The aim of the present paper is to study the relationship between international oil prices and international energy sector in the context of the current economic crisis. The research methodology consists in co-integration tests performed on daily data frequency for two of the most important spot oil prices used as a benchmark in oil pricing, mainly the West Texas Intermediate (WTI) and the Europe Brent and for the All Country World Energy Index, an MSCI index, that tracks the performance of the energy sector.
Key words: spot oil price, international capital markets, co integration
JEL Classification: G01, G15
Introduction
The purpose of our paper is capture the relationship between international oil markets and the international energy sector and focuses on the present economic crisis period by employing the co-integration technique.
With regard to the scientific literature concerning the subject of our analysis, Sauter and Awerbuch (2002) [5] provide a comprehensive review of the studies approaching oil price movements and their effect on economic and financial performance in IEA (International Energy Agency) countries, and tackle the effects of the oil price changes on the stock markets. The authors mention that the first study to analyze whether the reaction of international stock markets to oil shocks can be justified by current and future changes in real cash flows and/or changes in expected returns is that of Jones and Kaul (1996) that examine four markets: US, Canada, UK and Japan [1].
Papapetrou (2001), by focusing on the Greek market, uses a vector-autoregressive method in investigating the dynamic relationship between oil prices, real stock prices, interest rates, real economic activity and employment. The author concludes that impulse response functions show that oil prices are important in explaining stock price movements, the results suggesting that a positive oil price shock depresses real stock returns and that lasts for approximately four months [3].
Lake and Katrakilidis (2009) [2] investigated the impact of oil price returns and oil price volatility on the Greek, the US, the UK and the German stock markets, using monthly that covered the September 1999 - March 2007 period. The study concludes that both the Greek and the US stock market index returns are sensitive to the oil price returns changes. However, the German and the UK stock market returns are not influenced by the oil price returns movements
Before the 1980s many economists used linear regressions on (de-trended) non-stationary time series data, which Clive Granger [6] and others showed to be a dangerous approach that could produce spurious correlation. His 1987 paper with Robert Engle [7], formalized the co integrating vector approach, and coined the term. For his contribution to the technique's development Clive Granger shared the 2003 Nobel Memorial Prize.
Co-integration is an econometric property of time series variables. If two or more series are individually integrated but some linear combination of them has a lower order of integration then the series are said to be co-integrated. A common case is where the individual series are first-order integrated (I(1)) but some (co integrating) vector of coefficients exists to form a stationary linear combination of them.
It is often said that co integration is a means for correctly testing hypotheses concerning the relationship between two variables having unit roots (i.e. integrated of at least order one). A series is said to be "integrated of order "t" if one can obtain a stationary series by "differencing" the series t times. The usual procedure for testing hypotheses concerning the relationship between non-stationary variables was to run Ordinary Least Squares (OLS) regressions on data which had initially been differenced. Although this method is correct in large samples, co integration provides more powerful tools when the data sets are of limited length, as most economic time-series are.
In statistics, the Johansen test [8], named after Søren Johansen, is a procedure for testing co integration of several time series. This test does not require all variables to be in the same order of integration, and hence this test is much more convenient than the Engle-Granger test for unit roots which is based on the Dickey-Fuller (or the augmented) test.
There are two types Johansen [4] test, either with trace or with eigenvalue, and the inferences might be a little bit different. The null for trace test is the number of co integration vector r ≤ ?, for eigenvalue test is r = ?.
Just like a unit root test, there can be constant term, trend term, or both, or neither in the model. For a general VAR(p) model :
Xt = μ + ΦDt + ΠpXt-p +….+ Π1Xt-1 + et, t=1,…,T
There are two possible specifications for error correction: that is, two VECM (vector error correction models):
The longrun VECM:
ΔXt = μ + ΦDt + ΠXt-p + Γp-1ΔXt-p+1 + Γ1ΔXt-1 +….+ εt, t = 1,….,T
Where:
Γi = Π1+….+Πi - I, i = 1, ,p-1
The transitory VECM:
ΔXt = μ + ΦDt − Γp-1ΔXt-p+1 −……− Γ1ΔXt-1 + ΠXt-1 + εt, t = 1,….,T
Where:
Γi = (Πi+1+….+Πp) i = 1, ,p-1
In both VECM,
Π= Π1 +…….+ Πp − I
Inferences are drawn on Î , and they will be the same, so is the explanatory power.
Data description
We considered for the analysis daily time series for the period January 3, 2008 to March 30, 2010, on the one hand, the two most important spot oil prices, on the other hand, the international energy index calculated by MSCI Barra.
Oil market data were obtained from the Energy Information Administration - EIA (Agency for Statistics and analytical analysis of the U.S. Department of Energy) and the data for the MSCI index from Thomson Reuters (financial information group, the most important information source for companies and specialists).
Thus, the oil market was represented by London Brent Crude Oil spot prices, called the analysis and from now on Brent and Cushing OK WTI named WTI.
The MSCI index selected in analysis is the All Country World Energy Index - ACWIEN
Testing the stationarity of the time series. Were initially tested all the time series to identify whether they are stationary (unit root tests). In this sense, the graphs were made for each time series for both the oil market and the demand for capital market developments described (Fig. 1).
Fig. 1. All Country World Energy Index
Applying the ADF test to test stationarity. In order to verify the stationarity of the time series the Augmented Dickey-Fuller test was applied. Given the sample probability value (PValue) we can not reject the null hypothesis for the time series. Therefore, it can be concluded that time series studied are non-stationary (Table 1).
Table 1. Augmented Dickey-Fuller stationarity test for prices
Null hypothesis
t-Statistic
Prob.
BRENT has a unit root
-0.852665
0.9590
WTI has a unit root
-1.045257
0.9355
ACWIEN has a unit root
-1.312829
0.8836
All series were transformed by calculating the time series log returns (original time series were log and then the first difference has been applied). Both for the logarithmic series and return series the Augmented Dickey-Fuller test was conducted. The results are displayed in Table 2 and Table 3.
Table 2. Augmented Dickey-Fuller stationarity test on logarithmic series
Null hypothesis
t-Statistic
Prob.
BRENT_LOG has a unit root
-0.949399
0.9483
WTI_LOG has a unit root
-1.076681
0.9307
ACWIEN_LOG has a unit root
-1.262511
0.8955
Table 3. Augmented Dickey-Fuller stationarity test on returns
Null hypothesis
t-Statistic
Prob.
BRENT_R has a unit root
-23.43299
0.0000
WTI_R has a unit root
-23.57548
0.0000
ACWIEN_R has a unit root
-19.27053
0.0000
As it shows, following the changes made, we can assume the logarithmic time series are non-stationary (Prob.> 5% can not reject the null hypothesis of non stationarity) but their first difference is stationary (Prob. = 0, can reject the null hypothesis of non stationarity).
Testing time series co integration
Engle and Granger (1987) noted that a linear combination of two or more non-stationary series may be stationary. If such linear combination exists, is said that non-stationary time series are co integrated. Stationary linear combination is called the co integration equation and may be interpreted as a long-term equilibrium relationship between variables. Co integration test's goal is to determine whether non-stationary series in a group are or not co integrated. EViews implemented co integration tests based on VAR (vector autoregression) using the methodology developed in Johansen (1991, 1995a).
Given these issues, the analysis initially focused on the test for co integration for the pairs MSCI_LOG and WTI_LOG and respectively MSCI_LOG and BRENT_LOG. We considered in the analysis, the optimal length as determined for each pair of price-index, using different criteria, such as likelihood-ratio (LR ), Final Prediction Error (FPE), Akaike Information Criterion (AIC), Schwarz Information Criterion (SIC) and Hannan-Quinn Information Criterion (HQ). Test results are displayed in the following tables (Table 4, the spot price for Brent and WTI spot price table 5).
Table 4. Johansen cointegration test BRENT_LOG - ACWIEN_LOG
Optimal lag no = 7 sites
Hypothesized No. of CE(s)
Eigenvalue
Trace Statistic
Prob
None
0.034189
22.06560
0.0044
At most 1
0.004958
2.758578
0.0967
Trace test indicates 1 cointegrating eqn(s) at the 0.05 level
HypothesizedNo. of CE(s)
Eigenvalue
Max-Eigen Statistic
Prob
None
0.034189
19.30702
0.0073
At most 1
0.004958
2.758578
0.0967
Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level
Table 5. Johansen cointegration test WTI_LOG - ACWIEN_LOG
Optimal lag no = 6 sites
Hypothesized No. of CE(s)
Eigenvalue
Trace Statistic
Prob
None
0.034826
22.88595
0.0032
At most 1
0.005699
3.177585
0.0747
Trace test indicates 1 cointegrating eqn(s) at the 0.05 level
HypothesizedNo. of CE(s)
Eigenvalue
Max-Eigen Statistic
Prob
None
0.034826
19.70836
0.0062
At most 1
0.005699
3.177585
0.0747
Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level
Thus we conclude that the following pairs of indices are co-integrated: BRENT_LOG - ACWIEN_LOG and WTI_LOG - ACWIEN_LOG.
The following tables present the normalized coefficients, the estimate of the model (co-integrating equation).
Table 6 Normalized cointegrating coefficients: BRENT_LOG-ACWIEN_LOG
Variable
BRENT_LOG
ACWIEN_LOG
-1.677855
(0.12005)
Coefficient value
1.000000
Standard error
Table 7 Normalized cointegrating coefficients: ACWIEN_LOG-BRENT_LOG
Variable
ACWIEN_LOG
BRENT_LOG
-0.595999 (0.04573)
Coefficient value
1.000000
Standard error
Table 8 Normalized cointegrating coefficients: WTI_LOG-ACWIEN_LOG
Variable
WTI_LOG
ACWIEN_LOG
-1.677285 (0.13747)
Coefficient value
1.000000
Standard error
Table 9 Normalized cointegrating coefficients: ACWIEN_LOG-WTI_LOG
Variable
ACWIEN_LOG
WTI_LOG
-0.596202
(0.05103)
Coefficient value
1.000000
Standard error
Taking into account that the considered variables are co-integrated, we determined the error correction model that describes the short-run dynamics or adjustments of the co-integrated variables towards their equilibrium values. The error correction models stand for the one-period lagged co-integrating equation and the lagged first differences of the endogenous variables. In the first part of each table there are displayed the estimates of the co-integrating equation, while the second part presents the estimates of the speed of adjustment (to equilibrium) coefficient, their standard errors and the t-statistics.
Table 10 Vector Error Correction Estimates: BRENT_LOG-ACWIEN_LOG
Co-integrating Equation 1
BRENT_LOG(-1)
1.000000
ACWIEN_LOG(-1)
-1.677855
Standard errors
(0.12005)
t-statistic
[-13.9763]
C
2.119990
Error Correction:
D(BRENT_LOG)
D(ACWIEN_LOG)
Speed of adjustment
-0.041658
-0.002028
Standard errors
(0.01087)
(0.00924)
t-statistic
[-3.83117]
[-0.21942]
Table 11 Vector Error Correction Estimates: ACWIEN_LOG-BRENT_LOG
Co-integrating Equation 1
ACWIEN_LOG(-1)
1.000000
BRENT_LOG(-1)
-0.595999
Standard errors
(0.04573)
t-statistic
[-13.0340]
C
-1.263512
Error Correction:
D(ACWIEN_LOG)
D(BRENT_LOG)
Speed of adjustment
0.003402
0.069896
Standard errors
(0.01551)
(0.01824)
t-statistic
[ 0.21942]
[ 3.83117]
Table 12 Vector Error Correction Estimates: WTI_LOG- ACWIEN_LOG
Co-integrating Equation 1
WTI_LOG(-1)
1.000000
ACWIEN_LOG(-1)
-1.677285
Standard errors
(0.13747)
t-statistic
[-12.2013]
C
2.111528
Error Correction:
D(WTI_LOG)
D(ACWIEN_LOG)
Speed of adjustment
-0.037725
0.000805
Standard errors
(0.01093)
(0.00789)
t-statistic
[-3.45240]
[ 0.10205]
Table 13 Vector Error Correction Estimates: ACWIEN_LOG-WTI_LOG
Co-integrating Equation 1
ACWIEN_LOG(-1)
1.000000
WTI_LOG(-1)
-0.596202
Standard errors
(0.05103)
t-statistic
[-11.6843]
C
-1.258897
Error Correction:
D(ACWIEN_LOG)
D(WTI_LOG)
Speed of adjustment
-0.001351
0.063275
Standard errors
(0.01324)
(0.01833)
t-statistic
[-0.10205]
[ 3.45240]
Conclusions
Within the present paper we applied the Johansen test in order to study the co-integration of two of the most important benchmark oil spot prices and the worldwide energy sector index measured by MSCI. We have found that there is a co-integration relationship between both the Brent spot price and the AC World Energy Index and WTI spot price and the same energy sector index. In an economic sense we have found a relatively strong long term relationship between both oil spot prices and the MSCI energy index for the studied period. We conclude that even during a period of crisis oil prices remain an important determinant factor for world markets.
