the monthly index of industrial production for the OECD and six major non-OECD countries to measure the economic activity. Results for both models can be found in the supplementary material section.

However, two variations of the VAR model will be introduced in the forecasting literature of oil prices by using alternative ways of measuring the global economic activity. Ravazzolo and Vespignani (2015) have shown that the world steel production has a higher predictive accuracy of the world GDP as compared to the OECD industrial production and the Kilian shipping index. Therefore, it seems plausible to use this indicator in order to forecast the real price of Brent crude oil as well. In this case, the log difference of the crude oil price and of the steel production are used in this specification as this outperforms the model using the log-levels.

This model will be referred to as the ‘VAR Steel’ model. Additionally, the composite leading
indicator of the OECD and six major non-OECD countries will be used to measure the economic
activity. This indicator is available on a monthly basis and is designed to detect turning points
in business cycles with a lead time of 6 to 9 months. Although it is not a common proxy for the
world GDP itself, it might give an advantage for forecasting due to its leading co-movement
to the reference series.^{7} Here, using the log-levels of the oil price and the composite-leading
indicator outperforms the specification using log-differences. This model will be referred to as
the ‘VAR CLI’ model.

**2.2.6** **Non-Oil Industrial Raw Materials**

An additional way of constructing a real-time forecast would be to use the non-oil industrial raw materials index as discussed in Baumeister and Kilian (2012):

Y_{t}^{f}_{+}_{h}_{|}_{t} =Yt(1+*π*^{h,irm}_{t} −E(*π*_{t}^{n})), (5)

where*π*_{t}^{h,irm} is the percentage change of the Commodity Research Bureau (CRB) index of the
spot price of industrial raw materials other than oil over the preceding h months andE(*π*_{t}^{n})
is the expected inflation over the same time horizon. Baumeister and Kilian (2012) find MSPE
reductions of up to 25% in the short run for this model. Similarly, improvements have been
confirmed by Alquist et al. (2013) for the nominal WTI and by Manescu and van Robays (2016)
for the real price of Brent. This model will be referred to as the ‘CRB Index’ model.

**2.2.7** **Price Movements with Oil Sensitive Stocks**

S.-S. Chen (2014) has introduced another model that is easy to implement for forecasting the real price of oil. Using monthly data from 1984.10 to 2012.08 S.-S. Chen (2014) shows that using oil sensitive stock price indices can improve the forecasts of nominal and real crude oil prices at short horizons. In particular, the New York Stock Exchange (NYSE) Arca AMEX oil index, which is a price-weighted index of the leading international oil and natural gas companies, can be used to improve the MSPE ratio up to 21% for forecasting the real WTI and real Brent crude oil price. The suggestions made in this paper will be adopted and the model will be referred to as the ‘Oil Stock’ model.

7 In April 2012, the OECD replaced the index of industrial production covering all industry sectors excluding construction with the GDP as its new reference series.

**2.2.8** **Other Forecasting Methods**

There exists a broad variety of other models in the literature of forecasting oil prices. For the sake of clarity, only two promising possibilities will be discussed in this section. Hence, one can model the forecast for oil prices by using the spread between the spot prices of gasoline and crude oil or by using a time-varying parameter model of gasoline and heating oil spreads which are both proposed by Baumeister et al. (2017). Both models have been shown to be more accurate than a no-change forecast especially at forecasting horizons beyond 1 year for the WTI price. Nevertheless, as pointed out by Baumeister and Kilian (2015), there is no long enough time series available of the relevant Rotterdam market for the gasoline spot price in order to forecast the Brent crude oil price.

In addition, the forecasting ability of several other models have been extensively studied which are not discussed in further detail in this paper. However, the interested reader will find a large number of other related forecasting techniques in the literature, including the use of forward prices (Chernenko et al. 2004), different variations of future price models (Alquist and Kilian 2010; Reeve and Vigfusson 2011), risk adjusted futures prices (Pagano and Pisani 2009), the price of crack spread futures (Murat and Tokat 2009), exchange rates (Y.-C. Chen et al. 2010), convenience yield predictions (Knetsch 2007), relative inventory and low- and high-inventory variables (Ye et al. 2005, 2006), model selection with parameter restricted models (Y. Wang et al. 2015), professional survey forecasts (Sanders et al. 2009), high frequency financial variables (Baumeister et al. 2015), hybrid methods (Han et al. 2017; J.-L. Zhang et al. 2015), technical indicators (Yin and Yang 2016) and time-varying parameter models (Y. Wang et al. 2017).