On the impact of oil price fluctuations on stock markets: A
multivariate long-memory GARCH framework
Manel YOUSSEF and Lotfi BELKACEM
Abstract
This paper employs multivariate long memory GARCH models to simultaneously estimate
mean and conditional variance spillover effects between oil prices and different financial
markets. Since different financial assets are traded based on these market sector returns, it’s
important for financial market participants to understand the volatility transmission
mechanism over time and across these series in order to make optimal portfolio allocation
decisions. We examine weekly returns from January 1, 2003 to November 30, 2012 and find
evidence of significant transmission of shocks and volatilities between oil prices and some of
the examined financial markets. The findings support the idea of cross-market hedging and
sharing of common information by investors.
Keywords: oil prices, stock indices returns, oil volatility, contagion, DCC-multivariate (FI)
GARCH.

Research Laboratory for Economy, Management and Quantitative Finance (LaREMFiQ), IHEC, University of
Sousse; email: manel-youssef@live.fr

LaREMFiQ , IHEC, University of Sousse; email: lotfi.belkacem@yahoo.fr
1. Introduction
Dynamic return links and volatility spillover across capital markets are of greater interest to
the financial community since the increasing trend of financial globalization throughout the
world. In fact, if return and volatility are found to spread from one market to another,
portfolio managers and policy makers must adjust their actions to prevent contagion risks in
the event of market crashes or crises. This issue has recently received much attention from
finance practitioners and researchers and has been extensively investigated on the context of
international asset markets (Forbes and Rigobon, 2002, Syriopoulos, 2007 for stock market,
Barrassi et al., 2005; Wang et al., 2007 in the context of monetary markets, and Skintzi and
Refenes, 2006; Johansson, 2008 for bound markets). Results from these studies imply strong
evidence of significant return and volatility spillovers across markets, and confirm that the
degree of spillover is highly dependent on economic and financial integrations as well as on
the market situation and geographical proximity since the latter tend to be more important
during crisis periods than during tranquil ones, and more pronounced at the regional level than
at the international level as well.
It’s of great interest to expand this issue to the context of oil and stock markets. In fact, there
may be considerable transmission of return and volatility shocks between the markets due
essentially to cross-market hedging and changes in common information which, consequently,
affect market participant expectations. An empirical study of the intensity of spillover may
offers insights into building an accurate asset pricing and accurate forecast of return and
volatility of each market. In particular, investors need to know how the risk and value of their
portfolios are affected by important fluctuations of oil prices during recent years. The recent
continuum and rapid swings in oil prices would lead to significant modifications in energy
risk management and policies of roughly all countries, as oil is used as a benchmark for
different financial instruments and represent a crucial factor in international asset hedging
strategies for various economic agents (investors holding stocks of oil and oil-related
industries, oil producers and consumers…). These stylized facts raise the question of how oil
price fluctuations and their volatility affect financial markets.
In the existing literature, there are two main lines of research in the context of transmission of
shocks among financial time series. The first line consists on the cointegration analysis which
is often used to study co-movements between different financial markets over a long period of
time. The second line of research investigates the time path of volatility in financial variables
such as stock prices and stock returns. In this context, researches have used a various class of
models known as autoregressive conditional heteroscedasticity, ARCH, to estimate time
variant conditional variance. Recently, studies have focused more on the persistence and
transmission of volatility from one market to another. In this paper we combine elements of
these tow lines of research by investigating the volatility and shocks transmission mechanism
between oil prices and five major stock markets. Specifically, we focus on the relationship
between oil and the American, French, Britannic, Japanese and German stock markets.
In order to examine the relationship between oil and each of these major markets, we use a
recent class of multivariate GARCH models: the multivariate long-memory GARCH model
which allows estimating simultaneously mean and conditional variance transmission between
oil prices and stock market returns. Our models are estimated for weekly data from Mai 15,
2003, to Mai 15, 2011. Our results are important for building accurate asset pricing models,
forecasting volatility in stock returns. Furthermore, since many financial assets are traded
based on oil prices, it’s important for financial market participants to understand the volatility
transmission mechanism over time and across these series in order to make optimal portfolio
and allocation decisions.
The remaining part of the paper is structured as follows. Section 2 discusses findings of previous
works on interactions between oil prices and stock markets. Section 3 introduces the empirical
methodology we use to measure shock transmission and volatility spillover between oil and stock
markets. Section 4 presents the data. Section 5 discusses the empirical results and shows their
implications in oil-risk management. Concluding remarks are summarized in section 6.
2. Literature review
There is a body of literature on how different stocks markets and oil market interact over time
(Sadorsky, 1999; Sadorsky, 2001; Ciner, 2001; Basher and Sadorsky, 2006; Lescaroux and
Mignon, 2008, Park and Ratti, 2008). Sadorsky, 1999 used a vector autoregressive (VAR)
framework to examine the oil market. He finds that both oil prices and a univariate GARCH
measure of oil price volatility play important roles in affecting stock returns. Jones and Kaul,
(1996) provide evidence that the reaction of the US market to oil shocks may be completely
accounted for by the impact of these shocks on real cash flows.
In the context of emerging countries, Sadorsky and Basher (2006) employ daily and monthly
data to study 21 emerging countries in an international CAPM models. Their results show a
significant negative impact of oil prices in stock market returns. They argue that the results
are sensitive to the frequency of the data and the world CAPM model may not hold for all
countries. In another paper taking into account economic activity and employment,
Papapetrou (2001), find that oil price shocks affect stock market in Greece. Soytas and Oran
(2009) examine the volatility spillover from world oil spot markets to aggregate and
electricity stock index returns in Turkey. Their results revealed that world oil prices Granger
cause electricity index and adjust electricity index returns in volatility, but not aggregate
market index returns. An unexpected result reported by Narayan and Narayan (2010),
signaling a positive impact of oil price shocks on Vietnamese stock prices during the 20002008 period, using daily data and accounting for the nominal exchange rate.
Park and Ratti (2008) use a multivariate VAR framework to examine the effect of oil price
shocks and volatility on the stock returns of US and 13 European countries. They find
significant impact of oil price shocks on real stock returns in all countries. They find that in
many European markets but not in the US, higher volatility have tendency to depress real
returns. Finally the results show that many effects differ across countries.
Malik and Hammoudeh (2007) analyze the volatility transmission among the US equity
markets, the global crude oil market, and three Golf equity markets including Bahrain, Kuwait
and Saudi Arabia. They show that Golf equity market receive volatility from the oil market,
but stock market volatility only spills over into the oil market in the case of Saudi Arabia.
Malik and Ewing (2009) use a bivariate BEKK-GARCH (1, 1) model to examine the volatility
transmission between oil prices and five US sector indices including Financials, Industrials,
Consumer services, Health Care, and Technology. The empirical results support the existence
of significant transmission of shocks and volatility between oil prices and different stock
market sectors.
More recently, Arouri and Nguyen (2010) use different econometric techniques to study
short-term links between oil and stock prices in the aggregate as well as sector by sector
levels in Europe. They find that the reactions of stocks returns to oil price changes differ
greatly depending on the activity sector and the out-of sample analysis shows that adding oil
asset into a diversified portfolio of stocks allows to significantly improve its risk-return
characteristics. In the same line of research Arouri and al., (2011) investigate the volatility
spillovers between oil and stock markets in Europe using a recently developed VAR-GARCH
approach. Their results reveal significant volatility spillovers between oil price and sector
stock returns, with the spillover effects being more apparent from oil to stock markets, noting
that the intensity of volatilities interactions varies from one sector to another. Using the same
econometric approach, Arouri and al., (2011) analyze the return links and volatility
transmission between oil and stock markets in the Gulf Cooperation Council (GCC) countries
over the period 2005-2010. Their results point the existence of significant shock and volatility
spillovers between oil and stock markets in most cases, especially over the crisis period.
Examining the non-energy commodity markets, Ji and Fan (2012) examine the influence of
the crude oil market on non-energy commodity markets before and after the 2008 financial
crisis. The results reveal that the crude oil market has significant volatility spillover effects on
non energy commodity markets. The overall level of correlation strengthened after the crisis,
which indicates that the consistency of market price trends was enhanced affected by
economic recession.
The increasing degree of integration of major financial markets has lead market practitioners
and policy makers to focus on more understanding the volatility spillover effects from one
market to another. In this context, two axis of thinking have developed to explain the
phenomenon of volatility spillovers. First, volatility spillover may exist from cross-market
hedging and changes in common information, which may simultaneously alter expectation
across markets. A second factor to explain the mean and volatility spillover effects is that of
financial contagion, which means that, a shock to one country’s asset market may cause
changes in asset prices in another country’s financial market.
Engel’s (1982) ARCH model and the generalized version developed by Bollerslev (1986)
represent the most popular econometric tools used to model volatility of high frequency
financial time series data. Multivariate generalized autoregressive heteroscedasticity
(MGARCH) models have been used to investigate the volatility transmission effects among
different markets. Kearney and Patton (2000) used MGARCH to model the volatility spillover
mechanism among exchange rates in the European Monetary system. Cappiello, Engel and
Sheppard (2006) extend the basic Dynamic Conditional Correlation of Engle (2002) to
examine the correlations of global equity and bonds returns by allowing for more flexible
dynamic dependencies in the correlations and asymmetries, as well as switches, in the
correlations across regimes. More recently, Li and Majerowska (2008) investigate the
linkages between the emerging stock markets and the developed stock markets using the
BEKK parameterization of MGARCH. They find evidence of returns and volatility spillovers
from the developed to the emerging markets implying that foreign investors may reduce their
risk by adding emerging market stocks to their portfolio. Malik and Ewing (2009) used the
bivariate GARCH model to study the volatility transmission between oil returns and a
different market sector. The results reveal significant interactions between the volatility of
returns in the oil market and particular equity market sectors.
In this paper, we use a new class of MGARCH models which take into account different
characteristics of financial time series data like asymmetry effects and long memory of price
volatility. We use for the first time the multivariate Fractional Integrated Exponential GARCH
(FIEGARCH) model with time-varying construction to examine the volatility spillover
between oil price shocks and the major developed stock markets of America, UK, French,
German, and Japan, and estimate dynamic conditional correlation. Specifically we employ a
bivariate FIEGARCH model which allows us to study the volatility transmission between oil
returns and each stock market simultaneously.
3. Volatility
spillover
between
crude
oil
and
stock
markets:
𝑫𝑪𝑪 −
𝑭𝑰𝑬𝑮𝑨𝑹𝑪𝑯 (𝟏, 𝒅, 𝟏) model
Our present study seeks to investigate the volatility interaction between oil prices and five
stock markets through several GARCH-type models taking into account two new important
features of financial time series, namely the volatility asymmetry and the long memory. We
use the Fractionally Integrated Exponential GARCH (FIEGARCH) model proposed by
Bollerslev and Mikkelsen (1996) to construct a bivariate DCC-FIEGARCH (1, 𝑑, 1) model
that allows for, in addition to long memory feature, asymmetric reaction of conditional
volatility to news. The model is given by:
𝑟𝑖𝑡 = 𝑐1 + 𝑏1 𝑟𝑊𝑇𝐼,𝑡−1 + 𝜀𝑖𝑡
𝑟𝑊𝑇𝐼,𝑡 = 𝑐2 + 𝑏2 𝑟𝑖,𝑡−1 + 𝜀𝑊𝑇𝐼,𝑡
2
−1 (1−𝐿)−𝑑𝑖𝑖 [1+𝛼𝐿](𝛾 𝑧
1 𝑡−1 +𝛾2 [|𝑧𝑡−1 |−𝐸|𝑧𝑡−1 |])+𝑏3 𝜀𝑊𝑇𝐼,𝑡−1
ℎ𝑖,𝑡 = 𝑒 −𝜔𝑖 +(1−𝜙𝑖 𝐿)
2
−1 (1−𝐿)−𝑑𝑊𝑇𝐼𝑊𝑇𝐼 [1+𝛼𝐿](𝛾 𝑧
1 𝑡−1 +𝛾2 [|𝑧𝑡−1 |+𝐸|𝑧𝑡−1 |])+𝑏4 𝜀𝑖,𝑡−1
ℎ𝑊𝑇𝐼,𝑡 = 𝑒 −𝜔𝑊𝑇𝐼+(1−𝜙𝑊𝑇𝐼 𝐿)
(1)
(2)
ℎ𝑖,𝑊𝑇𝐼,𝑡 = 𝜌𝑖,𝑊𝑇𝐼,𝑡 √ℎ𝑖𝑖,𝑡 √ℎ𝑊𝑇𝐼,𝑊𝑇𝐼,𝑡
𝜌𝑖,𝑊𝑇𝐼,𝑡 =
𝑞𝑖,𝑊𝑇𝐼,𝑡
√𝑞𝑖𝑖,𝑡 𝑞𝑊𝑇𝐼𝑊𝑇𝐼,𝑡
Where 𝛾𝑗 ≠ 0, 𝑗 = 1,2, indicates the existence of leverage effects. By including the leverage
term we allow the conditional variance to depend both on sign and magnitude of expected
returns. This asymmetric model is an attempt to model another stylized fact about asset
returns, the effect of bad news: risky stocks respond differently to positive high gains and low
negative falls. The larger the leverage parameter value, the larger the risk.
𝑟𝑊𝑇𝐼 and 𝑟𝑖 represent weekly returns for crude oil and each stock market (S&P500, CAC40,
FTSE100, DAX and NIKKEI225) respectivly. 𝜀𝑖𝑡 and 𝜀𝑊𝑇𝐼,𝑡 are the innovation available
under the information set available at time 𝑡 − 1. 𝑏1 and 𝑏2 measures the mean spillover
effects of crude oil returns and each stoch returns, respectivly.
ℎ𝑊𝑇𝐼,𝑡 , ℎ𝑖,𝑡 , and ℎ𝑖,𝑊𝑇𝐼,𝑡 are the variance for crude oil and each stock market and the
covariance between them. 𝜌𝑖,𝑊𝑇𝐼,𝑡 is the correlation coefficient between crude oil end each
stock market. 𝑏3 and 𝑏4 measures the variance spillover effects of crude oil (stock market
index) on each stock market index (crude oil).
Correlation between crude oil market and stock index returns can reflect the degree in what
extent their prices move together in different periods. Taking into account the different
characteristics and sever price fluctuation of deffrent market, time-varying correlation is
necessarily estimated to investigate whether the relation between market is constant. In this
study we use the Daynamic Conditionnel Correlation DCC-GARCH modeles introduced by
Engle (2002). Let 𝑟𝑡 be the vector composed of two returns series, 𝑟𝑡 = (𝑟1 , 𝑟2 )′. Denoting by
𝐴(𝐿) the lag polynomial, we have:
𝐴(𝐿)𝑟𝑡 ⁄ℱ𝑡−1 = 𝜇𝑡 + 𝜀𝑡
(3)
Where 𝜀𝑡 is the error-term vector.
The DCC model is based on the hypothesis that the conditional returns are normally
distributed with zero mean and conditional covariance matrix 𝐻𝑡 = 𝐸[𝑟𝑡 𝑟 ′ |𝐼𝑇−1 ]. the
covariance matrix is expressed as follow:
𝐻𝑡 ≡ 𝐷𝑡 𝑅𝑡 𝐷𝑡
(4)
Where 𝐷𝑡 = 𝑑𝑖𝑎𝑔{√𝐻𝑖𝑡 } is a diagonal matrix of time-varying standard deviations issued from
the estimation of univariate GARCH processes:
2
ℎ𝑡 = 𝛼0 + 𝛼1 𝜀𝑡−1
+ 𝛽1 ℎ𝑡−1
(5)
And 𝑅𝑡 is the conditional correlation matrix of the standardized disturbances 𝜀𝑡 , avec
𝜀𝑡 =𝐷𝑡−1 𝑟𝑡 :
1
𝑅𝑡 = [
𝜌12,𝑡
𝜌12,𝑡
]
1
(6)
The matrix 𝑅𝑡 is decomposed into
𝑅𝑡 = 𝑄𝑡∗−1 𝑄𝑡 𝑄𝑡∗−1
(7)
Where 𝑄𝑡 is the positive definite matrix containing the conditional variances-covariances of
𝜀𝑡 and 𝑄𝑡∗−1 t is the inverted diagonal matrix with the square root of the diagonal elements of
𝑄𝑡 :
1/√𝑞11,𝑡
𝑄𝑡∗−1 = [
0
0
1/√𝑞22,𝑡
]
The DCC model is then given by:
𝑄𝑡 = (1 − 𝑎 − 𝑏)𝑄̅ + 𝑎𝜖𝑡−1 𝜖′𝑡−1 + 𝑏𝑄𝑡−1
(8)
(9)
where 𝑄̅ being the unconditional covariance of the standardized disturbances 𝜀𝑡 . The
dynamic conditional correlations are finally given by:
𝜌𝑖𝑗,𝑡 =
𝑞12,𝑡
√𝑞11,𝑡 𝑞22,𝑡
(10)
Note that, following Engle (2002), the estimation of this model is done using a two-step
maximum likelihood estimation method, the likelihood function being given by:
1
ln(𝐿(𝜃)) = − 2 ∑𝑇𝑡=1{𝑛 ln(2𝜋) + 𝑙𝑛|𝐷𝑡 |2 + ln(|𝑅𝑡 |) + 𝜀𝑡′ 𝐷𝑡−2 𝜀𝑡
4. Data
(11)
To examine the volatility spillover between oil price and stock market returns, we collect data
from five stock markets indices: the American market (S&P500), French market (CAC40),
Britannic market (FTSE100), German market (DAX) and he Japanese market (NIKKEI225).
The WTI futures price was selected as the international crude oil price (CO). We employ
weekly data over the period from January 01, 2003 to November 30, 2012. The chosen period
permits to examine the sensitivity of international stock market returns to the recent oil price
increase in 2007-2008. Weekly data seem to capture the dynamic interaction of oil and stock
prices better than daily and monthly data. The reason is that the use of daily data often
induces potential biases arising from, among others, the bid-ask bounce, non-synchronous
trading days, and the effect of illiquidity on asset prices, while monthly data may mask same
volatility transmission mechanisms due to time aggregation and compensation effects. Some
recent papers have empirically shown that using weekly data to examine the oil-stock market
relationships leads to better estimation and forecast results with respect to information and
forecasting evaluation criteria (Arouri and Nguyen, 2010, Arouri and al., 2011). Finally,
returns for both oil market and stock markets are calculated by taking the first differences of
the logarithm of the two successive prices. To investigate the different characteristics between
crude oil and each stock market before and after oil prices shock during 2007-2008, the
sample data were divided into two intervals. Since oil price increasing began in the mid-2007
until the first semester of 2008, we used 31 July 2007 as the date to divide the data. Those the
pre-shock sample covers January 2003-31 July 2007 (238 observations) and the post-shock
sample covers 1 August 2007- 30 November 2012 (279 observations).
4.1. Oil price and stock market movement
Fig. 1: Crude oil (WTI) and stocks market indices
Oil price evolution’s show some important peaks and troughs during the period under study.
The main peaks are observed between 2007 and 2008. Another peak is observed in June 2009,
where prices increased by more than 60% since the January 2009 price levels. All this oil
price fluctuations are generated by several aggregate demand-side oil price shocks. The first
one occurred during the Asian economic crisis, the second took place in 2000, where interest
rates decreased significantly creating a bust in the housing market and construction industries.
The third one took place in the period 2006–2007, a result from the rising demand of oil from
China and the fourth demand-side oil price shock took place in the global financial crisis of
2008.
Moving now to the analyze of stock market indices movement, it’s clear from (fig.1) that
stock market indices do not move in the same direction of oil prices. In fact, during the subperiod 2007-2008 stock market indices are decreasing where oil prices are increasing.
Table 1: statistics for weekly log returns for crude oil and stock market indices
Before choc (1/2003 -7/2007)
Mean
S.D
WTI
S&P500
CAC40
DAX
FTSE100
NIKKEI
0.3982
0.0412
0.0958
0.1048
0.01635
0.06118
4.1069
2.313
2.7815
3.2771
2.1301
2.736
Min
Max
Skewness
p-value
Excess kurtosis
p-value
J-B
p-value
ARCH-LM (10)
p-value
𝑄(20)
-19.234
-11.71
-12.126
-13.919
-8.8636
-11.292
11.155
7.4923
11.034
12.887
10.069
9.4687
-0.7210
-0.5455
-0.2121
-0.2131
-0.2842
-0.3013
0,0000
0,0000
0,06775
0,0664
1.8236
3.1186
1.6058
1.3590
0,0000
0,0000
0,0000
99,5450
201,0400
0,0000
0,0000
1.0693
0.3847
0,0143
0,0094
2.1513
0.4241
0,0000
0,0000
0,0672
50,8050
37,3620
91,1870
10,0000
0,0000
0,0000
0,0000
0,0067
3.9203
8.8065
10.830
5.1884
1.7304
0.0000
0.0000
0.0000
0.0000
0.0718
44.7074
31.7361
18.5089
19.8781
21.1905
8.4896
p-value
0.0012
0.04619
0.5539
0.4655
0.3859
0.9881
2
11.8787
52.1396
151.945
188.224
85.0497
31.9057
p-value
0.9201
0.0001
0.0000
0.0000
0.00000
0.0443
0.0685
-0.0211
-0.1879
-0.0276
-0.0420
-0.2275
𝑄 (20)
After choc (08/2007- 11/2012)
Mean
S.D
Min
Max
Skewness
4.876
3.1941
3.8161
3.806
3.2216
3.5878
-19.1
-20.084
-25.05
-24.347
-23.632
-27.884
25.125
11.356
12.432
14.942
12.583
11.45
-0.1909
-0.7970
-1.1250
-1.0134
-1.3373
-1.7325
0.1874
0,0000
0,0000
0,0000
0,0000
0,0000
Excess kurtosis
3.8395
5.8759
6.3795
6.9573
11.048
12.225
p-value
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
175.55
437.08
539.58
619.20
1523.5
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
14.263
5.4337
2.9517
5.5581
4.1636
1.6154
0.0000
0.0000
0.0016
0.0000
0.0000
0.1021
46.9897
27.0320
47.6909
38.9791
59.6045
16.9406
p-value
0.0005
0.1343
0.0004
0.0067
0.0000
0.6568
2
307.718
82.5870
46.8729
82.0510
52.5659
20.8473
p-value
J-B
p-value
ARCH-LM (10)
p-value
𝑄(20)
𝑄 (20)
1903.7
0.0000
p-value
0.0000
0.00061
0.0000
0.0000
0.4061
Note: S.D. is the standard deviation of WTI and stock indices returns, the descriptive statistics for cash daily
returns are expressed on percentage, J-B test is the Jarque- Béra (1980) normality test statistic,
𝑄(20) and 𝑄 2 (20) are the Ljung-Box Q-statistics of order 20 on the standardized and squared returns,
respectively.
Summary statistics for logarithm returns for crude oil and stock market returns before and
after the 2007-2008 oil price shock are reported in table 1. All the returns exhibit a high
degree of kurtosis with a fat tail and non-normal distribution, as indicated by the Jarque-Bera
test. According to the mean, it seems that oil price shock had a great negative impact on stock
market returns. The mean return for each stock market index is positive before the crude oil
shock and negative after the shock. In general the standard deviation reflects deviation before
and after shock, on the one hand, the WTI volatility is strongest indicating an increased risk
for crude oil market. On the other hand, stock markets volatilities increased after crude oil
shock, which imply that oil price increase depressed stock markets and increased markets
uncertainty. Furthermore, the Ljung-Box 𝑄 and 𝑄 2 statistics in table 1 provide strong evidence
of conditional heteroskedasticity for all markets. There for, the choice of a GARCH class
model can capture this market phenomenon better (Bollerslev, 1992).
Fig. 2 display weekly stock market and crude oil returns. We can see that crude oil and stock
markets follow similar movements over the study periods. Volatility clustering is manifestly
apparent for all the time series, i.e., large (small) changes tend to be followed by large (small)
changes over consecutive weeks. This characteristic reveals the presence of conditional
heteroscedasticity in the variance process of the return series, and thus justifies the use of
GARCH specifications to adequately model crude oil and stock market return volatility.
RCAC
RWTI
12.5
20
10.0
15
7.5
10
5.0
5
2.5
0.0
0
-2.5
-5
-5.0
-10
-7.5
-15
-10.0
2003
2004
2005
2006
2007
2008
2009
2007
2008
2009
2003
2010
2004
2005
2006
2007
2008
2009
2010
RSP
12.5
10.0
7.5
5.0
2.5
0.0
-2.5
-5.0
-7.5
-10.0
2003
2004
2005
2006
2010
RNIKKEE
15
10
5
0
-5
-10
-15
2003
2004
2005
2006
2007
2008
2009
2010
Fig.2: crude oil and stock market weekly returns.
Augmented Dickey–Fuller (ADF) and Phillips–Perron (PP) tests (panel A, table 2) reject the
null hypothesis of unit root for all the return series at the 1% significance level. The KPSS test
results reveal that the null hypothesis of stationarity cannot be rejected at the 1% significance
level. All the return series are therefore stationary, 𝐼(0), and suitable for long-range memory
tests. Note however that none of the return series displays long-range memory in their mean
equation, as indicated by the Lo’s (1991) test statistics with respect to raw returns (Panel B,
Table 2).
Table.2: unit root and long memory tests for crude oil and stock market returns
WTI
S&P500
CAC40
FTSE100
DAX
NIKKEI
Panel A: unit root and stationary
tests
ADF test
PP test
KPSS test
-24,4858
-27,1332
-29,4181
-29,4245
-27,5147
-26,7350
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
-45,7122
-50,6839
-49,0775
-48,4603
-47,0276
-44,5953
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0823
0,1315**
0,2383**
0,1046
0,1668
0,3138**
{<1}
{<1}
{<1}
{<1}
{<1}
{<1}
1,44791*
1,6190
1,5610
1.5210
1.6845
1,3983
{<0,4}
(0.0191)
(0.0388)
(0.0630)
(0.3464)
(0.4079)
4,9465
5,1586**
4,5799**
2.8212**
2.7532**
3,85971**
{<0,005}
0,0000
0,0000
0,0000
0,0000
0,0000
5,162
6,9368**
6,298**
3.8292**
3.3267**
4,9745**
{<0,005}
0,0000
0,0000
0,0000
0,0000
0,0000
Pannel B: long-memory test statistics
Return (𝑟𝑡 )
Lo's R/S test
Squared return
(𝑟𝑡2 )
Lo's R/S test
Absolute return | 𝑟𝑡 |
Lo's R/S test
Note: ADF is the augmented Dickuy Fuller (1979) unit-root test statistics, PP is the Phillip-Peron (1988) unitroot test statistics, KPSS is the Kwiatkowski, Phillips, Schmidt and Shin (1992) stationary test statistic. P-values
are given into brackets. ** denotes significance at 5% level.
To test whether long memory is present in the conditional variance of return series, we apply
three long memory tests to absolute and squared returns: the log periodogram regression
(GPH) test of Geweke and Porter-Hudak (1983), the Gaussian semi-parametric (GSP) test of
Robinson (1995), and the rescaled variance (V/S) test of Giraitis et al. (2003). The results of
these tests are reported in Table 3. The GSP and GPH tests (Panels A and B) for absolute and
squared returns reject the null hypothesis of no long-range memory at the 1% level for crude
oil and all stock returns. The evidence on the presence of long memory in squared and
absolute returns is consistent with several previous studies such as Kasman et al. (2009),
Kang et al. (2010), Chkili et al., (2012) for stock markets, and King et al., (2009), Aloui et
Mabrouk (2010), for crude oil market. The V/S test also rejects the null hypothesis of no longrange memory in the volatility of crude oil and stock returns.
Table. 3 : GPH, GSP and R/V tests results
WTI
S&P500
CAC40
FTSE100
DAX
NIKKEI
𝑚 = 𝑇 0.5
0,6104
0,8926
0,6426
0,6453
0,6483
0,3257
𝑚 = 𝑇 0.6
0,4923
0,6985
0,6335
0,6187
0,6398
0,5814
0.8
0,2429
0,2865
0,3608
0,4103
0,3124
0,4884
Pannel A: GPH (1983) test
Squared return
𝑚=𝑇
Absolute return
𝑚 = 𝑇 0.5
0,6889
0,8699
0,6265
0,6910
0,6132
0,4915
0.6
0,5762
0,7788
0,6455
0,6474
0,6651
0,5807
0.8
0,2186
0,2950
0,2934
0,3445
0,3030
0,4002
𝑚 = 𝑇/4
0,2221
0,2968
0,3004
0,2807
0,2753
0,4803
𝑚 = 𝑇/16
0,3703
0,8062
0,5174
0,4725
0,4685
0,5835
0,7425
0,6206
0,5938
0,4350
0,3941
0,5938
𝑚 = 𝑇/4
0,2411
0,3076
0,2746
0,2995
0,2798
0,3428
𝑚 = 𝑇/16
0,3978
0,7084
0,4965
0,4904
0,4814
0,5186
𝑚 = 𝑇/64
0,7608
0,6055
0,5146
0,4700
0,4464
0,4472
𝑚 = 10
3,0465
2,8498
2,7805
2,8212
2,7532
2,1612
𝑚 = 40
1,8241
1,6523
1,7204
1,7266
1,7019
1,4353
1,2387
1,2178
1,3048
1,3159
1,2968
1,2002
𝑚 = 10
3,1924
4,2073
3,3721
3,8293
3,3267
3,8094
𝑚 = 40
1,8950
2,0745
2,1886
2,2648
2,0091
1,7619
𝑚= 𝑇
𝑚=𝑇
Pannel B: GSP Robinson (1995a) test
Squared return
𝑚 = 𝑇/64
Absolute return
Pannel C: Rescaled Variance test
Squared return
𝑚 = 110
Absolute return
1,2783
1,4275
1,5520
1,6008
1,4405
1,3457
𝑚 = 110
2
Notes: (𝑟𝑡 ), (𝑟𝑡 ) and |𝑟𝑡 | are, respectively, log return, squared log return and absolute log return. (𝑚) denotes the
bandwidth for the Geweke and Porter-Hudak’s(1983) and the GSP Robinson (1995a) tests.
Table 4: Estimated parameters for the bivariate DCC(1,1)-FIEGARCH (1,d,1) model for each stock markets.
markets
U.S
Mean equation
𝑐1
𝑏1
𝜔𝑖
𝛼1
Variance equation
𝛽1
𝛾1
𝛾2
𝑑
𝑏3
𝑎
𝐷𝐶𝐶(1,1) parameters
𝑏
𝑎+𝑏
0.1939
-0.0241
1.1586
-0.3561
0.7063
-0.1781
0.2968
0.4620
-0.0021
0,0000
0,8406
( 1.295)
(-1.594)
(0.7956)
(-0.1938)
(0.3973)
(-1.496)
(5.026)
(0.4747)
-0.1837
(0,0000)
(2,025)
French
0.1275
-0.0495***
1.8669
0.7224
0.0770
-0.1089**
0.2150
0.5971
-0.0233*
0,0152
0,9728
(2.034)
( -2.944)
(4.740)
(1.316)
(0.2279)
(-2.081)
(3.572)
( 4.249)
(-1.860)
(2,0530)
(72,05)
Germany
0.2092
-0.0314**
2.0662
0.2249
0.9750
-0.2052***
0.2513
-0.3405
-0.0202*
0,0182
0,9765
(8.394)
(-2.572)
(26.40)
(0.9947)
(126.9)
(-3.987)
(4.685)
(-4.242)
(-1.770)
(2,4160)
(77,59)
U.K
0.0812
-0.0455***
1.5156
0.0740
0.9707
-0.2099***
0.1990
-0.1724
-0.0298**
0,0132
0,9822
0.9102
(-2.813)
(9.464)
(0.2540)
(82.94)
(-3.461)
(3.307)
(-1.496)
(-2.270)
(2,4230)
(112,4)
Japan
-0.0552
-0.0167**
2.1126
-0.3775
0.6005
-0.2361***
0.2439
0.3082
-0.0301**
0,0002
0,8304
(-3.456)
(-2.033)
(17.24)
(-0.8653)
(2.786)
(-3.379)
(1.454)
(2.134)
(-2.288)
(0,7501)
(2,584)
0,8406
𝜌
𝐿𝑉
0.0123 -5263.194
(0.4066)
0,988
0.06122 -5573.156
0,9947
0.0080
(0.9159)
-5637.941
(0.0708)
0,9954
0.0943
-5282.057
(0.9999)
0,8306
0.0458 -5695.660
(1.563)
Notes: values in brackets denote t-values. *, **, *** indicate significance at the 10%, 5% et 1% levels, respectively 𝑳𝑽 denote the log-likelihood.
5. Empirical study of volatility transmission between crude oil and stock markets
Analysis of the summary statistics in the previous section revealed that volatility of return
series under study may have long-memory component so that relationships between crude oil
and different stock markets are not entirely consistent. To further investigate the volatility
transmission mechanism between markets, we construct a bivariate FIEGARCH model for
crude oil and each stock market and we analyze the characteristics of time varying conditional
correlation.
5.1. Empirical study of mean-volatility spillover between crude oil and stock markets
Table 4 shows parameter estimates for bivariate DCC(1.1)-FIEGARCH(1.d.1) models
between crude oil and stock markets. From this table we can see that the long memory
parameter is statistically significant for major markets studied, indicating strong evidence of
long memory in the volatility of stock returns. Our estimated model can capture both mean
and asymmetric volatility transmission from crude oil to stock markets.
Regarding the interdependence of returns in mean equations, we find that lagged oil returns
significantly affect stock market returns in four out of five cases over the whole period:
French, German, UK and Japan. For these markets, an oil price shock has a negative and
statistically significatif impact on real stock returns. The constant terms for the stock returns
mean equations are only significant for French, German and Japan (both at the 5% and 1%
level).
Estimates of ARCH and GARCH coefficients, which capture shock dependence and volatility
persistence in the conditional variance equations, are statistically significant at conventional
levels in many cases. Moreover, the relatively small size of ARCH coefficients (𝛼) indicates
that conditional volatility does not change very rapidly under the impulsions, but it tends to
fluctuate gradually over time as suggested by the large magnitude of GARCH coefficients(𝛽).
The behavior of oil price volatility is typically similar to the patterns of stock market
volatility.
Regarding volatility transmission between oil and stock markets, there can be observed that
conditional volatility of stock markets is affected by innovations in the oil market as indicated
by the significance of the 𝑏3 coefficients for French, German, UK and Japan. This seems to
suggest that a shock originating from the oil market generally has a negative impact on stock
market volatility in these markets. In fact volatility transmission mechanism is always
significant and asymmetric from crude oil to stock markets except for the American market.
In fact, oil price increase influence negatively and significantly stock index returns. Increasing
oil prices led to a decreasing of financial assets and depression of financial markets as a result
of slow firm’s profits.
All estimates of 𝛾1 are statistically significant and negative, indicating the large effect of bad
news. This result suggests that a positive shock on the conditional variance ℎ𝑖𝑡 a time 𝑡 imply
a decrease in ℎ𝑖𝑡 at time 𝑡 + 1. The asymmetric effect related to the magnitude of the
innovation 𝑧𝑡 is captured by 𝛾2 and can be computed by the difference (|𝑧𝑡 | + 𝐸|𝑧𝑡 |). The
estimates of 𝛾2 are positive and statistically significant at the 1% level for all stock market
expect for japaneese market. In this case the negatif impact of increasing oil price is more
important than positif impact related to the decraese of crude oil price (Hamilton 1983, 2005).
This asymmetric effect is more and more important, since many authors (Mork, 1989 et Lee,
Ni et Ratti, 1995) show that oil price decreasing did not have any impact on the economic
activity. Possible explanations for this asymmetry rely on monetary policy, adjustment costs,
adverse effects uncertainty on the investment environment (Ferderer, 1996), and asymmetry
in petroleum product prices (for a detailed study, see Lardic and Mignon 2006, Hamilton,
1988, Mork, 1989 et Lee, Ni et Ratti, 1995).
5.2. Dynamic conditional correlation
To further explore the time varying characteristics of correlation between crude oil and stock
market indices and to compare change before and after oil price shock, we estimate the
dynamic conditional correlation coefficients. According to results in table 3, the values of
parameter 𝑏 are significant and close to one, which indicate that correlations between crude
oil and each stock market present strong persistence, which is consistent with the strong
volatility persistence of each market itself.
Fig.3 presents the dynamic conditional correlation between the crude oil market and stock
market returns. The correlation shows markedly different characteristics, before recent oil
price shock correlation decreased and increased successively. It is worth noting that the
correlations follow an increasing trend, from negative to positive values with the turning point
coincided with August 2008, especially for French, German and U.K suggesting that oil and
stock market are highly linked.
According to the graphs of time-varying conditional correlation between oil prices and stock
markets returns (Fig.3) we can see different change in the patterns of correlation which can be
explained. Since 2004, influenced by rapid growth in the global economy and strong demand
crude oil prices increased rapidly, while dynamic interaction between oil price and stock
market indices is weak. International investors were optimistic about the perspectives of crude
oil because it’s a strategic resource, so a large amount of speculative capital flowed to the
crude oil market, which further drop up oil prices. Since 2006 until mid 2008, oil prices rise
dramatically due to raising demand, mainly originated by China. In this stage correlation
between crude oil and stock markets increased for all countries. After august 2007, the
influence of the US subprime crisis began to hit, financial market started to suffer, correlation
between crude oil and stock markets increased. This high interaction between oil market and
stock markets can be explained by the fact that financial crisis caused stock markets to enter
bearish territories and caused oil prices to decline heavily, as also documented by Creti et al.
(2013).
Fig. 3: conditional correlation between crude oil and stock markets.
Summarizing all, direct volatility transmission between oil and sock returns is significantly
present in major cases studied. In fact oil price shocks have negative impact in stock markets,
since increasing oil prices depressed stock markets and correlation between these markets is
negative during oil markets shocks. In addition, asymmetric effect of oil shocks is statistically
positive and significant for all stock markets, indicating the large effect of bad news.
Finally, it is important to note that the set of data analyzed in this paper pertains to a very
turbulent period in financial markets and that consequently, systematic factors may have
played a role and biased the spillover results to some extent as spillovers usually increase
during crisis periods under the effects of important financial instability and economic
uncertainties.
6. Conclusion
In this paper we examined the transmission of shocks and volatility between crude oil market
and stock markets. We construct a bivariate DCC(1.1)-FIEGARCH (1.d.1), this asymmetric
parameterization is an attempt to model tow major stylized facts in the volatility of returns,
the long memory and the effect of bad news, risky stocks respond differently to positive high
gains and low negative falls. The larger the leverage parameter value, the larger the risk. We
uses weekly data for crude oil (WTI) and five international stock markets for the period
running from January 1999 to November 2012, to investigate whether oil price shocks are
transmitted to financial markets . Our findings show the existence of significant volatility
transmission between oil and different stock markets studied except for the American market.
It is clear that during tranquil period correlation between oil and stock market is weak, while
during oil price shocks correlation between these markets increased indicating that oil price
shocks depresses stock markets and increase their volatilities. Overall, this study is of
particular interest for portfolio management since it offers insight into markets that still
provide valuable opportunities for portfolio diversification.
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