International Review of Financial Analysis 17 (2008) 971–983

Contents lists available at ScienceDirect

International Review of Financial

Analysis

Component structure for nonstationary time series:

Application to benchmark oil prices
Ramaprasad Bhar a, Shawkat Hammoudeh b,⁎, Mark A. Thompson c
a
School of Banking and Finance, University of New South Wales, Sydney, Austrialia
b
Drexel University, Philadelphia, PA, USA
c
Augusta State University, Augusta, GA, USA

a r t i c l e i n f o a b s t r a c t

Article history: The oil market is characterized by several hundreds of different grades
Received 26 October 2007 of crude extracted from various locations on the planet, but prices of
Received in revised form 29 July 2008 those grades are structured with reference to only a handful of
Accepted 31 July 2008
benchmark varieties. In this context, the ability to predict near term
Available online 22 August 2008
benchmark oil prices takes on special importance. In this paper, we
explore an approach to model the benchmark oil price behaviors using
JEL classification:
C51
a structure of permanent and transitory components. This initial
E27 attempt seems very encouraging at least with respect to one-week
Q43 ahead forecast and deserves further investigation. In contrast to the
equities, the weekly oil permanent components do not seem to be
Keywords: explainable by fundamental factors. However, the returns of the short-
Permanent component run, transitory oil components or cycles, which differ in terms of their
Transitory component degrees of persistence, are mostly affected by contagion spillovers and
Kalman filter
not by the fundamentals. Their volatilities vary slightly in terms of
One-step ahead forecasts
their sensitivity to major geopolitical events. The overall findings
underscore the importance of benefiting more from spillover-catching
strategies over diversification ones in the short-run.
© 2008 Elsevier Inc. All rights reserved.

1. Introduction

Although there are hundreds of different grades of crude oil extracted in diverse geographical regions on
this planet, their prices are represented by a handful of benchmark or marker prices. The benchmarks, as
well as the spreads (or differentials) between two benchmarks, are economically important because they
are traded on major commodity centers. Understanding the behavior of these benchmarks is important in

⁎ Corresponding author. Tel.: +1 215 895 6673; fax: +1 215 895 6975.
E-mail addresses: R.Bhar@unsw.edu.au (R. Bhar), hammousm@drexel.edu (S. Hammoudeh), mthompson@aug.edu
(M.A. Thompson).

1057-5219/$ – see front matter © 2008 Elsevier Inc. All rights reserved.
doi:10.1016/j.irfa.2008.07.003
972 R. Bhar et al. / International Review of Financial Analysis 17 (2008) 971–983

the price discovery process of crude oil and its derivatives. The different grades are classified into groups
based on their specific gravity as measured by the American Petroleum Institute (API) degree and their
sulphur content. The API gravity categorizes crude into three main types: Light, Medium and Heavy. The
second property grades oil into sweet crudes that have relatively lower naturally occurring sulphur content
or sour crudes that are higher in sulphur.
The benchmarks for the light, sweet group are the West Texas Intermediate (WTI) in North America and
Brent in Europe and Africa. The medium crude group is benchmarked by Dubai–Oman crude. The Dubai
benchmark representing the medium, sour crudes is priced in balance to WTI and Brent. This benchmark
crude (which is now supplemented by Oman crude) is currently traded at the Dubai Mercantile Exchange
(DME) and London's International Commodity Exchange (ICE). WTI and Brent are much more liquid and
more actively traded than Dubai/Oman.
The heavy crude group is benchmarked by Mexican Maya, which is a heavy, sour crude and sells at a
significant discount to WTI and Brent. This benchmark is not actively traded and thus is illiquid. As the world
becomes more critically reliant on heavier and higher-sulphur streams, the emphasis is placed more on sour
crudes, and the heavy and medium grades will assume more importance in the oil price discovery process.
Understanding the dynamics of the oil grade benchmark prices and their volatilities is useful as the
relationships between them will change in the future as the structure of the oil market changes. For
example, the UK supply of the North Sea Brent is expected to drop from 1.7 million barrels a day to one
million barrels in just five years. The Norwegian production of the North Sea oil is at a thirteen-year low. Oil
refineries are being forced to accept a reduction in the discount on medium and heavy crudes relative to
Brent because of the tight balance between oil supply and demand and the persistence of backwardation. In
addition, Mexican oil production is falling faster than expected, and the Dubai benchmark will assume
more prominence as it is now supplemented by the less sour Oman crude and have financially settled
contracts traded on the newly established DME. Thus, understanding the behavior of the benchmarks is
important for both physical traders and financial players not just because of trading on their own contracts
and on their spreads, but also because of their functions in pricing other crude oil grades and hedging
against risk.
Methodologically, the traditional econometric approach to modeling oil prices has employed supply–
demand models. This approach has been more problematic in recent years due to inadequacy in modeling
uncertainty and accounting for structural changes in the oil markets, making the price less responsive to
the fundamentals. The results have shown that the oil supply and demand models have overpriced oil
(Huntington, 1994).
Recent advances in time series econometric techniques have shown that oil prices are nonstationary.
The more recent approach employs time series models that use first differences of the prices to deal with
the problem of nonstationarity (see Hammoudeh et al., 2003; Hammoudeh & Li, 2008; Lien & Wilson,
2001). However, the oil price level is a composite, which includes short-term and long-term components
that may be affected by different factors and thus behave differently. We will therefore gain more insight by
understanding how these two components behave in response to changes in fundamental, psychological
and contagion factors.
The component model provides a new approach to modeling oil prices in terms of both their short- and
long-run components. This approach enables us to use weekly oil prices to examine fundamental economic
factors traditionally done at much lower data frequencies. In addition, we can use the short-run component
to examine stylized facts of oil prices such as conditional volatility persistence and impacts of spillovers on
returns and volatility. The findings of this approach should give insightful evidence to oil market
participants regarding the short-run and long-run dynamics of the benchmark prices. Oil traders, in
particular, should benefit from these results in designing investment strategies to take advantage of profit
opportunities. To the best of our knowledge, this study reports and examines for the first time the
decomposition of nonstationary oil benchmark prices into two components and attempts to explain the
factors that govern their volatilities.
The broad objectives of the study are: (1) to use the component model to decompose each of the four oil
benchmarks (i.e., WTI, Brent, Dubai/Oman and Maya) into a short-term (cycle) and long-term (trend)
component in order to understand how these components are related and how they are affected by various
factors; and (2) to employ the ARCH model in order to have a better understanding of how their volatility
responds to inter-benchmarks' spillovers and long-term trends.
 R. Bhar et al. / International Review of Financial Analysis 17 (2008) 971–983 973

2. Brief review of the literature

The dynamic structures for the benchmark prices respond to forces that operate in both the short-
run and long-run. Most nonstationary economic time series are thought to be driven by at least two
factors of consequence. One of these factors is nonstationary and its dynamic is represented in some
form of a random walk structure. In the literature, this has been referred to as the permanent
component, long-term component, trend, etc. On the other hand, another factor is thought to be the
cyclical deviation and is usually represented as some form of autoregressive structure. This component
is also termed the transitory component, short-term component, cycle, etc. Depending on the problem
at hand, the noise structures of these two components may have uncorrelated or correlated covariance
specifications.
Some of the important applications of this approach are Nelson and Plosser (1982), Schwartz and Smith
(2000), Shirvani and Wilbratte (2007), and Stock and Watson (1988) to name a few. For macroeconomic
applications, some authors allow this component structure to be subjected to regime changes of varying
descriptions depending on what hypotheses are being tested (Kim & Piger, 2002; Lo & Piger, 2005).
Schwartz and Smith (2000) proposed a new way of thinking about commodity futures prices that
consists of a short-term component with mean reversion to a level that is uncertain and described the other
long-term factor. Although these factors are not directly observable, they may be inferred from traded
futures contracts on that commodity. Schwartz and Smith (2000) also showed that if there are long-dated
futures contracts traded on the commodity, then changes in the price of that contract have information
about the equilibrium price of that commodity. Similarly, the difference between the short-dated and long-
dated futures prices provides information about the short-term deviation in prices. This conceptual
framework of short-term and long-term components provides a viable way to price options on the relevant
futures contracts. Their application relates to oil as the commodity of interest.
Shirvani and Wilbratte (2007) adopted a component-based approach to decompose stock prices into
long-term trends and short-term cyclical components. In turn, they are able to explain the trend
component with the help of fundamentals for stock valuations. However, the cyclical components are
unrelated to such fundamentals. The cyclical components for the different countries appear to be related
due to contagion spillovers. They then discuss the implications of these findings in term of international
diversification strategies. To our knowledge, no paper has used the component model to either de-
compose the prices of the different crude oil grades or to examine the behaviors of the decomposed
components.
In this paper, we initially investigate the component structures of the four major benchmark oil price
series, which as indicated above have not been studied in this context before. The specification of the
transitory and permanent components is similar to those of Schwartz and Smith (2000). However, we infer
both components from the benchmark spot prices. We do not resort to future contracts in this initial
attempt as our basic focus is to forecast the benchmark oil prices one-step ahead and quantify the success of
this objective.
As in Shirvani and Wilbratte (2007), our next step is to determine the relevant explanatory variables in
these oil components. At this stage, although it is just a conjecture, we believe the long-term component
of a benchmark oil price would be determined by the supply and demand of the commodity. However, the
short-term component would most likely be governed by various transient events (e.g., contagions,
geopolitical events, severe weather conditions affecting production, psychological factors, etc.). Finally,
we would like to investigate whether all the benchmark oil price series can be modeled as driven by two
such factors, allowing for different sensitivities to the factors.

3. Data and model

The data comprised of weekly time series for the closing spot prices of the four oil grade benchmarks:
WTI, Brent, Dubai, and Maya. The weekly period covered by the data set is January 1991 to April 2006. The
spot price for WTI is quoted at Cushing, Oklahoma; Brent at London's International Petroleum Exchange;
and Dubai (currently) at Dubai Mercantile Exchange, International Commodity Exchange and Singapore
Exchange. Data for WTI and Brent prices were accessed from the EIA (Energy Information Administration)
website, while Dubai and Maya price data were obtained from Deutsche Bank.
974 R. Bhar et al. / International Review of Financial Analysis 17 (2008) 971–983

Table 1
Descriptive statistics of oil benchmark prices

Mean Maximum Minimum S.D. JB-Stat ADF

WTI 3.195 4.278 2.385 0.395 84.79 0.887
Brent 3.123 4.297 2.247 0.413 74.11 0.919
Dubai 3.039 4.204 2.272 0.404 84.85 0.943
Maya 2.893 4.047 1.847 0.423 19.58 0.759

Notes: The oil benchmark prices are in natural logarithms for the sample period of August 7, 1991 to April 26, 2006 for a total of
769weekly observations. JB-statistics give the Jarque–Bera statistics for the test normality of the data. All these series display
nonnormal behavior. The entries in ADF test are p-values for the null hypothesis that the series have unit roots.

The descriptive statistics in Table 1 demonstrate that the average weekly return (in natural logarithms)
follows the physical property structure of the oil grade with the highest (lowest) return being WTI (Maya).
The return of Dubai, the medium benchmark, is almost equidistance from WTI and Maya returns. Volatility
of the benchmarks, however, does not follow the physical structure as evidenced in Maya having the
highest volatility and WTI having the lowest, but with Brent having higher volatility than Dubai. The
relatively higher volatility of Maya is perhaps due to its location in an active hurricane area, the “complex”
refineries needed to process this oil type, the higher-than-expected decline in Mexican oil production due
to the government oil management policy, and the political unrest in Mexico. It may also have to do with
the changes in heavy oil supply at large. The benchmarks have a nonnormal distribution as displayed by
their respective Jarque–Bera statistics. They also have a unit root according to the Augmented Dickey–Fuller
(ADF) test.
The inter-correlations among the four benchmark prices presented in Table 2 suggest that the highest
contemporaneous correlation is between the two light, sweet benchmarks WTI and Brent (0.996), and the
lowest (0.971) is between the medium, sour (Dubai) and heavy, sour (Maya). However, all the correlations
are positive and close to one, implying that these benchmarks belong to one great pool and are thus
affected by strong, common global factors in the short-run.
The basic approach to the component modeling problem adopted here follows from the Schwartz and
Smith (2000) version. As mentioned above, this approach is suitable for nonstationary time series since the
four benchmark price series under investigation are nonstationary according to the ADF tests. We specify
the model for the oil benchmarks in discrete time, whereas Schwartz and Smith (2000) carry out their
analysis in continuous time and proceed to price European type derivatives on oil futures. However, to
calibrate their model, Schwartz and Smith also had to discretise the model. Since we are initially interested
in extracting the components and applying them to one-step-ahead forecasts, we simply specify the
benchmark component model in discrete time. At a later stage, we would like to focus on finding
explanatory variables for the extracted components and exploring any relationship or spillover between
the components of the different benchmarks used in this study.
The modeling exercise is based upon the unobserved component approach and is estimated using a
filtering algorithm. Logarithm of the benchmark oil price (st) is assumed to be a sum of two components — a
short-term (x1,t) component and a long-term (x2,t) component. The short-term component reverts back to
zero based upon its mean reversion factor (κ), and the long-term component evolves as a random walk with

Table 2
Inter-correlations between the oil benchmark prices

WTI Brent Dubai Maya

WTI 1
Brent 0.996 1
Dubai 0.990 0.992 1
Maya 0.973 0.976 0.971 1

Notes: The oil benchmark prices are in natural logarithms for the sample period of August 7, 1991 to April 26, 2006 for a total of 769
weekly observations. The correlations are significant at the 1% level or less.
 R. Bhar et al. / International Review of Financial Analysis 17 (2008) 971–983 975

a deterministic trend (µ2). These two components are described over the discrete-measurement interval
(Δt) by the following stochastic difference equations:

Δx1;t ¼ −κx1 Δt þ σ 1 Δz1 ð1Þ

Δx2;t ¼ μ 2 Δt þ σ 2 Δz2 ð2Þ

The standard deviations of the innovations are controlled by σ1and σ2whereas Δz1, Δz2 are the Wiener
increments having E (Δz1 · Δz2) = ρ12Δt. The measurement of (logarithm of) benchmark oil price is thus
given by:
 
st ¼ x1;t þ x2;t þ mt ; mt eN 0; σ 2m ð3Þ

Given a time series of prices on an oil benchmark, we may estimate the above model by casting it in
state-space form. Eq. (3) is the measurement equation, whereas the state dynamic is given by:

        
x1;t 0 1−κΔt 0 x1;t−1 e
¼ þ þ 1;t ð4Þ
x2;t μ 2 Δt 0 1 x2;t−1 e2;t

      
e1;t 0 σ 21 ρ12 σ 1 σ 2
eN ; X1 ; X1 ¼ Δt ð5Þ
e2;t 0 ρ12 σ 1 σ 2 σ22

The unknown parameters of this model as well as the two components may be filtered out from the
time series of observations on prices by application of Kalman filter and by maximizing the prediction-error
decomposition form of the likelihood function. The technical details of this may be found in Bhar and
Hamori (2005).

Table 3
Component model parameter estimates and diagnostic tests

WTI Brent Dubai Maya

σ2v 1.72E-04 1.39E-07 3.27E-05 1.71E-09
(9.95E-05) (1.37E-10) (6.35E-05) (1.79E-10)
σ21 0.09348 0.11361 0.09186 0.14617
(0.01088) (0.00744) (0.00820) (0.03399)
κ 0.63887 0.60088 0.60674 0.67645
(0.24187) (0.32739) (0.30380) (0.28932)
σ22 9.70E-12 2.21E-07 1.20E-07 8.86E-08
(6.46E-19) (4.65E-08) (3.28E-09) (4.08E-05)
µ2 0.11288 0.11518 0.12106 0.11243
(0.03855) (0.05133) (0.03637) (0.03863)
ρ12 −0.04261 −0.07262 −0.30795 0.61976
(0.00001) (0.01941) (0.02693) (8.46647)
Q(24) 0.111 0.163 0.819 0.028
ARCH(76) 0.277 0.295 0.187 0.147
Recursive T Test 0.737 0.591 0.786 0.721

Notes: The parameters reported here are described by the model in Eqs. (3) and (4) in the text. Specifically, σ2v is the variance of the error
term of the measurement of a benchmark oil price, κ represents the transitory component's speed of mean reversion to zero after a
short-term shock occurs, µ2 is the deterministic trend of the random walk and the coefficient ρ12 characterizes correlation between the
permanent and the transitory components for each benchmark. The numbers in the parentheses in the upper panel are standard errors
computed using the Hessian matrix at the maximum likelihood point. The diagnostics tests are reported in the lower panel. The Q(24)
statistic reports the p-values for the portmanteau tests using the measurement error and the null hypothesis is that the residual series
is white noise. ARCH(76) reports the p-values for the heteroscedasticity using the squared error series. The null hypothesis in this case
is that there is no ARCH effect. The ARCH test is described in Harvey (1990, p. 222). Similarly, if the model is correctly specified then
Recursive T has a Student's t-distribution (see Harvey, 1990, p. 157). The entries for Recursive T Test are also p-values for the null
hypothesis that the model is correctly specified.
976 R. Bhar et al. / International Review of Financial Analysis 17 (2008) 971–983

4. Results

In this section, we discuss the results of the oil component models for the four benchmarks, examine the
correlations among the stationary transitory components of those reference prices, and analyze their
conditional volatilities.

4.1. Estimates of the component models

The results of the oil component models are given in Table 3. Most of the estimated parameters of these
models are statistically significant and the residual diagnostics strongly support the modeling approach.
Specifically, the residual diagnostics indicate that there are no ARCH effects and that the model is correctly
specified according to the ARCH test and Recursive T Test, respectively. The measurement error variance σ2v
is small for all four series implying that the component model captures the oil price dynamics well. This is

Fig. 1. Component structures of WTI crude oil.

 R. Bhar et al. / International Review of Financial Analysis 17 (2008) 971–983 977

Fig. 2. Component structures of Brent crude oil.

an indirect validation of the efficacy of our approach. The results suggest that the volatility for the four
benchmarks is greater for the transitory components than for the permanent components. This is expected
since the transitory components by nature are influenced more by the events at the time rather than simply
the supply/demand dynamics of oil sources in the case of permanent components.
The strongest observation we can make is that the transitory component of the Maya benchmark has the
highest volatility of the four benchmarks analyzed. This sheds some light on why the Maya benchmark price
has the highest historical volatility. This heavy crude is affected by changes in Mexican government's policies
and regulations regarding oil reserve management1 and by oil-importing governments' environmental
regulations. It may be possible that other oil fundamentals matter more for this heavy crude than among the
other benchmarks. The difference among the four benchmarks in terms of volatility of the permanent

1
See M. O'Grady, “Playing Monopoly in Mexico.” Wall Street Journal, April 7, 2008, p. A12.
978 R. Bhar et al. / International Review of Financial Analysis 17 (2008) 971–983

component is minimal compared to that for the transitory components. Brent displays the highest permanent
volatility (2.21E-07).
The speed of mean reversion to zero for the transitory component, which is given by κ, is also the
highest (0.676) for the Maya grade. This benchmark's responses to shocks or short-term factors such as
hurricanes in the Gulf of Mexico or geopolitical events die out more quickly than for the other benchmarks.
The lowest speed of adjustment for the transitory component is for Brent. Again, it is for Maya that the
correlation ρ12 between the permanent and the transitory components is positive and the highest (0.619),
whereas it is negative for all the other benchmarks. Maya's permanent and transitory components may
both be affected positively by strong common factors, which is extraordinary because transitory
components are usually affected by noises, psychological factors, or contagions and move negatively
with the permanent components which are affected more by the fundamentals. The parameter µ2 refers to
the average growth rates for the permanent components and the estimates of these rates are similar in

Fig. 3. Component structures of Dubai crude oil.

 R. Bhar et al. / International Review of Financial Analysis 17 (2008) 971–983 979

values. These estimates are expected to be similar since the permanent components are mainly driven by
supply/demand concerns and the commodities are (more or less) substitutable.
Figs. 1–4 give the permanent and temporary (transitory) oil components for the four benchmarks. These
plots illustrate that the component categories for each oil benchmark could be highly correlated with one
another, which is confirmed in Table 3.

4.2. Correlations between transitory components

As expected, the (contemporaneous) correlation coefficients are higher between the permanent
components of the benchmarks than between the transitory components because of the former's
sensitivity to common global factors (see Table 4). Changes in the fundamental factors may affect all the
benchmarks, while short-term factors such as geopolitical events or weather conditions may only affect

Fig. 4. Component structures of Maya crude oil.

980 R. Bhar et al. / International Review of Financial Analysis 17 (2008) 971–983

Table 4
Correlations between extracted oil components

WTI Brent Dubai Maya

A. Transitory component
WTI 1
Brent 0.967 1
Dubai 0.982 0.947 1
Maya 0.966 0.960 0.959 1

B. Permanent component
WTI 1
Brent 0.991 1
Dubai 0.999 0.987 1
Maya 0.995 0.991 0.994 1

Note: The correlations are significant at the 1% level or less.

one geographical region and one type of crude oil. Interestingly, the highest correlation coefficient
is between WTI and Dubai, regardless of whether the permanent or the transitory components are
used.
However, one of our main focuses in this study is of the forecast ability of the component structures. In
the traditional statistical sense, the forecast ability of a model is judged by some measure of association
between the forecasts and the realizations. However, there is an alternative to R-square measures and this
is given by Theil's Inequality Coefficient, which is reported in Table 5. It was originally proposed in 1961 and
has been employed by several researchers since then (Theil, 1961).

4.3. Conditional volatility of transitory components

Since the long-term trends or permanent components are generally viewed as reflections of the impacts
of the fundamentals, they tend to be explainable in terms of common fundamentals related to a common
economic policy and the state of economic activity that affect supply and demand. In contrast, the short-
term cycles or transitory components are widely viewed to be affected for oil by noise or shorter-term
factors such as hurricanes and geopolitical events that are related to the business cycle.
In contrast to the stock and other commodity markets, the weekly permanent components of the oil
benchmarks' returns and volatility were not affected by weekly fundamental economic variables such as
short-term interest rates and default risk, but only by the other benchmarks' long-run components.2 This
finding implies synchronization in the long-run among the benchmarks themselves, but not between them
and the long-run trends of economic fundamentals. This limits the long-run diversification potential across
these four oil benchmarks as they are all driven by similar underlying oil fundamentals (i.e., they all move in
the same direction by common forces).
The short-term oil cycles in the mean equations of the models estimated in Table 6 (for the most part)
are not affected by other benchmarks' oil permanent components.
This finding is consistent with other stock market studies where short-run cycles are unaffected by
long-run oil fundamentals. However, the short-run cycles of the four oil benchmarks are related to the
other benchmarks' past cyclical components, suggesting they are all affected by contagion spillovers. As a
result of being affected by contagion spillovers, the benchmarks are less suitable for diversification
potential in the short-run. An implication of this finding is that in the short-run oil investors and traders can
be anticipatory and position themselves in a certain benchmark to benefit from the contagion spillover
from the other benchmarks. If the transaction costs are not prohibitive, traders can switch from one
benchmark to another based on the relative persistence of the benchmarks of interest. That is, the traders
may benefit from more of a leap-frogging spillover strategy than a diversification strategy in the short-run.

2
The results show that the oil returns and volatilities of the long-run trends are only explainable by their other benchmarks'
permanent components, but not long-run economic fundamentals, underscoring the difficulty of predicting oil prices and their
volatilities in the long-run. Full table of results (for the permanent components) are available upon request.
 R. Bhar et al. / International Review of Financial Analysis 17 (2008) 971–983 981

Table 5
One-step ahead forecast performance

WTI Brent Dubai Maya

TIC 0.0072 0.0074 0.0069 0.0091

Notes: TIC is Theil's Inequality Coefficient for forecast performance. The TIC is given by the following expression. The variable of
interest is Zt for t = 1, 2,…, T, and its estimated value is given by Ẑt:
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2
1=T∑Tt¼1 zt − zbt
TIC ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
1=T∑T z2 þ 1=T∑T zb
t¼1 t t¼1 t

This coefficient lies between 0 and 1. For a perfect forecast its value is 0. Thus, a smaller entry implies a better model. For additional
details of this measure and its other applications, the readers may refer to Bali and Weinbaum (2007).

The main exception to long-run oil fundamentals not affecting the short-run oil cycles is the Maya
benchmark, where Maya's short-run cycle is affected by the long-run movements of WTI and Brent. This is
interesting in light of our finding that Maya has the highest speed of adjustment, and is thus the least
persistent, most resilient, and mean-reverting benchmark. There seems to be more beneficial asset
diversification for including heavy and medium crudes as represented by Maya and Dubai in a portfolio in a
longer run than including heavy and light crudes as priced in WTI or Brent and Maya.
However, the short-run mean cycles of the four oil benchmarks are related to the other benchmarks'
past cycle returns or short-term transitory components, suggesting that they are all affected by contagion
spillovers, which makes them unsuitable diversification assets in the short-run. An implication of this
finding is that in the short-run oil investors can be anticipatory and position themselves in a certain
benchmark to benefit from the contagion spillover from the other benchmarks. If the transaction costs are
not prohibitive, they can switch from least persistent benchmark such as Maya to the most persistent such

Table 6
ARCH models' estimations for (transitory component) conditional volatility

WTItran Brenttran Dubaitran Mayatran

Mean
Constant 0.0073 − 0.0217 0.0210 −0.0050
FFRtran −0.0060 − 0.0044 −0.0049 0.0006
Hurricane 0.0006 0.0059⁎ −0.0019 0.0061⁎
Geopolitical −0.0098 − 0.0024 −0.0160 −0.0039
ΔWTIperm – − 0.0848 −0.0449 0.1728⁎⁎⁎
ΔBrentperm 0.0404 – 0.0196 −0.1507⁎⁎
ΔDubaiperm −0.0097 0.0550 – 0.0080
ΔMayaperm −0.0472⁎ − 0.0102 −0.0372 –
WTItran – 0.3069⁎⁎⁎ 0.3076⁎⁎⁎ 0.7171⁎⁎⁎
Brenttran 0.1474⁎⁎⁎ – 0.3982⁎⁎⁎ 0.2920⁎⁎⁎
Dubaitran 0.2210⁎⁎⁎ 0.5060⁎⁎⁎ – 0.1188⁎⁎⁎
Mayatran 0.4377⁎⁎⁎ 0.1767⁎⁎⁎ 0.1201⁎⁎⁎ –
AR(1) 0.9782⁎⁎⁎ 0.9729⁎⁎⁎ 0.9823⁎⁎⁎ 0.9492⁎⁎⁎
MA(1) −0.2421⁎⁎⁎ − 0.3919⁎⁎⁎ −0.4843⁎⁎⁎ 0.0434

Variance
Constant 0.0002⁎⁎⁎ 0.0003⁎⁎⁎ 0.0001⁎⁎⁎ 0.0003⁎⁎⁎
ARCH(1) 0.2502⁎⁎⁎ 0.2068⁎⁎⁎ 0.5622⁎⁎⁎ 0.1197⁎⁎⁎
Geopolitical 0.0001⁎⁎⁎ b0.0001 0.0002⁎⁎⁎ 0.0001⁎⁎
Log likelihood 2106.4 1987.9 2054.3 1913.3
F-statistic 12869.1⁎⁎⁎ 7717.6⁎⁎⁎ 10648.0⁎⁎⁎ 9932.5⁎⁎⁎
ARCH LM 0.0465 0.4130 1.6984 0.0676

Notes: ⁎, ⁎⁎, ⁎⁎⁎ indicate significance at the 10%, 5%, and 1% levels, respectively. Δ is the first difference operator. Superscripts perm
and tran represent the permanent and transitory components for the benchmarks. FFR is the federal funds rates; Hurricane is a
dummy variable for the hurricane season; Geopolitical is a political risk dummy variable that represents the September 11, 2001
attack and the 2003 Iraq War.
982 R. Bhar et al. / International Review of Financial Analysis 17 (2008) 971–983

as Brent. The benefits of the spillover strategy should outweigh those of the diversification strategy in the
short-run.
In the variance equations of the transitory (i.e., short-run cyclical component) models, almost all the oil
short-run cycles' volatilities are heightened by geopolitical events and past psychological factors. A geopolitical
event occurring in Iran, Nigeria, Venezuela or the Middle East should increase the volatility of the oil
benchmarks in the short-run, with Dubai being affected the most. The implication of such a finding is in
formulating portfolio strategies. Investors can benefit from knowing that Dubai's short-run oil cycle was more
sensitive to geopolitical risk than Brent's oil cycle (which was not significantly affected by geopolitical risk).

5. Conclusions

The oil market is characterized by hundreds of different grades of crude located in different places on
the globe. The oil prices of those grades are, however, structured with reference to the prices of only a
handful of benchmark varieties. Moreover, the predictability of the co-movements and volatilities of the
benchmark prices as composite variables are not well explained by economic fundamental factors because
each price includes two components that are affected by different factors and behave differently in the
short and long-run. Therefore, we analyze the dynamics of the permanent and transitory components of
the price in order to understand the price return and volatility in the benchmark oil markets.
The component model findings suggest that physical traders and financial players should pay particular
attention to the Maya transitory component because it has the highest volatility and tends to revert to zero
the fastest. In the long-run, the attention should focus on Brent, which has highest permanent volatility and
greater persistence.
The ARCH results (available upon request) show that the oil returns and volatilities of the long-run
trends are only explainable by their other benchmarks' permanent components, but not long-run economic
fundamentals, underscoring the difficulty of predicting oil prices and their volatilities in the long-run. This
is reinforced by the results that the oil short-run cycles for the returns are also not explainable by their own
and other benchmarks' permanent components (with the main exception of the Maya benchmark).
The short-run cycles of the four oil benchmarks are related to the other benchmarks' past cycle returns
or short-term transitory components. They are all affected by contagion spillovers from other benchmarks'
transitory components. This finding suggests that a short-run oil investment strategy that benefits from
spillovers among the benchmarks is more beneficial than a benchmark diversification strategy that
includes those benchmarks as a hedge against risk, as is the case in commodity and stock markets.
Specifically, an anticipatory benchmark spillover strategy in the short-run that uses a less persistent
benchmark and moves over to another (more persistent) benchmark could be a beneficial strategy. In
addition, investors may also gain from knowing that Brent and Maya's short-run cycles are significantly
affected by the hurricane season. However, both the short-run interest rate cycle (i.e., federal funds rate)
and the geopolitical events did not significantly affect the short-run cycles of the oil benchmarks on a
weekly basis. Finally, the impact of major geopolitical events on benchmark volatilities in the case of such
events occurring in Iran, Nigeria, Venezuela or the Middle East should increase the volatility of the oil
benchmarks in the short-run, with Dubai being most affected. Those who benefit from volatility should pay
more attention to Dubai benchmark in the case of political events and less to the Brent benchmark.

Acknowledgements

The authors wish to thank Adam Sieminski and Amanda Lee of the Deutsche Bank for providing us with
the Dubai and Maya data. The authors also thank the editor, Jonathan Batten, and an anonymous reviewer
for helpful comments on earlier versions of the paper.

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