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sustainability Article Forecasting Long-Term Crude Oil Prices Using a Bayesian Model with Informative Priors Chul-Yong Lee 1 and Sung-Yoon Huh 2, * 1 Korea Energy Economics Institute (KEEI), 405-11 Jongga-ro, Jung-gu, Ulsan 44543, Korea; [email protected] 2 Haas School of Business, University of California Berkeley, 2220 Piedmont Avenue, Berkeley, CA 94720, USA * Correspondence: [email protected]; Tel.: +1-510-642-7989 Academic Editor: Marc A. Rosen Received: 30 November 2016; Accepted: 23 January 2017; Published: 27 January 2017 Abstract: In the long-term, crude oil prices may impact the economic stability and sustainability of many countries, especially those depending on oil imports. This study thus suggests an alternative model for accurately forecasting oil prices while reflecting structural changes in the oil market by using a Bayesian approach. The prior information is derived from the recent and expected structure of the oil market, using a subjective approach, and then updated with available market data. The model includes as independent variables factors affecting oil prices, such as world oil demand and supply, the financial situation, upstream costs, and geopolitical events. To test the model’s forecasting performance, it is compared with other models, including a linear ordinary least squares model and a neural network model. The proposed model outperforms on the forecasting performance test even though the neural network model shows the best results on a goodness-of-fit test. The results show that the crude oil price is estimated to increase to $169.3/Bbl by 2040. Keywords: Bayesian estimation; oil price; forecasting model; informative priors 1. Introduction Oil prices and oil price volatility both play important roles in affecting the global economy, although the effects are asymmetric depending on periods, regions, sectors, reason of oil shock, and others. Different views on the impact of changes in oil prices on the global economy have been suggested. For example, Sadorsky [1], Barsky and Kilian [2], Kilian [3], Segal [4], Morana [5], and Kilian and Murphy [6] present a good account of these different views. Through this debate, several studies found that higher oil prices have an adverse impact on the global economy [5,7,8]. Moreover, such adverse economic impact of higher oil prices on oil-importing countries such as South Korea is found to be even more severe [9,10]. In order to make appropriate decisions about the direction of economic policy, therefore, it is important to accurately forecast future oil prices with effective models [11]. In June 2008, global oil prices, which had been on an upward trend since 2003, surged to $134/Bbl (for West Texas Intermediate, WTI). Oil prices fell after the global economic recession of 2008 but started to rise in early 2009. In terms of growth rate, an overall downward trend in global oil demand growth is projected until 2040 [12]. Studies have suggested a possible explanation for this projected slowdown in oil demand growth, such as structural changes of the global economy [13], consumer reactions and government policies [14], and shale gas development in the United States [15]. After the Organization of the Petroleum Exporting Countries (OPEC) decided to maintain oil production in 2014, the crude oil price dropped to less than $50/Bbl. The price has stayed at mid-$40/Bbl on continued sluggish oil demand and strong shale supply in 2015 and 2016. Consequently, anxieties over oil price volatility and another oil crisis have been growing. In this context, knowing the long-term trend in Sustainability 2017, 9, 190; doi:10.3390/su9020190 www.mdpi.com/journal/sustainability
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Page 1: Forecasting Long-Term Crude Oil Prices Using a … · Forecasting Long-Term Crude Oil Prices Using a Bayesian Model with Informative Priors ... reason of oil shock, and

sustainability

Article

Forecasting Long-Term Crude Oil Prices Using aBayesian Model with Informative Priors

Chul-Yong Lee 1 and Sung-Yoon Huh 2,*1 Korea Energy Economics Institute (KEEI), 405-11 Jongga-ro, Jung-gu, Ulsan 44543, Korea; [email protected] Haas School of Business, University of California Berkeley, 2220 Piedmont Avenue, Berkeley, CA 94720, USA* Correspondence: [email protected]; Tel.: +1-510-642-7989

Academic Editor: Marc A. RosenReceived: 30 November 2016; Accepted: 23 January 2017; Published: 27 January 2017

Abstract: In the long-term, crude oil prices may impact the economic stability and sustainability ofmany countries, especially those depending on oil imports. This study thus suggests an alternativemodel for accurately forecasting oil prices while reflecting structural changes in the oil market byusing a Bayesian approach. The prior information is derived from the recent and expected structureof the oil market, using a subjective approach, and then updated with available market data. Themodel includes as independent variables factors affecting oil prices, such as world oil demand andsupply, the financial situation, upstream costs, and geopolitical events. To test the model’s forecastingperformance, it is compared with other models, including a linear ordinary least squares model and aneural network model. The proposed model outperforms on the forecasting performance test eventhough the neural network model shows the best results on a goodness-of-fit test. The results showthat the crude oil price is estimated to increase to $169.3/Bbl by 2040.

Keywords: Bayesian estimation; oil price; forecasting model; informative priors

1. Introduction

Oil prices and oil price volatility both play important roles in affecting the global economy,although the effects are asymmetric depending on periods, regions, sectors, reason of oil shock, andothers. Different views on the impact of changes in oil prices on the global economy have beensuggested. For example, Sadorsky [1], Barsky and Kilian [2], Kilian [3], Segal [4], Morana [5], andKilian and Murphy [6] present a good account of these different views. Through this debate, severalstudies found that higher oil prices have an adverse impact on the global economy [5,7,8]. Moreover,such adverse economic impact of higher oil prices on oil-importing countries such as South Koreais found to be even more severe [9,10]. In order to make appropriate decisions about the directionof economic policy, therefore, it is important to accurately forecast future oil prices with effectivemodels [11].

In June 2008, global oil prices, which had been on an upward trend since 2003, surged to $134/Bbl(for West Texas Intermediate, WTI). Oil prices fell after the global economic recession of 2008 butstarted to rise in early 2009. In terms of growth rate, an overall downward trend in global oil demandgrowth is projected until 2040 [12]. Studies have suggested a possible explanation for this projectedslowdown in oil demand growth, such as structural changes of the global economy [13], consumerreactions and government policies [14], and shale gas development in the United States [15]. After theOrganization of the Petroleum Exporting Countries (OPEC) decided to maintain oil production in 2014,the crude oil price dropped to less than $50/Bbl. The price has stayed at mid-$40/Bbl on continuedsluggish oil demand and strong shale supply in 2015 and 2016. Consequently, anxieties over oil pricevolatility and another oil crisis have been growing. In this context, knowing the long-term trend in

Sustainability 2017, 9, 190; doi:10.3390/su9020190 www.mdpi.com/journal/sustainability

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Sustainability 2017, 9, 190 2 of 15

crude oil prices is essential for ensuring future economic stability in many countries because significantchanges in crude oil prices and unstable oil supplies may seriously impact their economies, whichdepend on crude oil imports and exports. Sophisticated forecasting models are able to reliably predictlong-term crude oil prices and provide updated information based on fluctuating market conditionsto all concerned parties, thereby contributing to reasonable decision-making by policymakers andcompany managers. Table 1 summarizes the previous research on crude oil price forecasting models.

Table 1. Previous Research on Crude Oil Price Forecasting Models

Models Authors Objects Characteristics

Time-Series Models

[16] Brent Oil Price GARCH Model

[17] WTI Oil Price VECM Model

[18] WTI Oil Price, Brent Oil Price, MayaOil Price, Bonny Light Oil Price VECM Model

Time-Series Models [19] Oil Price in Permian of Texas Dynamic optimization model

General EquilibriumModels [20] WTI Oil Price National Energy Modeling System

(NEMS)

Dephi Approach [21] WTI Oil Price, Brent Oil Price Survey the expert panel

Others

[22] WTI Oil Price Compare the forecasting performanceof WTI oil futures price

[23] WTI Oil PriceCompare the forecasting performanceof WTI oil futures price (before 1, 3, 6, 9,12 months)

[24] WTI Oil Price Conduct Granger Causality testbetween WTI oil futures and spot price

Morana [16] conducted research on oil price volatility by applying the generalized auto-regressiveconditional heteroscedasticity (GARCH) model of Bollerslev [25], which can explain a conditionalvariance that changes over time, to forecasting the Brent oil price. GARCH models have excellentaccuracy in short-term forecasting but are hard to apply for mid- and long-term forecasting.Auto-regressive integrated moving average (ARIMA) methodology cannot only apply any time-seriesdata but also reflect the wild volatility of time-series data [26]. Besides time-series models such asARIMA and GARCH models, the vector error-correction model (VECM) has also been employed toforecast oil prices by using the interrelationship between the futures price and the spot price of crudeoil [17,18].

Pindyck [19] estimated the oil price needed to maximize the producer’s profit in a perfectlycompetitive and monopolistic market using dynamic optimization. In his results, oil prices followeda U-shape pattern in the case of a small initial reserve endowment but then showed a rise over timein the case of a large initial reserve endowment. Even though Pindyck [19] explained the changingpattern in oil prices, his approach is difficult to apply to actual data and is limited in that it examinesfactors driving oil price fluctuations only from the supply side.

Alternatively, Energy Information Administration (EIA) [20] provides long-term forecasts of WTIoil prices by using the National Energy Modeling System. Many research institutes have used EIAforecasts as credible data. A Delphi approach, which repeatedly collects opinions to derive the jointsubjective view of experts, can also be used to forecast oil prices. For example, Reuter’s News Agencyforecasts WTI and Brent oil prices by surveying an expert panel.

Using prices determined in the futures oil market has been suggested as a forecastingmethodology [22–24]. Such an approach tests if the futures price is an unbiased predictor of thespot price at the maturity time. Yoon [22] used WTI spot and futures prices from July 2000 to June 2004as sample data, selecting the forecasting period that yielded the most accurate forecasts by comparingquarterly forecasts based on futures prices from the previous one to six months with the average of the

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quarterly WTI oil prices. Similarly, Abosedra and Baghestani [23] evaluated forecasting accuracy bycomparing futures prices (1, 3, 6, 9, and 12 months out) with WTI spot prices from January 1991 toDecember 2001. Yanagisawa [24] analyzed if futures prices from a certain time could be appropriatelyused to forecast spot prices by testing the Granger causality between WTI spot prices and futuresprices. While forecasting oil prices using futures prices shows accurate performance in the short term,it is inappropriate for mid- and long-term forecasting.

Previous research on oil price forecasting models has generally assumed that the current trend inoil prices will continue in the future and thus that factors influencing oil will have the same effectsin the future. However, factors influencing oil prices have changed structurally over time. In the1960s, supply-side factors determined the crude oil price, and this trend continued until the oil pricecollapse of the mid-1980s. Consequently, an oil pricing system linked to the oil market has existedsince the late 1980s, and the crude oil price has been determined by demand as well as supply. In the1990s, especially, emerging markets such as China and India led oil prices to rise. Since 2000, financialfactors, including the penetration of speculative forces, a weakening dollar, and the financial crisis,have attracted attention as possible determinants of global oil prices. For example, Morana [27] foundthat financial shocks have considerably contributed to oil price increase since early 2000s, and to amuch larger extent since mid-2000s. Among several financial factors, speculative expectation has beenindicated as an important determinant of the price for a commodity [18]. Studies have also providedsupport for the role of speculation in the oil market, especially for its role in the rise of crude oilprices [18,28–30]. However, the role of speculation in causing the significant changes in oil prices isstill debatable. Several studies are not supportive of speculation being an important determinant ofthe real oil prices [6,31]. Even though the global oil market paradigm has been changing continuously,previous forecasting models have rarely reflected such structural changes.

This study thus presents alternative model that reflect the structural changes in the oil marketusing Bayesian inference The model reflects the expected structure of the oil market in the priordensity function by using subjective approaches. Occasionally, the subjective approach is sufficient,as experts may make good forecasts. Expert opinion, however, causes bias and uncertainty [32].To improve the reliability of judgmental forecasts, this study employs Bayesian updating with actualdata. Bayesian models, which forecast more accurately than traditional time-series analysis, aregenerally used in forecasting researches of GDP, inflation, the consumer prices, and the exchangerate [33,34]. The proposed model is a type of Bayesian normal multiple regression model withinformative priors. It applies the recent and expected structure of the oil market to parameters’ priorinformation using a subjective approach and then derives the parameters’ posterior density functionby updating with available market data. To test the forecasting performance of the proposed model,it is compared to benchmark models, including an ordinary least squares (OLS) linear model and aneural network model using out-of-sample forecasting performance. The results forecast for 2040 bythe proposed model are analyzed through comparison with the results of other research.

Most previous studies excluding International Energy Agency (IEA) [35] and EIA [36] forecastcrude oil prices in the short term rather than the medium or long term. As such, this study cancontribute to preparing quick and accurate oil market countermeasures by forecasting long-term oilprices. Bayesian approaches to forecasting the global oil price, which have not been employed inprevious research, make this study’s model highly applicable. The forecast oil prices reported here canthus be used to inform reasoned decision making by the government and the private sector.

This rest of the paper proceeds as follows. Section 2 introduces the paper’s suggested Bayesianmodel and benchmark models for comparison. Section 3 presents the estimated model’s results andthe results of the tests of forecasting performance. It also forecasts crude oil prices in 2040 using theestimated models. Finally, Section 4 summarizes the results and discusses some implications.

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2. Model Specification

For Y with n× 1 observed values as the dependent variable, the normal multiple linear regressionmodel is as follows:

Y = XB + ε (1)

where there are k explanatory variables, X is an n× k matrix, B a k× 1 parameter vector to be estimated,and ε is an n × 1 error-term vector. This equation assumes that ε follows the multivariate normaldistribution with mean 0n and σ2In as the covariance matrix. The likelihood function can then beexpressed via the following equation:

p(Y|X, B, σ2) =σ−n

(2π)n/2 exp[− 12σ2 (Y− XB)′(Y− XB)] (2)

If the configuration of the prior density function is not known, it is convenient to use thedistribution of a special series. Because a well-known family of distributions is usually used, the priordensity function is called as a conjugate prior if both it and the posterior density function belong tothe same distribution family. A conjugate prior is usually used because this makes the mathematicalcomputation of the likelihood function as simple as under a standard model, such as a normal model.Linear models, like that above, usually use a normal distribution for the parameter prior densityfunction and an inverse gamma distribution for the prior density function of σ2. In other words,

B∣∣σ2 ∼ N(B, W)1

σ2 ∼ G(s−1, v)(3)

By assuming a conjugate prior, the posterior density functions of each parameter also have thesame configuration. In this case, the posterior density function can be estimated analytically [36].The posterior density function of parameter B, which is estimated by multiplying the prior densityfunction and the likelihood function, then follows the multivariate normal distribution with averagevector B and variance-covariance matrix F.

p(B|X, Y, σ) ∝1σk exp[−1

2(B− B)′F(B− B)] (4)

whereB = (W−1 + S−1X′X)−1(X−1B + S−1X′XB̂)F = W−1 + S−1X′XB̂ = (X′X)−1X′YS = n−1(Y− XB̂)′(Y− XB̂)

(5)

As statistical methods have developed, the posterior density function can now be estimatedmore easily using a Gibbs sampler [37]. This method selects a random number from the conditionalprobability distribution of each variable by generating a sequence of random samples. Because themultidimensional joint probability distribution hardly generates a direct random sample, such asequence serves to approximate the marginal distribution in order to create the joint probabilitydensity function. Gibbs sampling is an example of a Markov chain algorithm in that the randomnumbers iteratively generated from the conditional probability distribution of each variable have thejoint probability density function as a limiting distribution. In addition, the limiting distribution of arandom sample generated from the conditional probability density functions of each variable becomesthe marginal probability distribution.

To estimate the posterior density function, Equation (3) generates the following Gibbs sample onthe first sequence after assuming that the appropriate initial values are B(0) and σ(0).

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B(1) ∼ p[B∣∣∣X, Y, σ(0)]

σ(1) ∼ p[σ∣∣∣X, Y, B(1)]

(6)

In above equation, the conditional probability distributions of B and σ follow a normal distributionand an inverse gamma distribution, respectively. When this process is appropriately iterated, the resultof k iterations is as follows:

B(k) ∼ p[B∣∣∣X, Y, σ(k−1)]

σ(k) ∼ p[σ∣∣∣X, Y, B(k)]

(7)

Thus, Gibbs samples B(k) and σ(k) and Gibbs sample series, B1(k), . . . , Bm

(k) and σ1(k), . . . , σm

(k),can be obtained by iterating this process m times. By using Gibbs samples, the posterior densityfunction can be obtained, and the posterior average and variance can be computed.

This study uses the Gibbs sampler method to estimate the posterior density function of theparameters, iterating 100,000 times. Because the parameters derived from the initial sequence may bemeaningless, the derived parameters from the initial 10,000 iterations are discarded. The posteriordensity function of the parameters obtained through this estimation process is used for forecasting theoil price. Determining how to reflect the parameters’ prior density function can be problematic. Oneoption is taking them from the advice of oil market experts. In other words, the relative importanceof oil price determinants is derived from experts’ judgments. Excellent forecasts can be derivedfrom experts’ judgment [38], but since experts’ opinions involve much uncertainty and bias, somerecalibration is necessary. To do so, this study updates the parameter estimates derived from expertjudgments via a Bayesian method using available market data.

When deriving the prior density function of the parameters from expert judgment, the relativeimportance of oil price determinants is as in the below equation. In other words, the relative importanceof each variable is derived from the partial worth of each variable, which is calculated using realisticcoefficient levels and each explanatory variable (i.e., the partial worth of each explanatory variable isderived by multiplying the parameter by the range of the variable’s value [39]).

Relative importancexi=

Part Worthxi∑k

Part Worthk

where Part Worthxi = βi × (Maxxi −Minxi )(8)

From the parameter values collected from expert judgment, the normal density function withmean and variance is derived via bootstrapping; this is then used as a prior density function. However,surveying expert judgment incurs a cost and takes time. As an alternative method, the researcher’sjudgment of the prior information can be used, with the mean and variance of the normal distributionset at the same value by the generic rule [40].

The prior density function of the parameters derived from their relative importance is updatedin a Bayesian method using actual market data. There is a scale difference between the parameterfrom the prior density function and the estimated coefficient representing the relationship betweenexplanatory and dependent variables, and recalibration of constants is useful for adjusting for this.As the difference between the estimates derived from the prior information and real market dataincreases, the usefulness of Bayesian updating decreases. To recalculate the constant terms, the methodsuggested by Train [41] is employed. If PT , P̂0

T , and α0 are the crude oil price observed in the last year,the crude oil price estimated in the last year, and the average of the estimated constants, respectively, anefficient constant term recalibration can be derived by iterating the following process until a constantapproximate to the special value is obtained.

α1 = α0 + ln(PT

P̂0T) (9)

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In Equation (9), the superscript 0 refers to the initial point of a sequence. By using the posteriordensity function of the estimated parameters and the recalibrated constants, the crude oil price canfinally be forecast.

3. Empirical Analysis and Results

3.1. Data Description

This study uses world oil demand as a determinant of oil price. The general relationship betweenthe crude oil price and world oil demand is that an increase in oil demand causes oil prices to rise whilea decrease in oil demand leads to an oil price fall. Oil supply is another factor influencing the crude oilprice. For example, the possibilities that production capacity and production decisions of OPEC playan important role in oil price changes have been highlighted in conventional views [42,43]. AmongOPEC members, the role and behavior of Saudi Arabia, which can effectively host the bulk of the sparecapacity in oil markets, is especially found to be crucial [44,45]. Recent studies on OPEC’s ability toinfluence oil prices include [46–50]. The first and second oil crises of the 1970s were the results of chaosin the global oil market caused by an OPEC-engendered oil supply disruption. Similarly, even thoughcrude oil demand increased consistently worldwide after the outbreak of the Iraq war in 2003, OPEC’sspare oil production capability significantly decreased to below 1 million b/d. Such a tight crude oilmarket led to a rapid increase in the global oil price from the second half of 2003 until the end of 2004.Therefore, this study uses global oil supply as a basic factor influencing crude oil prices. Hamilton [51]and Hamilton [52] indicated global oil demand and supply are key factors of oil price fluctuation.

Recently, the oil market has moved with changes in the dollar exchange rate and stock prices.This trend has been noticeable since 2005, as oil and gold have become recognized as valuable ways tosecure assets amid the spread of unconfirmed information and a rapidly weakening dollar. Institutionalchanges in the financial market for oil, including the development of various financial derivatives andmore convenient cashing out, have also encouraged investment funds to enter the oil market. Thisstudy thus includes financial factors when forecasting the crude oil price. It is not easy to decide whichfinancial factor to select as a variable. Even though the scale of the WTI noncommercial net position maybe regarded as capturing the level of speculation, the noncommercial net position, in which speculativeand non-speculative forces are mixed, is not generally considered appropriate for forecasting oil prices.The correlation between the WTI spot price and the scale of the noncommercial net position is less than0.2, indicating that the two are unconnected. Meanwhile, the dynamic relationship between commodityprices and exchange rates has attracted much attention, although the direction of causality betweenthese two is still controversial among studies [53–55]. For example, Blomberg and Harris [56] indicatedexchange rate movements as an important stimulus for commodity price changes. Other studies alsofound that movements in US dollar exchange rates influence commodity price changes [57–59] and oilprices are no exception. While researchers have focused on various factors that influence internationaloil prices, the US dollar index is included as a major variable and is confirmed as an important factorfor oil price changes [60–66]. Moreover, its influence and control power on oil price increases graduallyand further strengthens after the global financial crisis in 2008 [62]. Many studies demonstrated anegative relationship between oil prices and the US dollar exchange rates [60–66]. Possible linkagesbetween the dollar index and oil price are suggested by Chai et al. [62]. Elbeck [60] clearly shows thisinverse relationship and demonstrates that the price of crude oil rises as the strength of the US dollardiminishes. This study thus employed the US dollar index as a proxy for financial factors because aweakening dollar usually encourages speculators to invest in commodity-related financial products,such as gold and oil: to make up for losses from a falling dollar, investors purchase commodity-relatedfinancial products.

Even though a product’s price should theoretically equal its marginal cost, the price ofnon-renewable resources such as oil is higher than the marginal cost even in a competitive market.Still, the global oil price is correlated with the marginal cost, and changes to the marginal cost over

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time influence the global oil price. Therefore, this study considered upstream costs when forecastingoil prices.

Additionally, geopolitical events can influence oil prices. Historically, the first and secondoil crises, wars in the Middle East, hurricanes, and cold snaps have all influenced oil prices. Theforecasting models introduced here thus use dummy variables to reflect serious geopolitical events,with 1 indicating the existence of such a situation.

In addition, this study analyzed the factors affecting oil prices by taking into accountnon-commercial net positions of the future market, the US commercial petroleum stocks, globaleconomic growth rate, and call on OPEC. However, these variables did not have a significant effect onoil prices although we are willing to provide the results using these additional variables upon request.Therefore, significant results were obtained on considering the demand and supply of world oil, dollarindex, average upstream cost, and geopolitical events. Since 39 time series data are used in this study,the degree of freedom is reduced when too many explanatory variables are used.

Table 2 summarizes the variables included in the forecasting model. The WTI spot price is usedas the dependent variable, and world oil demand and supply, the US dollar exchange rate, upstreamcosts, and geopolitical event dummies are used as explanatory variables. The analysis examines 1976to 2014 and the data trends during these periods are shown in Figure 1.

Table 2. Variables Used in the Crude Oil Price Forecasting Model.

Determinant Variable Description Data Source

WTI Spot Price WTI Annual average price, $/Bbl [67]World Oil Demand DEMAND Annual average demand, 1000 b/d [67]World Oil Supply SUPPLY Annual average supply, 1000 b/d [67]Financial Factor DOLLAR Value of dollar for major currencies (Dollar Index) [21]Upstream Cost COST Exploring, developing, and producing cost of crude oil [68]

Geopolitical Events GP Dummy variable (outbreak of oil crises, major wars, andeconomic recession: 1; nothing: 0) [69]

Sustainability 2016, 9, 190 7 of 15

forecasting models introduced here thus use dummy variables to reflect serious geopolitical events, with 1 indicating the existence of such a situation.

In addition, this study analyzed the factors affecting oil prices by taking into account non-commercial net positions of the future market, the US commercial petroleum stocks, global economic growth rate, and call on OPEC. However, these variables did not have a significant effect on oil prices although we are willing to provide the results using these additional variables upon request. Therefore, significant results were obtained on considering the demand and supply of world oil, dollar index, average upstream cost, and geopolitical events. Since 39 time series data are used in this study, the degree of freedom is reduced when too many explanatory variables are used.

Table 2 summarizes the variables included in the forecasting model. The WTI spot price is used as the dependent variable, and world oil demand and supply, the US dollar exchange rate, upstream costs, and geopolitical event dummies are used as explanatory variables. The analysis examines 1976 to 2014 and the data trends during these periods are shown in Figure 1.

Table 2. Variables Used in the Crude Oil Price Forecasting Model.

Determinant Variable Description Data SourceWTI Spot Price WTI Annual average price, $/Bbl [67]

World Oil Demand DEMAND Annual average demand, 1000 b/d [67] World Oil Supply SUPPLY Annual average supply, 1000 b/d [67] Financial Factor DOLLAR Value of dollar for major currencies (Dollar Index) [21] Upstream Cost COST Exploring, developing, and producing cost of crude oil [68]

Geopolitical Events GP Dummy variable (outbreak of oil crises, major wars, and

economic recession: 1; nothing: 0) [69]

Figure 1. Data for dependent and explanatory variables from 1976 to 2014.

3.2. Model Estimation

To estimate the proposed model, the parameters’ prior density function must first be set. As explained in Section 3, a survey of expert judgment or researchers’ subjective opinions can be used for estimating the prior density function. Here, it was estimated using researchers’ opinions due to time limitations. Thus, any researchers using this model should be sufficiently informed to recognize the current status and future prospects of the oil market by monitoring market movements. To reflect the current status of the oil market (in which prices are significantly influenced by supply factors in response to the shale gas boom), this study uses prior information, weighting the factors as

Figure 1. Data for dependent and explanatory variables from 1976 to 2014.

3.2. Model Estimation

To estimate the proposed model, the parameters’ prior density function must first be set.As explained in Section 3, a survey of expert judgment or researchers’ subjective opinions can be used

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for estimating the prior density function. Here, it was estimated using researchers’ opinions due totime limitations. Thus, any researchers using this model should be sufficiently informed to recognizethe current status and future prospects of the oil market by monitoring market movements. To reflectthe current status of the oil market (in which prices are significantly influenced by supply factors inresponse to the shale gas boom), this study uses prior information, weighting the factors as follows:20% for world oil demand, 50% for world oil supply, 10% for the US dollar, 10% for upstream costs,and 10% for geopolitical events. The relative importance of variables is derived from estimates usingthe linear model and monthly data for the last three years of the estimation period, 2007–2009.

The Bayesian model is updated via the WinBugs program using available data on the past oilmarket. After updating the model, the constant terms are revised based on the final oil price in thetime-series used in the estimation.

To test the goodness-of-fit and forecasting performance of the developed Bayesian models, OLSand neural network models are used as benchmarks. These models are widely used not only forforecasting oil prices but also for forecasting exchange rates and economic growth. By comparing theBayesian models with these benchmarks, goodness-of-fit and forecasting performance can be assessed.The OLS model is estimated via Eviews. The neural network model carries out learning by placingexplanatory variables in the input layer and dependent variables in the output layer. Through learning,the difference between the classification value generated and the actual value is gradually reduced toreach the final classification value. The input variables are transformed by a transfer function whentransferred from the input layer to the middle layer or from the middle layer to the output layer.A Bipolar Sigmoid Function produced the best fit; it has the following configuration.

Yt = f (n

∑i=1

XiWi) =

1− exp(−λn∑

i=1XiWi)

1 + exp(−λn∑

i=1XiWi)

(10)

The model used here has four hidden layers for each variable (of six total, including a constantterm). Therefore, 24 parameters were estimated (6 × 4).

The out-of-sample performance measure tests how accurately a model forecasts future demandusing the given data. It evaluates the accuracy of the forecast demand by calculating the error betweenforecast estimates and actual demand data after dividing the period studied into estimating andforecasting periods. Mean absolute percentage error (MAPE) is used to measure the error betweenforecast demand estimates and actual demand data, as it is common in research on demand forecasting.

MAPE =

L∑

t=1

|Pt−P̂t|Pt

L× 100 (11)

Here, P̂t is the estimated forecast, Pt is the actual data, and L is the observed period; MAPEmeasures the averaged forecasting error over period L.

3.3. Testing Model Goodness-of-Fit

To test the goodness-of-fit of the proposed model, the oil price is estimated and compared to actualdata; this is done using data on oil price determinants and WTI oil prices from 1976 to 2014. Since theresults might differ according to the data used, comparative analysis was undertaken, running fromthe first 34 data-points to the final 38, in consecutive order.

Table 3 shows the goodness-of-fit of the proposed model and benchmark models. The best modelat explaining past performance using past data is the neural network model. Most MAPE values forthe neural network model are below 12%. This result stems from the flexibility of the neural networkmodel: as it forecasts based on learning, not a normalized program, it explains the data best. A neural

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network model using a bipolar sigmoid function with a non-linear configuration has the highestestimation accuracy.

Table 3. Comparison of MAPE Values among Forecasting Models. (Unit: %).

ModelsPeriod

1976~2009 1976~2010 1976~2011 1976~2012 1976~2013

Proposed Model 27.76 18.33 14.51 19.24 14.64Linear Model 13.49 13.40 13.43 13.55 13.49

Neural Network Model 10.71 11.38 11.20 11.68 11.90

Note: The best MAPE is shown in bold.

Indeed, the goodness-of-fit of both the proposed model and the OLS model is inferior to thatof the neural network model. Since both models form a linear relationship between the explanatoryand dependent variables, they are less flexible. The MAPE of the proposed model remains highafter revising the constant terms because the revision was conducted using recent data; were itconducted over the whole period, the model goodness-of-fit would be better as the value of MAPEwould be reduced. This is not done because the purpose of the proposed model is to maximizeforecasting accuracy, not goodness-of-fit. If a model with excellent goodness-of-fit has inferiorforecasting accuracy, it is likely worthless as a forecasting model. This is a central concern in forecastingstudies. The goodness-of-fit is examined to understand the implications when comparing forecastingperformance across models.

3.4. Testing the Models’ Forecasting Performance

To test the models’ forecasting performance, an out-of-performance test is conducted. This methodcompares a model’s forecast results with the recent actual data, with the model estimated using adataset omitting this recent data. Table 4 helps explain the concept of the out-of-performance test.Among these tests, one-step-ahead forecasts compare the model’s forecast for 2014 with the actual datafor 2014, where the model is estimated after removing 2014 data from the set of available data, 1976 to2014. Other forecasts, such as two-step-ahead or five-step-ahead forecasts, use analogous concepts.

Table 4. Establishing the Test of the Model’s Forecasting Performance.

Out of Sample Observation Period Forecasting Period

One-ahead 1976~2013 2014Two-ahead 1976~2012 2013~2014

Three-ahead 1976~2011 2012~2014Four-ahead 1976~2010 2011~2014Five-ahead 1976~2009 2010~2014

The forecasting performance test, like the test of goodness-of-fit, uses the MAPE. As shown inTable 5, the neural network model, which proved the best in terms of goodness-of-fit, shows poorresults in the short term. However, its forecasting performance rapidly rises as the forecasting periodbecomes longer. The MAPE value for the neural network model in a three-step-ahead forecast is2.29%, which is the best result. The neural network model also shows the second-best results in thefour-step-ahead and five-step-ahead forecasts.

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Table 5. Results of Testing Forecasting Performance. (Unit: %).

1-Ahead 2-Ahead 3-Ahead 4-Ahead 5-Ahead

Proposed Model 0.46 0.65 4.71 4.27 5.15Linear Model 1.56 1.45 5.75 7.89 10.20

Neural Network Model 2.20 1.71 2.29 4.98 7.56

Note: The best MAPE is shown in bold.

The proposed model has the best forecasting performance because it is estimated by subjectivelyreflecting the characteristics of the oil market in the prior parameter density function. This is asurprising result when considering the proposed model’s poor goodness-of-fit and highlights thateven models with poor goodness-of-fit can have excellent forecasting performance. This result arisesbecause the proposed model uses the structure of the oil market (which will change in the present orfuture) as the prior information for determining the parameters. The proposed model, which focuseson the structure of the oil market that will develop in the present or future, does not explain past oilprices well. However, the purpose of this study is to develop a model for forecasting future oil prices,not explaining the past, and the proposed model fits this purpose. Some principles recommend notto use the within-sample fit of the model to select the most accurate forecasting model [70]. The OLSmodel shows a poor result in terms of goodness-of-fit but a strong result for short-term forecastingperformance. This is because the constant of the estimated linear model is revised using time-seriesdata for the final period. Such a linear model in which the constant term is revised seems simple butforecasts well.

As shown in Table 5, five-step-ahead forecasting performance is poor for all models: all MAPEvalues exceed 5%. The models were estimated using data that changed rapidly from 2006 to 2013: oilprices rapidly increased from 2005 to 2008, drastically dropped in 2009, then again increased until2011. The proposed model may solve such problems: if the signal that oil prices will suddenly rise iscaptured, the proposed model can accurately forecast oil prices by reflecting this information in theparameters’ prior density function. In the forecast results, only the 2014 characteristics were reflectedin the parameters’ prior density function in order to fairly compare among models.

3.5. Forecasting the Long-Term Crude Oil Price

This section presents results of forecasting oil prices until 2040 using the proposed model.To estimate the model, the prior distribution of parameters from experts’ opinion is first set consideringfuture trends in the oil market. We try to collect prior information based on reliable market reportsincluding [12,13,20,35] and the authors’ insight into the oil market. The mean and variance of thenormal distribution of parameters are set at the same value by the generic rule. This methodology isrecommended to be used by researchers with expertise in the international oil market. Non-experts onthe international oil market can gather prior information through survey of oil market experts.

OPEC’s market strategies have been attracting international concern in recent years, and theirimportance will grow in the future. As oil reserves of non-OPEC countries are drying up and majorinternational oil suppliers’ ability to increase production is weakening, OPEC’s strategies will becomemore important factors. According to the long-term forecasts of the IEA and EIA, OPEC’s market sharewill increase from about 40% at present to over 60% after 2020, and over 90% of additional demandwill depend on OPEC in 2040. Therefore, demand and supply in the global oil market will depend onOPEC’s market strategies (production policies); this study thus imposed a 40% weight on the priordistribution of the global supply variables.

Long-term oil prices will almost entirely depend on the global economic situation. If the globaleconomy recovers in the future, global oil demand will increase. If there is a global economic recoveryafter 2016, global oil demand will steadily grow. Since oil demand factors are consistently importantin determining the oil price, this study placed a weight of 30% on the prior distribution of the globaldemand variables. Since the possibility of a financial sector bubble (caused by the withdrawal of

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speculative funds and speculative demand) is expected to be low, this study imposed a 15% weight onthe prior distribution of financial variables and a 7.5% weight on the prior distribution of variablesrelated to upstream costs and geopolitical factors based on past trends, respectively. From the givenrelative importance of the variables, means of the prior distribution of the parameters are derived inEquation (8). The variances of the variables set at the same to means by the generic rule.

Table 6 depicts the estimated mean and standard deviation for the posterior distributions.According to the estimation results, more demand, less supply, lower dollar index, higher upstreamcost, and geopolitical events positively affect the crude oil price.

Table 6. Long-Term Oil Price Forecasts. (Unit: $/Bbl).

Time The Proposed Model EIA [20] IEA [35]

2017 46.6 50.0 -2018 52.0 54.6 -2019 57.3 69.5 -2020 62.6 78.6 792021 68.0 85.2 -2022 73.3 91.0 -2023 78.6 95.6 -2024 84.0 99.6 -2025 89.3 104.5 -2026 94.6 110.3 -2027 100.0 115.7 -2028 105.3 120.7 -2029 110.6 126.3 -2030 116.0 131.3 1112031 121.3 138.6 -2032 126.6 146.3 -2033 132.0 154.3 -2034 137.3 162.9 -2035 142.6 169.8 -2036 148.0 179.3 -2037 153.3 186.7 -2038 158.7 196.9 -2039 164.0 205.9 -2040 169.3 217.3 124

Note: IEA’s forecasts are based on new policies scenario. The forecasts of the proposed model and EIA [20] areprices in nominal dollars and IEA’ forecasts are prices in 2015 dollars.

4. Discussion and Conclusions

This study developed a model to forecast long-term oil prices that takes into account changesin the oil market and can inform government policies and business decision-making. A Bayesianapproach, specifically a Bayesian normal multiple regression model with informative priors, was usedfor forecasting. World oil demand and supply, the financial situation, upstream costs, and geopoliticalevents were used in the model as factors affecting oil prices. To test the forecasting performance of themodel, it was compared to estimates from OLS and neural network models. The goodness-of-fit wasthe best for the neural network model due to its flexibility, gained by connecting explanatory variableswith dependent variables in a nonlinear form.

Because the goal was maximizing forecasting accuracy rather than goodness-of-fit, however,this study focused on the model with the best forecasting performance. On this test, the proposedmodel outperformed the linear and neural network models. The proposed model gained improvedforecasting performance by reflecting recent and expected market information in its parameters usinga prior density function. The linear model also showed good forecasting results by recalibrating itsconstant term based on recent market data. On the other hand, the neural network model lagged inforecasting performance. Because the oil market structure changes constantly, a neural network model,

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which reflects average past trends in parameters, has limits for predicting the oil market. However, theproposed model also has uncertainty because prior information on parameters depends on experts’judgments. If experts misjudge the situation, they may forecast a distorted oil market. If expertsunderstand the global oil market and have accurate intuition, however, the proposed model will havethe best forecasting performance.

This study forecasts oil prices until 2040 using the proposed model and data on explanatoryvariables from the EIA. Greater relative importance was placed on oil supply based on a generalconsensus that the future oil market situation will depend on OPEC’s oil producing policies. The crudeoil price was estimated to increase to $170/Bbl in 2040. The EIA and IEA have forecasted that in2040 the oil price will reach $217/Bbl and $124/Bbl, respectively. The price estimated here is lowerthan the EIA estimate and higher than that of IEA because this study employs moderate assumptionsregarding the future oil market—i.e., that the future market will not be tight and that a speculativebubble is unlikely.

This study is significant in two ways. First, it employed a Bayesian approach to develop amodel that is able to explain the global oil market’s volatility and provide more accurate forecaststhan those of previous studies. Second, while most oil price forecasting models have focused onlyon short-term forecasts, this study estimated long-term forecasts. Its results can thus contribute topreparing quick and accurate countermeasures to a rapidly changing oil market. For example, it ispossible to predict transition speed to alternative energies including solar photovoltaic and wind.As public- and private-sector entities, such as airline companies and oil refineries, make long-termplans based on oil price forecasts, the price forecast here can be used to make policies and strategies inboth of these sectors.

Several limitations of this study deserve mention. First, this study does not consider the possibilitythat oil price fluctuations may influence crude oil supply and demand. As the oil price rises, demanddecreases and supply increases, and these changes then in turn influence the oil price again. Thisendogenous relationship has been captured in the recent strands of literature [3,6,71,72], althoughsome earlier studies treated the price of oil as exogenous [73,74]. The Bayesian model suggestedhere cannot reflect this circular structure, while it focuses on improvements in forecasting accuracy.As another benchmark model, the vector autoregressive (VAR) model was used and estimated in thisstudy, in order to reflect this endogenous relationship. Its estimation results are not presented onaccount of limited space. However, the results show lower forecasting accuracy. Models consideringsuch endogenous relationships, such as the VAR model, have their own drawbacks for long-termforecasting; for example, see [75–77] for further details. Therefore, an alternative model that relaxesthe assumption of an exogenous relationship among the oil price, demand, and supply is required,which is a direction for future research. Second, the model presented in this study did not accountfor the possibility in variation of the relative importance over time. According to our preliminaryanalysis, relative importance varies over time. We analyzed the variation of relative importance from1996 to 2009 and obtained relevant results. The variation of relative importance over time has its rootsin different reasons. For example, a structural shift in oil market power is highlighted by previousstudies [78,79]. However, the central part of our study is to enhance forecasting accuracy by usingboth experts’ judgment and available market data. Our model partly overcomes the assumption ofconstant relative importance by updating itself with available market data. Moreover, as the oil marketdynamics are changing continuously, it may not be very meaningful to assume future variation inrelative importance at the present point of time. In order to address time variation in the relativeimportance, however, the presented model can produce an updated forecasting result periodicallywith a different relative importance. A Bayesian model with time-varying coefficients may also be apossible alternative.

Acknowledgments: This work was supported by the Korea Energy Economics Institute (KEEI) grant funded bythe South Korean Prime Minister’s Office.

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Author Contributions: Chul-Yong Lee designed the study, outlined the methodology, developed and estimatedthe model, and wrote the manuscript. Sung-Yoon Huh reviewed the related literature, set up forecasting scenarios,interpreted the results, and revised the manuscript. All authors have read and approved the final manuscript.

Conflicts of Interest: The authors declare no conflict of interest.

References

1. Sadorsky, P. Oil price shocks and stock market activity. Energy Econ. 1999, 21, 449–469. [CrossRef]2. Barsky, R.B.; Kilian, L. Oil and macroeconomy since the 1970s. J. Econ. Perspect. 2004, 18, 115–134. [CrossRef]3. Kilian, L. Not all oil price shocks are alike: Disentangling demand and supply shocks in the crude oil market.

Am. Econ. Rev. 2009, 99, 1053–1069. [CrossRef]4. Segal, P. Oil price shocks and the macroeconomy. Oxf. Rev. Econ. Policy 2011, 27, 169–185. [CrossRef]5. Morana, K. The oil price-macroeconomy relationship since the mid-1980s: A global perspective. Energy J.

2013, 34, 153–190. [CrossRef]6. Kilian, L.; Murphy, D.P. The role of inventories and speculative trading in the global market for crude oil.

J. Appl. Econ. 2014, 29, 454–478. [CrossRef]7. Timilsina, G.R. Oil prices and the global economy: A general equilibrium analysis. Energy Econ. 2015, 49,

669–675. [CrossRef]8. Archanskaia, E.; Creel, J.; Hubert, P. The nature of oil shocks and the global economy. Energy Policy 2012, 42,

509–520. [CrossRef]9. International Energy Agency (IEA). Analysis of the Impact of High Oil Prices on the Global Economy; OCED/IEA:

Paris, France, 2004.10. Peersman, G.; Van Robays, I. Cross-country differences in the effects of oil shocks. Energy Econ. 2012, 34,

1532–1547. [CrossRef]11. Hsu, T.-K.; Tsai, C.-C.; Cheng, K.-L. Forecast of 2013–2025 crude oil prices: Quadratic sine-curve trend model

application. Energy Sources Part B 2016, 11, 205–211. [CrossRef]12. Organization of the Petroleum Exporting Countries (OPEC). 2015 World Oil Outlook; OPEC Secretariat:

Vienna, Austria, 2015.13. International Energy Agency (IEA). Medium-Term Oil Market Report; OCED/IEA: Paris, France, 2015.14. Finley, M. The oil market to 2030: Implications for investment and policy. Econ. Energy Environ. Policy 2012,

1, 25–36. [CrossRef]15. Choi, D. The Effect of Shale Gas Revolution on Oil Industry; The Institute of Energy Economics Japan: Tokyo,

Japan, 2013.16. Morana, C. A Semiparametric Approach to Short-term Oil Price Forecasting. Energy Econ. 2001, 23, 325–338.

[CrossRef]17. Bekiros, S.D.; Diks, C.G.H. The Relationship between Crude Oil Spot and Futures Prices: Cointegration,

Linear and Nonlinear Causality. Energy Econ. 2008, 30, 2673–2685. [CrossRef]18. Kaufmann, R.K.; Ullman, B. Oil Prices, Speculation, and Fundamentals: Interpreting Causal Relations among

Spot and Future Prices. Energy Econ. 2009, 31, 550–558. [CrossRef]19. Pindyck, R.S. The Optimal Exploration and Production of Non-renewable Resources. J. Political Econ. 1978,

86, 841–861. [CrossRef]20. Energy Information Administration (EIA). Annual Energy Outlook 2016; U.S. Department of Energy:

Washington, DC, USA, 2016.21. Reuters. 3000 Xtra Hosted Terminal Platform; Reuters: London, UK, 2015.22. Yoon, W. Comparison of Price Predictive Abilities between Futures Market and Expert System for WTI

Crude Oil Price. Resour. Environ. Study 2005, 14, 201–220.23. Abosedra, S.; Baghestani, H. On the Predictive Accuracy of Crude Oil Futures Prices. Energy Policy 2004, 32,

1389–1393. [CrossRef]24. Yanagisawa, A. Usefulness of the Forward Curve in Forecasting Oil Prices; Energy Working Papers; The Institute

of Energy Economics: Tokyo, Japan, 2009.25. Bollerslev, T. Generalized Autoregressive Conditional Heteroskedasticity. J. Econ. 1986, 31, 307–327.

[CrossRef]

Page 14: Forecasting Long-Term Crude Oil Prices Using a … · Forecasting Long-Term Crude Oil Prices Using a Bayesian Model with Informative Priors ... reason of oil shock, and

Sustainability 2017, 9, 190 14 of 15

26. Box, G.P.E.; Jenkins, G.M. Time Series Analysis: Forecasting and Control; Holden Day: San Francisco, CA,USA, 1978.

27. Morana, C. Oil price dynamics, macro-finance interactions and the role of financial speculation. J. Bank. Financ.2013, 37, 206–226. [CrossRef]

28. Cifarelli, G.; Paladino, G. Oil price dynamics and speculation: A multivariate financial approach. Energy Econ.2010, 32, 363–372. [CrossRef]

29. Lammerding, M.; Stephan, P.; Trede, M.; Wilfling, B. Speculative bubbles in recent oil price dynamics:Evidence from a Bayesian Markov-switching state-space approach. Energy Econ. 2013, 36, 491–502. [CrossRef]

30. Roberts, D.; Ryan, L. Evidence of speculation in world oil prices. Aust. J. Manag. 2015, 40, 630–651. [CrossRef]31. Fattouh, B.; Kilian, L.; Mahadeva, L. The Role of Speculation in Oil Markets: What Have We Learned So Far?

The Oxford Institute for Energy Studies: Oxford, UK, 2012.32. Armstrong, J.S. Principles of Forecasting; Kluwer Academic Publishers: Norwell, MA, USA, 2001; pp. 57–58.33. Koop, G.; Potter, S. Forecasting in Dynamic Factor Models Using Bayesian Model Averaging. Econ. J. 2004, 7,

550–565. [CrossRef]34. Li, H.; Wells, M.T.; Yu, C.L. A Bayesian Analysis of Return Dynamics with Stochastic Volatility and Levy

Jumps. Rev. Financ. Stud. 2008, 21, 2345–2378. [CrossRef]35. International Energy Agency (IEA). World Energy Outlook 2016; IEA Publications: Paris, France, 2016.36. Zellner, A. An Introduction to Bayesian Inference in Econometrics; Wiley and Sons: New York, NY, USA, 1971.37. Koop, G. Bayesian Econometrics; Wiley: Chichester, UK, 2003.38. Armstrong, J.S. Judgmental Bootstrapping: Inferring Experts’ Rules for Forecasting. In Principles of Forecasting;

Kluwer Academic Publishers: Norwell, MA, USA, 2001; pp. 171–192.39. Green, P.E.; Srinivasan, V. Conjoint analysis in consumer research: Issues and outlook. J. Consum. Res. 1978,

5, 103–123. [CrossRef]40. Putsis, W.P., Jr.; Srinivasan, V. Estimation Techniques for Macro Diffusion Models. In New Product Diffusion

Models; Mahajan, V., Muller, E., Wind, Y., Eds.; Kluwer Academic Publishers: Boston, MA, USA, 2000.41. Train, K. Discrete Choice Method with Simulation; Cambridge University Press: Cambridge, UK, 2003.42. Cremer, J.; Weitzman, M.L. OPEC and the monopoly price of world oil. Eur. Econ. Rev. 1976, 8, 155–164.

[CrossRef]43. Young, D.P.T. The nature of OPEC and oil price changes. Energy Econ. 1994, 16, 107–114. [CrossRef]44. Alkhathlan, K.; Gately, D.; Javid, M. Analysis of Saudi Arabia’s behavior within OPEC and the world oil

market. Energy Policy 2014, 64, 209–225. [CrossRef]45. Kaufmann, R.K.; Bradford, A.; Belanger, L.H.; Mclaughlin, J.P.; Miki, Y. Determinants of OPEC production:

Implications for OPEC behavior. Energy Econ. 2008, 30, 333–351. [CrossRef]46. Kaufmann, R.K.; Dees, S.; Karadeloglou, P.; Sánchez, M. Does OPEC matter? An econometric analysis of oil.

Energy J. 2004, 25, 67–90. [CrossRef]47. Wirl, F.; Kujundzic, A. The impact of OPEC conference outcomes on world oil prices 1984–2001. Energy J.

2004, 25, 45–62. [CrossRef]48. Gallo, A.; Mason, P.; Shapiro, S.; Fabritius, M. What is behind the increase in oil prices? Analyzing oil

consumption and supply relationship with oil price. Energy 2010, 35, 4126–4141. [CrossRef]49. Cavallo, A. Elephant in the room: How OPEC sets oil prices and limits carbon emissions. Bull. Atom. Sci.

2013, 69, 18–29. [CrossRef]50. Loutia, A.; Mellios, C.; Andriosopoulos, K. Do OPEC announcements influence oil prices? Energy Policy

2016, 90, 262–272. [CrossRef]51. Hamilton, J.D. Understanding Crude Oil Prices; NBER Working Paper No. 14492: Cambridge, MA, USA, 2008.52. Hamilton, J.D. Causes and Consequences of the Oil Shock of 2007-08; NBER Working Paper No. 15002;

National Bureau of Economic Research: Cambridge, MA, USA, 2009.53. Chen, Y.-C.; Rogoff, K.S.; Rossi, B. Can exchange rates forecast commodity prices? Q. J. Econ. 2010, 125,

1145–1194. [CrossRef]54. Trezzi, R. Exchange rates and commodity prices: Granger causality in the time-frequency domain.

Appl. Econ. Lett. 2014, 21, 224–227. [CrossRef]55. Zhang, H.J.; Dufour, J.-M.; Galbraith, J.W. Exchange rates and commodity prices: Measuring causality at

multiple horizons. J. Emp. Financ. 2016, 36, 100–120. [CrossRef]

Page 15: Forecasting Long-Term Crude Oil Prices Using a … · Forecasting Long-Term Crude Oil Prices Using a Bayesian Model with Informative Priors ... reason of oil shock, and

Sustainability 2017, 9, 190 15 of 15

56. Blomberg, B.; Harris, E.S. The commodity-consumer price connection: Fact or fable? Econ. Policy Rev. 1995, 1,21–38.

57. Pindyck, R.S.; Rotemberg, J.J. The excess co-movement of commodity prices. Econ. J. 1990, 100, 1173–1189.[CrossRef]

58. Sadorsky, P. The empirical relationship between energy futures prices and exchange rates. Energy Econ. 2000,22, 253–266. [CrossRef]

59. Zhang, Y.-J.; Fan, Y.; Tsai, H.-T.; Wei, Y.-M. Spillover effect of US dollar exchange rate on oil prices.J. Policy Model. 2008, 30, 973–991. [CrossRef]

60. Elbeck, M. Advancing the design of a dynamic petro-dollar currency basket. Energy Policy 2010, 38, 1938–1945.[CrossRef]

61. He, Y.; Wang, S.; Lai, K.K. Global economic activity and crude oil prices: A cointegration analysis. Energy Econ.2010, 32, 868–876. [CrossRef]

62. Chai, J.; Guo, J.-E.; Meng, L.; Wnag, S.-Y. Exploring the core factors and its dynamic effects on oil price:An application on path analysis and BVAR-TVP model. Energy Policy 2011, 39, 8022–8036. [CrossRef]

63. Ji, Q. System analysis approach for the identification of factors driving crude oil prices. Comput. Ind. Eng.2012, 63, 615–625. [CrossRef]

64. Aloui, R.; Ben Aïssa, M.S. Relationship between oil, stock prices and exchange rates: A vine copula basedGARCH method. N. Am. Econ. Financ. 2016, 37, 458–471. [CrossRef]

65. Coudert, V.; Mignon, V. Reassessing the empirical relationship between the oil price and the dollar.Energy Policy 2016, 95, 147–157. [CrossRef]

66. Jawadi, F.; Louhichi, W.; Ben Ameur, H.; Cheffou, A.I. On oil-US exchange rate volatility relationships:An intraday analysis. Econ. Model. 2016, 59, 329–334. [CrossRef]

67. British Petroleum (BP). BP Statistical Review of World Energy 2015; BP: London, UK, 2015.68. Center for Global Energy Studies (CGES). Upstream Costs and the Price of Oil; Center for Global Energy

Studies: London, UK, 2015.69. Korea National Oil Corporation (KNOC). Understanding Oil Industry; Korea National Oil Corporation: Ulsan,

Korea, 2016.70. Armstrong, J.S. Evaluating Forecasting Methods. In Principles of Forecasting; Kluwer Academic Publishers:

Norwell, MA, USA, 2001; pp. 443–472.71. Economou, A.; Agnolucci, P. Oil Price Shocks: A Measure of the Exogenous and Endogenous Supply Shocks of

Crude Oil; Society of Petroleum Engineers: Richardson, TX, USA, 2016.72. Kilian, L. Oil price shocks: Causes and consequences. Annu. Rev. Resour. Econ. 2014, 6, 133–154. [CrossRef]73. Lee, K.; Ni, S.; Ratti, R.A. Oil shocks and the macroeconomy: The role of price volatility. Energy J. 1995, 16,

39–56. [CrossRef]74. Ferderer, J.P. Oil price volatility and the macroeconomy. J. Macroecon. 1996, 18, 1–26. [CrossRef]75. Cooley, T.F.; LeRoy, S.F. Atheoretical macroeconometrics: A critique. J. Monetary Econ. 1985, 16, 286–308.

[CrossRef]76. Davids, R.A.; Zang, P.; Zheng, T. Sparse vector autoregressive modeling. J. Comput. Graph. Stat. 2016, 25,

1077–1096. [CrossRef]77. Moon, K.-S. A understanding of vector autoregressive model. J. Korean Off. Stat. 1997, 2, 23–56. (In Korean)78. Huppmann, D.; Hloz, F. Crude oil market power: A shift in recent years. Energy J. 2012, 33, 1–22. [CrossRef]79. Weber, F. Eastward Shifting Oil Markets and the Future of Middle Eastern Benchmarks; The Oxford Institute for

Energy Studies: Oxford, UK, 2015.

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