econometric models for oil price

CESifo Forum 1/200929

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ECONOMETRIC MODELS FOROIL PRICE FORECASTING:A CRITICAL SURVEY

GILIOLA FREY*MATTEO MANERA**ANIL MARKANDYA***ELISA SCARPA****

Introduction

In the last two years the price of oil and its fluctua-tions have reached levels never recorded in the his-tory of international oil markets. In 2007, the WestTexas Intermediate (WTI) oil price, one of the mostimportant benchmarks for crude oil prices, aver-aged around 72 $/b, while in 2008 the WTI price wasaround 100 $/b, with an increase of nearly 38 per-cent over the previous year. Within the past sixmonths, WTI daily spot prices ranged from almost150 $/b in early July to about 30 $/b towards the endof 2008.

The determinants of past, current, and future levelsof the price of oil and its fluctuations have been thesubject of analysis by academics and energy experts,given the relevance of crude oil in the worldwideeconomy. Although the share of liquid fuels in mar-keted world energy consumption is expected todecline from 37 percent in 2005 to 33 percent in2030, and projected high oil prices will induce manyconsumers to switch from liquid fuels when feasible,oil will remain the most important source of energy,and liquid fuel consumption is expected to increase

at an average annual rate of 1.2 percent from 2005 to

2030 (EIA 2008).

The crucial question of whether oil prices will rise in

the future or will decline again is timely. According

to EIA (2009), for example, under current economic

and world crude oil supply assumptions, WTI prices

are expected to average 43 $/b in 2009 and 55 $/b in

2010. The possibility of a milder recession or a faster

economic recovery, lower non-OPEC production in

response to current low oil prices and financial mar-

ket constraints, and more aggressive action to lower

production by OPEC countries could result in a

faster and stronger recovery in oil prices. Conse-

quently, it is extremely important for economists to

provide accurate answers to the complex problem of

forecasting oil prices.

This study aims at investigating the existing econo-

metric literature on forecasting oil prices. In particu-

lar, we (i) develop a taxonomy of econometric mod-

els for oil price forecasting; (ii) provide a critical

interpretation of the different methodologies; and

(iii) offer a comprehensive interpretation and justifi-

cation of the heterogeneous empirical findings in

published oil price forecasts. The paper is structured

as follows: we first introduce the historical frame-

work which is necessary to understand oil price

dynamics. The following section discusses and criti-

cally evaluates the different econometric models for

oil price forecasting proposed in the literature.

Finally we comment on alternative criteria for eval-

uating and comparing different forecasting models

for oil prices.

International oil markets: A historical framework

The history of oil consumption and prices goes back

to the second half of the 19th century. The introduc-

tion of oil distillation in 1853 gave rise to the use of

kerosene for home lighting. Not until the end of the

century did oil gain a much more relevant role, due

to its use for the generation of electricity. At that

time, the United States was the principal consumer

and its North-Eastern region was the main source of

* Eurizon Capital, Milan.** University of Milan-Bicocca, Milan.*** BC Basque Centre for Climate Change, Bilbao.**** Edison Trading, Milan.A previous version of this paper was presented at the First FEEMConference on the Economics of Sustainable Development held atthe Fondazione Eni Enrico Mattei (FEEM), Milan, January 2525,2007. The authors would like to thank Marzio Galeotti, AlessandroLanza, Michael McAleer and Yves Smeers for insightful discussion,as well as seminar participants at the University of Bath, FEEMand the University of Milan-Bicocca for helpful comments. Theauthors would also like to thank Linda Isola for excellent editorialassistance. This study does not necessarily reflect the views ofEurizon Capital and Edison Trading.

oil supply. The increasing consumption and the sub-sequent depletion of US North-Eastern reservessoon caused oil prices to rise, and Standard Oil, theoil company with a monopoly position at that time,was not able to control them. By the beginning of the20th century, oil production was extended to Texas,generating over-supply and price reductions. In themeanwhile, oil consumption spread to Europe andoil reserves were also discovered in Iraq and SaudiArabia, but the United States still remained the mainconsumer and maintained its dominance over theworld oil market.

One of the major economic agents in the world oilmarket in that period was the Texas RailroadCommission (TRC) that was founded in 1891 as aregulatory agency aimed at preventing discrimina-tion in railroad charges, later also controlledpetroleum production, natural gas utilities as wellas motor carriers. Given its dominant position inthe US market, TRC was able to set oil prices byeffectively fixing production quotas, at least untilthe formation of the Organization of PetroleumExporting Countries (OPEC). The other majoractors in the world oil markets were the so-calledseven sisters, five of which were American com-panies (Standard Oil of New Jersey (Esso),Standard Oil of California (Chevron), StandardOil of New York (Mobil), Gulf Oil and TEXA-CO), together with Royal Dutch Shell and theAnglo Persian Oil Company (BP). The seven sis-ters started to operate after the break-up ofStandard Oil by the US government. Their fairlycomplete monopoly and ability to work as a cartelallowed them to take control over oil prices forabout fifty years.

World War II definitely marked the predominance ofoil as an energy source. The excess of oil due to thecooperation between the United States and SaudiArabia offered America and its allies a privilegedaccess to this crucial resource. During the 1950s, newoil reserves were discovered in the Middle East, andnew producers entered the market, making it diffi-cult to limit oil production for the sake of controllingoil prices. In 1960 the Middle Eastern countriesformed the OPEC, a cartel meant to avoid competi-tion among its members and to prevent unsoughtprice reductions. In 1970, for the first time, the grow-ing US economy was not able to feed its increasingneed of oil from domestic sources and became animporting country. The effects of this dependencybecame visible very soon after the Yom Kippur War

in 1973, when the United States and many otherWestern countries supported Israel, catalyzing thereaction of the Arab exporting countries whichdeclared an embargo. As a result, within six monthsthe price of oil increased by 400 percent. Since 1973,the stability of oil prices has vanished, starting a peri-od of large price fluctuations.

A second phase of uncertainty affected world oilprices in 1979 and 1980, when the Iranian Revolutionand the Iraq-Iran War pushed oil prices to double.This period also revealed the inability of OPEC toact as a cartel. Saudi Arabias warning that highprices would reduce consumption remained unheed-ed and prices kept on rising, while oil demanddecreased. Furthermore, non-OPEC countries,attracted by the possibility of large gains at the highprice level, increased their oil production and, conse-quently, helped match oil supply and demand. Later,between 1982 and 1985, OPEC policy was devoted tostabilize prices by setting production quotas belowtheir previous levels. Unfortunately, this strategy wasoften hampered by the behaviour of some members,that kept on producing above their quotas. Duringthis period, Saudi Arabia played the swing produc-er role, adjusting its production to demand in orderto prevent price falls until 1986. Yet, burdened bythis role, this country changed its strategy thereafterand increased its oil production, causing an abruptprice decrease.

Prices kept on falling until the Gulf War of 1990. Theinvasion of Kuwait in this year created a suddenprice reversal, which was only normalized after 1993,when Kuwaiti exports outran their pre-war levels. Inthe early 1990s oil consumption started to rise again,aided by the growth of the Asian economies. Theincreasing rate of production by OPEC to meet thedemand was then the origin of the drastic pricereduction that occurred between 1997 and 1998,when the Asian growth slowed due to the financialand economic crises, and OPEC was faced by a mas-sive oversupply at the same time. In 1999 the pricesrose again, supported by the OPECs strategy ofreducing quotas, which was successful in spite of theincrease in non-OPEC production, at least until theterrorist attack of September 11, 2001. During theyears between 2002 and 2005, the majority of oil pro-ducer countries continued to adopt the policy of fix-ing low production quotas. This strategy, togetherwith the inadequate response of non-OPEC coun-tries to the increase in the oil demand, led to anincrease in oil prices, which have kept on rising until

CESifo Forum 1/2009 30

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the second half of 2008, when the monthly averageprice of WTI fell from 133 $/b in July 2008 to 41 $/bin December 2008 and January 2009.

Econometric models for oil price forecasting

In the existing empirical literature on oil price fore-casting one can distinguish among three categoriesof econometric models:

time series models exploiting the statistical prop-erties of the data, namely autocorrelation andnon-stationarity;

financial models based on the relationshipbetween spot and future prices; and

structural models describing how specific eco-nomic factors and the behaviour of economicagents affect the future values of oil prices.

The following subsections will illustrate the mainfeatures of each class of econometric models for oilprice forecasting, as well as the most relevant contri-butions which can be classified according to our pro-posed taxonomy.

(a) Time series models

Time series models aim at predicting future oil pricesby exploiting relevant characteristics of historicaldata. In this respect, a wide range of models havebeen proposed which can be divided into three maingroups, depending on their assumptions about thedata-generation process: martingale sequences,autoregressive models and mean-reverting specifica-tions. Given their simplicity, time series models haveoften been used as a benchmark for the forecastingperformance of financial and structural models. Inparticular, the random walk model (a particular caseof martingale sequence) is generally used to assesswhether more complex and expensive models areindeed justified by an improvement in their forecast-ing performance.

A martingale sequence for the oil spot price S is astochastic process such that the expected value of Sat time t+1 conditional on all available information Iup to time t is equal to the actual value of the oil spotprice at time t:

(1)

Its applications in finance go back to the introduc-tion of the efficient market hypothesis (EMH),often credited to Fama (1965), which states that, inthe presence of complete information and a largenumber of rational agents, actual prices reflect allavailable information and expectations for thefuture. In other words, current prices are the bestpredictor of tomorrows prices. A widely used formof the martingale process is the random walk spec-ification:

(2)

where t is an uncorrelated error term with zeromean and constant variance. According to thismodel, prices deviate from their current level onlybecause of casual fluctuations. The random walkwith drift represents a simple extension of this for-mula, which introduces a linear trend in the datageneration process:

(3)

In this case prices are assumed to constantly increase(decrease) from their previous level, except for sto-chastic deviations.

Oil prices can follow an autoregressive (AR)process:

(4)

where p is the order of the AR(p) process, p(L) isthe polynomial in the lag operator L of order p, andt is a white noise error term. Notice that this processcan either be explosive or stable depending onwhether the roots of the characteristic equationassociated with p(z) = 0 are outside or inside theunit circle. In the case of autoregressive processes,prices are not driven by random fluctuations, insteadthey are predictable from their history.

Oil prices can also be driven by a mean revertingprocess. This assumption comes from the evidencethat prices in financial markets tend to go back totheir average level after a shock. According to thisapproach, prices can neither be explained by the ran-tt

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dom walk assumption nor simply inferred from theirpast values. Given a long-run equilibrium level S*t ofthe oil spot price and a mean reversion rate , meanreverting models can be described as:

(5)

According to equation (5), future price variationsdepend on the disparity between actual and long-runprice levels, where the latter can be specified to be afunction of a set of exogenous variables.

More generally, error correction models (ECM) aredesigned to capture movements towards an equilib-rium level. Given two variables, X and Y, and anequilibrium level between the two variables, Y=X,variable Y tends to adjust to deviations from thisequilibrium according to the following scheme:

(6)

where Y*t = ^ Xt is the estimated equilibrium valuefor Y (see e.g. Engle and Granger 1987; Stock andWatson 1993).

In the empirical literature on oil price modelling andforecasting, several contributions provide empiricalevidence that is supportive of the EMH. Forinstance, Morana (2001) notices that, during the peri-od between January 4, 1982 and January 21, 1999, oilprices appeared to be characterized by a stochastictrend and exhibited alternating periods of high andlow volatility. Since these features can be a symptomof underlying dependencies in the behaviour of oilprices, Morana (2001) suggests to use a martingaleprocess to describe oil price dynamics. The reliabilityof a random walk model is also assessed byChernenko et al. (2004) with an application to thecrude oil future market.

Abosedra (2005) observes that the behaviour of theWTI spot price, S, during the period from January1991 to December 2001 can be approximated by arandom walk process with no drift. Consequently,the author proposes to forecast the one-month-ahead price of crude oil for every day using the pre-vious trading days spot price and to use the month-ly average of these daily forecasts to obtain amonthly predictor of the future oil price X.To assess

the statistical properties of this univariate forecast,the author suggests estimating the following rela-tionship:

(7)

and to test the null hypothesis = 0 and = 1, that isto test for the unbiasedness of X. However, sincecointegration between S and X can lead to biasedestimates of and in equation (7), the author fol-lows Phillips and Loretan (1991) and suggests a non-linear estimation of and and :

(8)

Both single and joint tests of the null hypotheses = 0 and = 1, suggest that X is an unbiased pre-dictor for future oil prices. Furthermore, theabsence of autocorrelation in the residuals con-firms the efficiency of the proposed forecastmethod.

The empirical evidence on autoregressive specifi-cations is much more controversial. Bopp andLady (1991) use an autoregressive specification todescribe monthly heating oil prices from the NewYork Mercantile Exchange (NYMEX). Theiranalysis covers the period between December1980 and October 1988, and confirms the goodperformance of the autoregressive model. Anautoregressive representation is used by Lalondeet al. (2003) to analyze the behaviour of WTIcrude oil prices. The authors show that this modelhas a very poor forecasting ability. Ye et al. (2005)verify the performance of an autoregressive speci-fication with seasonal effects in predicting month-ly oil prices in the period from January 2000 toJanuary 2003. Their model takes into account theconsequences of the reduction of OPEC produc-tion from 1999, using a leverage variable and adummy variable capturing the effects of the twintowers terrorist attack, of which impact is sup-posed to extend from October 2001 to March2002:

(9)


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A dynamic forecasting exercise shows the poor per-formance of this model, which is not able to captureoil price variations.

Pindyck (1999) analyzes the stochastic dynamics ofcrude oil, coal and natural gas prices using a largedata set covering 127 years, and tries to assesswhether time series models are helpful in forecastinglong horizons. The analysis ranges from 1870 to 1996,considering nominal oil prices deflated by wholesaleprices (p) (expressed in 1967 USD). The author pro-poses a model which accounts for fluctuations in boththe level and the slope of a deterministic time trend:

(10)

where 1t and 2t are unobservable state variables.Assuming normally distributed and uncorrelatederror terms, Pindyck computes a Kalman filter to esti-mate model (10). This procedure is a recursive esti-mate that calculates parameters via MaximumLikelihood, along with optimal estimates of the statevariables. The initial values are usually estimatedusing OLS and assuming that the state variables areconstant parameters. The author concentrates onthree sub-samples (18701970, 19701980, 18701981)and the full dataset to compare the forecasting abilityof the proposed model with respect to a model withmean reversion to a deterministic linear trend:

(11)

Results show that the deterministic trend model per-forms better in forecasting oil prices. Neverthelessequation (10) provides a more accurate explanationof oil prices fluctuations.

Radchenko (2005) proposes a univariate shifting-trends model for the long-term forecasting of energyprices:

(12)

which is a modified version of Pindyck (1999), wherethe error term is assumed to be an autocorrelatedprocess, rather than a simple white noise. In particu-lar, the author exploits the same dataset used byPindyck (1999) and considers four different forecast-ing horizons: 19862011, 19812011, 19762011,19712011. Radchenko (2005) suggests embeddingequation (12) into a Bayesian framework andobtains results similar to Pindyck (1999), except forthe autoregressive parameters , 1 and 2 whichappear less persistent. However, the author noticesthat forecasts from shifting-trend models cannotaccount for OPEC cooperation, thus predictingunreasonable oil price declines.As a solution, he sug-gests combining model (12) with an autoregressivemodel and a random walk model, which can be con-sidered a proxy for future cooperation. Results con-firm that forecasts can be improved by a combina-tion of different models.

A comprehensive comparison of the different time-series models proposed is offered by Zeng andSwanson (1998), who analyze four futures markets gold, crude oil, Treasury bonds and S&P500. Theauthors compare the performance of a random walkspecification with an autoregressive model and anerror correction model, where the deviation fromthe equilibrium level (ECT) is assumed to be equalto the difference between the future price for tomor-row and the futures for todays price, which is gener-ally called the price spread:

(13)

Daily data from April 1, 1990 to October 31, 1995,with a rolling out-of-sample forecast over the periodbetween April 1, 1991 and October 31, 1995, showsthat ECM are preferable when short forecast hori-zons are considered.

Prices may revert to a non-constant and uncertainvalue, which can evolve stochastically through time.Factor models are the direct translation of thisassumption, as they are meant to infer from the datathe nature of the stochastic unobservable factorsthat drive a given phenomenon. Schwartz and Smith(2000) provide an interesting example of a factormodel, where the spot price of a general commodityis decomposed into two factors, one capturing theequilibrium value (t), the other the short-run depar-

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tures from equilibrium (t). The short-run compo-nent t is assumed to follow an Ornstein-Uhlenbeckprocess reverting to a zero mean:

(14)

while the long-run level t is modelled according to aBrownian motion:

(15)

with dz and dz indicating the correlated incrementsof standard Brownian motion processes. Clearly, theOrnstein-Uhlenbeck process and the Brownianmotion represent the extension in continuous timeof the mean reverting process and the random walkprocess, respectively. Model shown in equations (14)and (15) can be generalized by including anotherstochastic factor, as the three factors model pro-posed by Schwartz (1997), where a stochastic inter-est rate is added as the determinant of spot pricesand it is modelled as a mean-reverting process.

(b) Financial models

The relationship between spot (S) and futures (F)prices can be represented as:

(16)

where F(t,T) is the futures price at time t for maturityT, r is the interest rate, S(t) is the asset price at time t.The underlying assumption is that it is possible toreplicate the payoff from a forward sale of an asset byborrowing money, purchasing the asset,carrying theasset until maturity and then selling the asset. Thiskind of arbitrage is known as the cost-of-carry arbi-trage. Referring to commodities (e.g. oil), relation-ship shown in equation (16) is no longer valid, unlessit is modified to include the costs of storage (w):

(17)

However, the activity of storing oil can provide somebenefits, which are generally indicated with the term

convenience yield (). Consequently, in the com-modities market, the future-spot relationshipbecomes:

(18)

From equation (18) the market can be either in con-tango (future price exceeds spot price) or in back-wardation (spot price exceeds future price), accord-ing to the relative size of w and .

Financial econometric models generally assume thatfutures and forward prices can be unbiased predic-tors for the future values of the spot price:

(19)

In order to test for unbiasedness, the followingmodel can be specified:

(20)

In equation (20), Ft is an unbiased predictor of St+1if the joint hypothesis 0 = 0 and 1 = 1 is not reject-ed (unbiasedness hypothesis), and it is also an effi-cient predictor if no autocorrelation is found in theerror terms (efficiency hypothesis). It is worth notic-ing that a violation of the unbiasedness hypothesisis generally interpreted as the presence of a riskpremium.

Fama and French (1987) propose a detailed com-parison between storage costs and risk premiaapplied to commodity markets. Although theirstudy does not include crude oil prices, it clearlyshows that empirical evidence in favour of storagecosts is easier to detect than the existence of riskpremia. Following this seminal paper, a significantpart of the empirical literature has focused on riskpremium models, although the findings on the exis-tence of a risk premium are mixed. An attempt tomodel the cost of storage relationship has been pro-posed by Bopp and Lady (1991), who include in theregression a proxy which measures the number ofmonths until expiration of the contracts corre-sponding to the futures price. Using monthly dataon NYMEX heating oil from December 1980 to


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October 1988, they confirm the statistical adequacyof this relationship. However, they also propose asimple random walk specification and a regressionmodel of spot prices on futures prices, which seemto perform equally well. Samii (1992) estimates theWTI futures oil price (three and six months) as afunction of the WTI spot price and an interest rate,using daily data for the years 19911992 andmonthly data over the period 19841992. In partic-ular, the author shows that oil storage should influ-ence spot prices in the intermediate run, while inthe long run prices should be led by a premium.Unfortunately, Samii (1992) does not find anyrobust evidence for either of the two hypotheses ofcost storage and risk premium. The conclusion isthat the interest rate does not play a relevant role,whereas spot and futures prices are highly correlat-ed, although it is not possible to identify the causaldirection of the relationship between spot andfutures prices.

Gulen (1998) extends model shown in equation (20)by incorporating the effects of posted price (C), i.e.the price at which oil is actually bought or sold by anoil company.The author proposes posted prices as analternative predictor to futures prices and statesthat, if futures prices are the best predictor, thenposted prices should have no explanatory power inthe following regression model:

(21)

Gulen (1998) analyzes monthly data of WTI spotand futures prices for one-, three- and six-monthahead, computed as a simple mean of daily data andcovering the period between March 1983 andOctober 1995. He shows that futures prices outper-form the posted price and that futures prices are anefficient predictor of spot prices. However, the post-ed price seems to have a predictive content, althoughlimited to the short run.

Zeng and Swanson (1998) use an ECM to forecastoil prices over the period 19911995. The specifica-tion of the long-run equilibrium refers to the cost-of-storage approach specified in equation (18), as theECT is defined as:

(22)

where cl denotes the number of days for the deliverycycle. As described in the previous section, Zeng andSwanson (1998) estimate also a random walk, anautoregressive model and an ECM, where the ECTis given by the price spread. The empirical evidenceis supportive of the ECM. Chernenko et al. (2004)focus on the spreads between spot price and futuresas well as forward prices by estimating the followingmodification of model (20):

(23)

In particular, the authors strategy is to test for theabsence of risk premia and, if the null is rejected, toinvestigate whether risk premia are time-varying orconstant by testing for 1 = 1. Results show thatfutures and forward prices do not generally outper-form the random walk model and cannot be consid-ered as rational expectations for the spot price.Furthermore, when the oil market is analyzed, riskpremium does not seem to be a relevant factor, whilethe empirical performance of futures prices is veryclose to the random walk specification.

Chin et al. (2005) examine how accurate futuresprices are in forecasting spot prices. They analyzethe relationship between three-, six- and twelve-month ahead futures prices and the current spotprice for crude oil (WTI), gasoline (Gulf Coast),heating oil (No.2 Gulf Coast) and natural gas(Henry Hub). Assuming that the spot price followsa random walk with drift and rational expectations,the authors estimate a logarithmic version of equa-tion (23) with OLS and robust standard errors. Forthe period from January 1999 to October 2004, theauthors show that futures prices at different maturi-ties are unbiased predictors of spot oil prices, andthey find empirical evidence in favour of the effi-cient market hypothesis.

The two hypotheses of storage costs and risk premi-um are tested by Green and Mork (1991) for the oilmarket during the period 19781985. They concen-trate on Mideast Light and African Light/North Seamonthly prices using Generalized Method ofMoments (GMM) estimates. The most interestingresult is that in the years 19781985 there is no evi-dence of unbiasedness/efficiency, while the subperi-od 19811985 seems to support the hypothesis ofefficiency in the oil financial market. Serletis (1991)analyzes daily spot and futures prices of NYMEX

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heating oil and crude oil over the period betweenJuly 1, 1983 and August 31, 1988, as well as daily spotand futures prices of unleaded gasoline over theperiod between March 14, 1985 and August 31, 1988.The aim of his contribution is to measure the fore-cast information contained in futures prices and thetime-varying risk premium. The empirical findingssuggest that variations in the premium worsen theforecasting performance of futures prices.

Moosa and Al-Loughani (1994) use monthly datafrom January 1986 to July 1990 on WTI spot, three-and six-month futures prices to test unbiasednessand efficiency. Given the presence of cointegrationbetween spot and futures prices, they extend equa-tion (20) in an error correction form:

(24)

In this case, unbiasedness corresponds to the nullhypothesis 0 = 0, 1 = 1, 2 = 1, i = i = 0, i.Results show that futures prices are neither unbiasednor efficient. Assuming rational expectations andusing a GARCH-in-mean specification to take intoaccount non-constant volatility, the authors analyzethe structure of the risk premium, which turns out tobe time-varying.

Morana (2001) shows that one-month ahead for-ward prices are a poor predictor of futures spotprices, since in more than 50 percent of the casesthey fail to predict the sign of oil price changes. Theauthor compares the forecasting ability of the Brentforward price with the accuracy of a simple randomwalk model, using daily data from November 2, 1982to January 21, 1999 and considering a long forecast-ing horizon (May 2, 1985January 21, 1999) and ashort forecasting period (November 21,1988January 21, 1999). The decomposition of themean squared forecast error (MSFE) and the signtests show that forecasting with forward prices orwith a random walk does not yield significantly dif-ferent results. Specifically, over a short time horizonboth methods are biased, while, when a longer timeperiod is considered, they do produce unbiasedforecasts, although their performance resemblesthat of a random guess. Nevertheless, Morana(2001) points out that an appropriate use of forward

prices can be promising, as they are reliable predic-tors when oil price volatility is small. FollowingBarone-Adesi et al. (1998) and Efron (1979), theauthor uses bootstrap methods to approximate theoil price density function, which is characterized bytime-varying volatility. The resulting confidenceintervals for oil price forecasts confirm that fore-casting with forward prices future values of theprice of oil is less reliable, as the confidence inter-vals tend to widen as volatility increases. Cortazarand Schwartz (2003) use a three factor model toexplain the relationship between spot and futuresprices. Daily data from the NYMEX over the peri-od 19912001 confirm the accuracy of the model.The authors propose a minimization procedure asan alternative to the standard Kalman filterapproach, which seems to produce more reliableresults.

Another interesting evaluation of financial models iscarried out by Abosedra (2005), who compares theperformance of futures prices (F) with a simple uni-variate forecast (X). As already mentioned,Abosedra (2005) assumes a random walk processwith no drift for spot crude oil prices (S), and sug-gests using the previous trading day spot price toforecast the one-month ahead price of crude oil forevery trading day. The monthly forecast is set equalto the simple average of the daily forecasts. Usingthe approach described in the section related to timeseries models, the author establishes that the for-ward price and the simple univariate forecast areunbiased and efficient predictors for the future valueof the spot price of oil.A more formal comparison ofthe two predictors is based on testing whether theforecast error related to each forecast can beimproved by the information contained in the otherforecast. This comparison corresponds to a test ofthe null hypothesis 1 = 0 and 1 = 0, i = 1,..., n, inmodels:

(25)

(26)

Results show that futures prices can reduce the uni-variate forecast error, while the converse is not true.


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These findings lead to conclude that futures pricesare semi-strongly efficient.

Murat and Tokat (2009) analyze the relationshipbetween crude oil prices and the crack spreadfutures. In the oil industry the crack spread is definedas the difference between the price of crude oil andthe price of its products. In other words, the crackspread represents the profit margin that can beobtained from the oil refining process. An ECM isspecified to assess the direction of the causal rela-tionship between crude oil price and crack spread, aswell as to predict the price of oil from the crackspread futures, using weekly data from the NYMEXover the period from January 2000 to February 2008.The empirical evidence suggests that the crackspread helps to predict oil prices. When its perfor-mance is compared with a random walk model and aregression of the spot price on futures oil prices, theauthors find out that both crack spread and crude oilfutures are preferable to the random walk specifica-tion, although futures prices are slightly more accu-rate than the crack spread futures.

(c) Structural models

Structural models relate the oil price behaviour to aset of fundamental economic variables.The variablesthat are typically used as the economic drivers of thespot price of oil can be grouped into two main cate-gories: variables that describe the role played byOPEC in the international oil market, and variablesthat measure current and future physical oil avail-ability. In this context researchers have generallyconsidered measures of OPEC behaviour, such asproduction quotas, overproduction, capacity utilisa-tion and spare capacity. It is well known that OPECperiodically establishes the quantity of oil to be pro-duced by its members (OQ) in order to pursue oilmarket stability. It is also well acknowledged that, onseveral occasions, some OPEC countries have decid-ed to produce more than their fixed production quo-tas.This overproduction (OV) is computed as the dif-ference between OPEC production (OP) and quo-tas. Another relevant factor is production capacity.This variable is introduced in structural models intwo different ways. On the one hand, some authorshave used capacity utilization (CU), computed as100 times the ratio between production and produc-tive capacity (PC). On the other hand, some authorshave proposed spare capacity (SC), defined as thedifference between production and productivecapacity.

Besides the impact of OPEC, many authors havealso recognized the importance of the current andfuture availability of physical oil. According to thisview, the most crucial variable is represented by thelevel of inventories. Stocks are the link between oildemand and production and, consequently, they area good measure of price variation. Most authorshave considered two kinds of stocks, namely gov-ernment (GS) and industrial (IS). Due to theirstrategic nature, government inventories are notgenerated by a supply-demand mechanism and aregenerally constant in the short run. This explainsthe decision of many researchers to introduce intheir models industrial stocks that vary in the shortrun and are able to account for oil price dynamics.When industrial inventories are considered, theyare generally expressed in terms of the deviationfrom their normal level (ISN), which is defined asthe relative inventory level (RIS). Operationally,RIS is calculated as:

(27)

In equation (27), ISNt indicates the de-seasonalizedand de-trended industrial stock level, i.e.

(28)

where t is a linear trend and Di is a set of monthlydummies, used to detect seasonal variations. Sincegovernment stocks are not subject to seasonality,their relative level (RGS) is specified as follows:

(29)

being GSNt the de-trended government stock level,defined as:

(30)

Zamani (2004) presents a short-term quarterly fore-casting model of the real WTI price (W) thataccounts for both the role of OPEC and the physicaloil availability. Besides the significance of both kinds

tttISNISRIS =

ii

i

tDtISN

++12

2=

10=

tttGSNGSRGS =

tGSNt 10= +

of relative inventory levels, the author includes in hismodel OPEC quotas, overproduction and non-OECD demand (DN) as explanatory variables. Inparticular, Zamani (2004) proposes an ECM, esti-mated using the two-step approach by Engle andGranger (1987), where the long-run equilibrium isspecified as:

(31)

and the short-run dynamics is described by:

(32)

In equations (31) and (32), D90 is a dummy vari-able for the Iraqi War in the third and fourth quar-ter of 1990. Using data for the period 19882004,Zamani (2004) shows that an increase in all theexplanatory variables generates a reduction of theprice of oil, while the dummy variable and the non-OECD demand positively affect the real WTI price.It is worth noticing that the in-sample dynamicforecasts computed on the basis of this model arequite accurate, according to standard forecast eval-uation criteria.

Ye et al. (2002, 2005 and 2006) use relative oil inven-tory levels to forecast oil prices. Ye et al. (2002)describe oil prices as a function of RIS and of a vari-able accounting for a lower-than-normal level ofinventories. The specification is empirically testedusing a monthly dataset which covers the periodfrom January 1992 to February 2001. This model isgeneralized by Ye et al. (2005), who use monthly datafrom 1992 to 2003 to analyze the relationshipbetween WTI spot price and oil stocks. Defining rel-ative industrial inventories as described in equations(27) and (28), they suggest modeling the WTI spotprice as:

(33)

where D01 is a dummy variable for the periodbetween October 2001 and March 2002, which takesinto consideration the consequences of the terroristattack on 11 September 2001, and S99 is a leveragevariable which captures the impact on the oil marketof a structural change in the OPECs behaviour. Theevaluation of this model is conducted through acomparison with a pure time series model and thefollowing regression:

(34)

where relative inventories are substituted by indus-trial inventories, which are assumed to affect oilprices with a one-month lag and to depend on thedeviation from their previous year level. One-, two-,three- and six-month ahead forecasts over the peri-od from January 2000 to January 2003 show thatequation (33) outperforms the other two specifica-tions.When considering the three-month ahead fore-casts, equation (34) produces more satisfactoryresults in the presence of a price trough, while equa-tion (33) is more accurate in the presence of pricepeaks. More recently, Ye et al. (2006) extend thework by Ye et al. (2005), allowing for asymmetrictransmission of inventory changes to oil price. Theauthors claim that the response of the oil priceshould be different, depending on the level of therelative stocks:

(35)

(36)

where LIS is the low inventory level, HIS is the highlevel of inventories, and IS is the standard deviation


Focus

ttttt RGSRISOVOQS ++++= 54321

ttt DDN +++ 9076

iti

m

i

iti

m

i

t OVOQS +++ 21=

1

1=

0=

iti

m

i

iti

m

i

RGSRIS ++

4

1=

3

1=

tttiti

m

i

DDN ++++

165

1=

90

ttjj

j

iti

i

t SSDRISS +++++ 11

5

0=

3

0=

0 9901=

ttjj

j

tt ISSDSS ++++ 9901= 110

5

0=

110

ttt ISIS ++ )( 122

+

otherwiseLIS

RISifRISLIS

t

IStIStt

0=

=


Focus

of IS for the entire period. The specification pro-posed for the forecasting model introduces both lin-ear and non-linear terms, according to the followingscheme:

(37)

Results show that the use of asymmetric behaviorhelps to predict oil prices and that the forecastingability of equation (37) is stronger than the simplelinear specification.

Kaufmann (1995) outlines a model for the world oilmarket that accounts for changes in the economic,geological and political environment. This model isdivided into three blocks: demand, supply and realoil import prices (PCO), analyzed over the period19541989. Due to the presence of two dominant oilproducers in the period under scrutiny, the authormodels oil prices as a function of the behaviour ofboth agents:

(38)

where WD is the world oil demand, DOPEC is adummy variable for the strategic behaviour ofOPEC, S74 is a step dummy for the 1974 oil shock,and SOECD is the level of OECD stocks. Equation(38) appears to have a good explanatory power indetecting oil price variations. It is interesting to notethat the key factor in OPECs behaviour is OPECcapacity.

Focusing on the recent history of oil prices,Kaufmann et al. (2004 and 2006) modify equation(38) by excluding the role of the TRC. The new spec-ification places much more emphasis on OPECsbehaviour, since it accounts for OPEC overproduc-tion besides OPEC quota and capacity utilization.Furthermore, the modified model outlines theimpact of a new variable the number of days of for-ward consumption (DAYS) proxied by the ratio ofOECD oil stocks to OECD oil demand. Their analy-sis is centered on the following equation:

(39)

where DS are seasonal dummies and D90 is adummy variable for the Persian Gulf War in the thirdand fourth quarters of 1990. The two studies carriedout based on quarterly data differ with respect to thetime period considered, which is 19862000 inKaufmann et al. (2004), while Kaufmann et al. (2006)refer to the time interval 19842000. An error cor-rection representation of equation (39) is estimatedvia the Dynamic OLS (DOLS) approach proposedby Stock and Watson (1993) and using FullInformation Maximum Likelihood (FIML). Resultsindicate that OPEC quotas, production and capacityutilization are important in affecting oil prices. In-sample dynamic forecasts from the first quarter of1995 to the third quarter of 2000 suggest that theperformance of the model depends on the consid-ered time period, although the proposed specifica-tion is able to capture the consequences of variousexogenous shocks on the oil price level.

Merino and Ortiz (2005), extending the variousworks of Ye et al. (2002, 2005 and 2006), investigatewhether some explanatory variables can account forthe fraction of oil price variations that is notexplained by oil inventories. The authors acknowl-edge as possible sources of variation: the differencebetween spot and futures prices; speculation definedas the long-run positions held by non-commercials ofoil, gasoline and heating oil in the NYMEX futuresmarket; OPEC spare capacity along with the relativelevel of US commercial stocks; different long-runand short-run interest rates. Exploiting causality andcointegration tests, the authors identify the impor-tance of the speculation variable which, among oth-

St =0 +1St1 +j=0

5

jD01 j + S99 +i=0

k

iRISt i

+i=0

k

( iLISt i + iLISt i2)

j

+i=0

k

(iHISt i + iHISt i2) + t

2 210 1

1

=t t TRC tt

t

PCO PCOCU CU

PCO

+

12

1

t t tt

t t

PC PC OPCU

PC WD

+ +

3 1( )t tDOPEC DOPEC +

4 5 174t tS PCO + +

6 ( )t

t t

t

OPSOECD

WD + +

tttt OVOQDAYSPCO ++++= 3210

ttii

i

t DDSCU ++++ 904

3

1=

4

ers, appears to add systematic information to themodel. Given the presence of cointegration, theauthors eventually propose an error correctionmodel, where oil prices are function of the percent-age of relative inventories on the total current levelof inventories and of speculation (SPEC):

(40)

Data from January 1992 to June 2004 show that spec-ulation helps predicting prices throughout the wholesample, except for the period 20002001.

A different approach in forecasting oil prices is pro-posed by Lalonde et al. (2003), who test the impactof the world output gap and of the real US dollareffective exchange rate gap on WTI prices. A com-parison with a random walk and with an AR(1) spec-ification suggests that both variables play an impor-tant role in explaining oil price dynamics. In Dees etal. (2007) oil prices are driven by OPEC quotas andcapacity utilization, which are shown to be statisti-cally relevant over the period 19842002. Sanders etal. (2009) investigate the empirical performance ofthe EIA model for oil price forecasting at differenttime horizons. This model is a mixture of structuraland time series specifications, which includes supplyand demand as the main factors driving oil prices,and takes into account the impact of past forecasts.The authors find that EIA three-quarter ahead oilprice forecasts are particularly accurate.

Evaluation and comparison of oil price forecastmodels

In this study we have described three broad classesof econometric models that have been proposed toforecast oil prices. We have also presented the differ-ent and often controversial empirical results in therelevant literature. Any attempt to compare alterna-tive oil price forecasts should be based on a compre-hensive evaluation of the underlying econometricapproach and model specification.

There are a number of statistical issues which shouldbe accounted for in the development of an econo-metric model. Heteroskedasticity (both uncondition-

al and conditional) as well as autocorrelation in theerrors of a regression model are common problems,which, if unsolved, lead to misleading statisticalinference. Another issue that comes up frequentlywhen dealing with financial data is non-stationarity,as it is acknowledged that prices are often integratedof order one, or even two. Granger and Newbold(1974) warn that spurious regressions may arise inthe presence of non-stationary variables. However,when non-stationary prices are cointegrated, it isthen possible to overcome the spurious regressionproblem and to embed in the forecasts the informa-tion provided by the existence of one (or more thanone) long-run equilibrium.

Out of the 26 papers we have reviewed, 20 provide atest for autocorrelation, 15 for heteroskedasticityand 20 account for non-stationarity and cointegra-tion (see Table 1). Needless to say, the absence ofexplicit references to the use of heteroskedasticityand error autocorrelation tests as well as to a sys-tematic check for the presence of unit roots in theanalyzed series does not imply that those issues havenot been accounted for, and, above all, it cannot beinterpreted as evidence for the presence of het-eroskedasticity, autocorrelation or non-stationaritiesin the analyzed data. Rather, it denotes that someauthors consider it unimportant to test the statisticaladequacy of their models.

The frequency of the data influences the statisticalcharacteristics of the series, as low frequencies tendto smooth volatility. As a consequence, the choice ofthe data frequency can produce significant effects onthe performance of a forecasting model. In general,if daily data are more volatile than their weekly,monthly and yearly averages, low-frequency oilprices can be more easily predicted than their high-frequency counterparts. The data frequencies usedby the contributions reviewed in our survey are nothomogeneous. Yet monthly data are most widelyemployed by each of the three classes of models,while weekly data are used just twice.

In addition, the literature surveyed in our paper canhelp to answer another question: what is the gain, ifany, from using a large set of control variables in aforecasting model? In other words, why dont wesimply follow the idea that all relevant informationto forecast the oil price is embedded in the priceitself? Random walks, martingale processes and sim-ple autoregressive models root their justification onthis idea. In this respect, random walk and martin-


Focus

t

t

t

t

t

tSPEC

IS

RIS

IS

RISW +++

3

1

1

210=

tttWSPEC +++

1514


Focus

gale models exploit the actual value of the price to

forecast its future values, while autoregressive speci-

fications evaluate also the lagged price values. These

models have been used in many papers as bench-

marks to check the forecasting performance of more

complex specifications. Specifically, 9 papers out of

26 use the random walk model as a benchmark,

while 4 papers compare the forecasting results of

their econometric models with simple autoregressive

specifications. It is important to notice that the ran-

dom walk and the autoregressive model never out-

perform the more general specifications.

Structural models are generally considered to be an

extension of autoregressive specifications that inte-

grate the information embedded in the price history

using proxies for particular relevant aspects of the

oil market and the world economy. Among the sur-

veyed papers belonging to this category, two

(Lalonde et al. 2003; Ye et al. 2005) use a benchmark

model as a comparison. Of these two contributions,

only Ye et al. (2005) show that structural models out-

perform time series specifications. Financial models

are based on different assumptions, as they arise

either from the arbitrage theory or from the REH.

Out of 13 papers in this group, 6 formally compare

their models with a benchmark, either a randomwalk or an autoregressive specification.

The comparison with specifications which could dif-fer from the standard benchmark models is system-atically used in the papers we have reviewed as ageneral strategy to assess the accuracy of oil priceforecasts. In Tables 2 to 4 we report the criteria pro-posed by the reviewed literature to evaluate theforecasting accuracy of a model, and also demon-strate that model comparison is common practice forvirtually all of the structural, financial and timeseries models considered in this survey. Someauthors (e.g. Radchenko 2005) suggest that, ratherthan selecting among different forecasts producedby different models, a good strategy is to combinethe forecasting performance of different specifica-tions. By combining the forecasted values obtainedfrom an autoregressive, a random walk and a shiftingtrend model, it is possible to obtain significantincreases in the accuracy of the forecasts.

The type of econometric model used in forecastingthe price of oil seems to affect the type of forecaststhat is produced. As Tables 2 to 4 clearly show, themajority of time series and structural specificationsmainly use dynamic forecasts to assess the perfor-

Table 1

Diagnostic checking and time series properties of the data

Year Authors Serial correlation HeteroskedasticityNon stationarity and

cointegration

1991 Bopp and Lady X

1991 Green and Mork X X X

1991 Serletis X X X

1992 Samii X

1994 Moosa and Al-Loughani X X X

1995 Kaufmann X X

1998 Gulen X

1999 Pindyck X X X

2000 Schwartz and Smith X X

2001 Morana X X X

2002 Ye et al. X

2002 Zeng and Swanson X X

2003 Cortazar and Schwartz X X

2003 Lalonde et al. X X

2004 Chernenko et al. X X

2004 Zamani X

2005 Abosedra X X

2005 Chin et al. X X X

2005 Kaufmann et al. X X X

2005 Merino and Ortiz X

2005 Radchenko X X X

2005 Ye et al. X X X

2006 Kaufmann et al. X X X

2006 Ye et al. X X X

2007 Dees et al X

2009 Murat and Tokat X

Notes: X indicates the the authors have checked for serial correlation and/or heteroskedasticity and/or nonstationarity and

cointegration.

mance of the analyzed model, while in the class offinancial models static and dynamic forecasts havebeen equally employed. Given the well-known dif-ference between static and dynamic forecasts, thelatter seem to be more reasonable in the presentcontext. Graphical evaluation of the forecasting per-formance of a given econometric specification hasbeen widely used for structural models and, thoughin a limited number of cases, for time series modelsas well. Conversely, graphical methods are rarelyconsidered in financial models. Finally, it is worthy tonote that the measures of forecast errors commonly

used by the surveyed articles are the root meansquared error (RMSE), the mean absolute percent-age error (MAPE), the mean average error (MAE)and the Theil inequality coefficient (Theil) (see alsoTables 2 to 4). Those criteria have been taken intoaccount mainly by time series as well as structuralmodels, and only in few cases by financial models.Despite the relatively large number of criteria, whichare available to evaluate the forecasting perfor-mance of each proposed model, it is not possible toidentify which class of models outperforms the oth-ers in terms of forecasting accuracy.


Focus

Table 2

Criteria for comparing in-sample and out-of-sample forecasts: time series models

In-sample forecasts

Type of

forecast Model comparison Forecast evaluation

Year Authors

Static Dynamic

Graphical

evaluationFormal Informal RMSE MAPE MAE Theil Others

2005 Abosedra X X X

2005 Ye et al. X X X X X X X X

Out-of-sample forecasts

1991 Bopp and

Lady X X X X X X

1999 Pindyck X X X

2000 Schwartz and

Smith X X X X

2001 Morana X X X X X X

2002 Zeng and

Swanson X X X X X X

2003 Lalonde et al. X X X X X

2004 Chernenko et

al. X X X


2005 Radchenko X X X X

Notes: X indicates the presence of a specific criterium; RMSE = root mean squared error; MAPE = mean absolute percentage

error; MAE = mean absolute error

Table 3

Criteria for comparing in-sample and out-of-sample forecasts: financial models

In sample forecasts

Type of forecastModel

comparisonForecast evaluation

Year Authors

Static Dynamic

Graphical

evaluationFormal Informal RMSE MAPE MAE Theil Others

1992 Samii X

1998 Gulen X

2004 Chernenko et al. X X X

2005 Chin et al. X X X X X

1994 Moosa and Al-

LoughaniX X

2005 Abosedra X X X

Out of sample forecasts

1991 Bopp and Lady X X X X X X

2001 Morana X X X X X X

2002 Zeng and

Swanson X X X X X X

2003 Contazar And

SchwartzX X X X X X

2009 Murat and Tokat X X X X X X


error; MAE = mean absolute error


Focus

References

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Chernenko, S., K. Schwarz and J. H. Wright (2004), The InformationContent of Forward and Futures Prices: Market Expectations and thePrice of Risk, FRB International Finance Discussion Paper 808.

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Efron, B. (1979), Bootstrap Methods: Another Look at theJackknife, Annals of Statistics 7, 126.

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Engle, R. F. and C. W. J. Granger (1987), Co-integration and ErrorCorrection: Representation, Estimation and Testing, Econometri-ca 55, 251276.

Fama, E. F. (1965),The Behaviour of Stock Market Prices, Journalof Business 38, 420429.

Fama, E. F. and K. R. French (1987), Commodity Future Prices:Some Evidence on Forecast Power, Premiums, and the Theory ofStorage, The Journal of Business 60, 5573.

Granger, C. W. J. and P. Newbold (1974), Spurious Regressions inEconometrics, Journal of Econometrics 2, 111120.

Greenand, S. L. and K. A. Mork (1991), Towards Efficiency in theCrude Oil Market, Journal of Applied Econometrics 6, 4566.

Gulen, S. G. (1998), Efficiency in the Crude Oil Futures Markets,Journal of Energy Finance and Development 3, 1321.

Kaufmann, R. K. (1995), A Model of the World Oil Market forProject LINK: Integrating Economics, Geology, and Politics,Economic Modelling 12, 165178.

Kaufmann, R. K. (2004), Does OPEC Matter? An EconometricAnalysis of Oil Prices, The Energy Journal 25, 6791.

Lalonde, R., Z. Zhu and F. Demers (2003), Forecasting and Analyz-ing World Commodity Prices, Bank of Canada, Working Paper200324.

Merino, A. and A. Ortiz (2005), Explaining the So-called PricePremium in Oil Markets, OPEC Review 29, 133152.

Moosa, I. A., and N. E. Al-Loughani (1994), Unbiasedness andTime Varying Risk Premia in the Crude Oil Futures Market,Energy Economics 16, 99105.

Morana, C. (2001), A Semiparametric Approach to Short-term OilPrice Forecasting, Energy Economics 23, 325338.

Murat, A. and E. Tokat (2009), Forecasting Oil Price Movementswith Crack Spread Futures, Energy Economics 31, 8590.

Phillips, P. C. B. and M. Loretan (1991), Estimating Long-runEconomic Equilibria, Review of Economic Studies 58, 407436.

Pindyck, R. S. (1999), The Long-run Evolution of Energy Prices,The Energy Journal 20, 127.

Radchenko, S. (2005), The Long-run Forecasting of Energy PricesUsing the Model of Shifting Trend, University of North Carolina atCharlotte, Working Paper.

Samii, M. V. (1992), Oil Futures and Spot Markets, OPECReview 4, 409417.

Sanders, D. R., M. R. Manfredo and K. Boris (2009), EvaluatingInformation in Multiple Horizon Forecasts: The DOEs EnergyPrice Forecasts, Energy Economics 31, 189196.

Schwartz, E. and J. E. Smith (2000); Short-term Variations andLong-term Dynamics in Commodity Prices, ManagementScience 46, 893911.

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Serletis A. (1991), Rational Expectations, Risk and Efficiency inEnergy Futures Markets, Energy Economics 13, 111115.

Stock, H. J., and Watson M. W. (1993), A Simple Estimator ofCointegrating Vectors in Higher Order Integrated Systems,Econometrica 61, 783820.

Ye, M., J. Zyren and J. Shore (2002), Forecasting Crude Oil SpotPrice Using OECD Petroleum Inventory Levels, InternationalAdvances in Economic Research 8, 324334.

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Table 4

Criteria for comparing in-sample and out-of-sample forecasts: structural models

In sample forecasts

Type of forecastModel

comparisonForecast evaluation

Year Authors

Static Dynamic

Graphical

evaluation Formal Informal RMSE MAPE MAE TTheill Otherss

2002 Ye et al. X

2004 Zamani X X

2005 Merino and

OrtizX X X


2007 Dees et al. X X X X X

2006 Ye et al. X X X X X X X X X

2006 Kaufmann et

al.X X X X

Out of sample forecasts

2003 Lalonde et al. X X X X X


2006 Ye et al. X X X X X X X X X


error; MAE = mean absolute error.

Ye, M., J. Zyren and J. Shore (2006), Forecasting Short-run CrudeOil Price Using High and Low Inventory Variables, EnergyPolicy 34, 27362743.

Zamani, M. (2004), An Econometrics Forecasting Model of ShortTerm Oil Spot Price, Paper presented at the 6th IAEE EuropeanConference, Zurich, 23 September.

Zeng, T. and N. R. Swanson (1998), Predective Evaluation ofEconometric Forecasting Models in Commodity Future Markets,Studies in Nonlinear Dynamics and Econometrics 2, 159177.


Focus

econometric models for oil price

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