《船舶采购、销售和运营 Ship Purchase, Sales and Operations》课程教学资源（资料）Return and volatility spillovers between china and world oil markets

Economic Modelling 42(2014)413-420 Contents lists available at ScienceDirect Economic Modelling ELSEVIER journal homepage:www.elsevier.com/locate/ecmod Return and volatility spillovers between china and world oil markets CrossMark Bing Zhang,Peijie Wang b.1 Department of Finance and Insurance,Nanjing University,PR China School of Management,University of Plymouth.UK ARTICLE INFO ABSTRACT Article history: We examine return and volatility spillovers between China and world oil markets.This topic is of great Accepted 3 July 2014 importance because China is the world's second-largest oil importer and has exhibited substantial growth in Available online 8 August 2014 oil consumption.Extending Diebold and Yilmaz's(2012)method of catching spillover dynamics,it is found that return and volatility spillovers between China and world oil markets are bi-directional and asymmetric. Keyword达： The Chinese oil market is highly affected by world oil markets and exerts an influence on world oil markets. China World oil market although to a lesser extent.Moreover,the volatility spillover index has increased significantly since the peak of Spillover index the last financial crisis in September 2008.Although the US oil market impacts China's market most in terms Financial crisis of spillover,the influence of China's oil market on the world oil market has intensified in recent years. Volatility 2014 Elsevier B.V.All rights reserved 1.Introduction at levels referenced to those of international markets to maintain the incentive for the exploration and production of crude oil within China. A deep understanding of return and volatility spillovers between Consequently,the sharp fluctuations in world oil prices may have a China and world oil markets is of great importance.First,China is the great impact on China's institutions,individuals and even entire econo- world's second-largest oil consumer behind the US.The increasing my.Second,the 2008 subprime crisis in the US heavily influenced the demand for and greater dependence on imported crude oil in China world economy,including the Chinese economy.After the financial could lead to closer connections between Chinese and international oil crisis,an enormous drop in world oil prices made the co-movement markets.China's oil import reached 305.9 million tons in 2011 and between China and world oil prices even more tightly linked.This was ranked second in the world.However,China uses only one tenth development has reignited the researcher's interest in the return and of the per capita oil consumption of the US,so there is plenty of room volatility spillover effect between China and world oil markets.It is of for the country's consumption to (attempt to)grow.This phenomenon importance to know whether international market linkages have promises to maintain strong pressure on energy prices for the foresee- strengthened after the financial crisis.Third,understanding return and able future(BP.2011).According to the International Energy Agency. volatility spillovers between China and world oil prices is helpful for in- China's oil consumption growth represented over a third of the world's stitutional and individual investors to engage in effective risk manage- oil consumption growth in 2010.IEA forecasts that China's oil consump- ment and superior asset allocation.For policy makers and regulators, tion will continue to grow during 2012 and 2013 at a moderate pace. more information about spillover characteristics of China and the Even so,the anticipated oil growth of over 0.8 million barrels per day world oil markets they obtain will enable better energy policies.During between 2011 and 2013 would represent 64%of the projected growth the crisis,the world witnessed increasing volatility spillovers across in world oil demand during the 2-year forecast period.2 Since 1998. markets.There exists great practical value in measuring and monitoring the market mechanism of oil pricing has gradually been established in such spillovers-both to provide "early warning systems"for emergent China,and crude oil in the Chinese domestic market has been priced crisis and to track the progress of potential crises.Finally,the impact of China's increased oil demand on oil prices has become a hot topic of debate in recent financial press,these debates prompt us to conduct a further investigation. The spillover effect among different markets is a hot topic that has Corresponding author at:Department of Finance and Insurance,Business School, recently attracted a large volume of empirical research.Lanza et al. Nanjing University.210093.PR China.Tel:+86 25 83621102. E-mail address:zhangbing@njueducn(B.Zhang). (2005)examine heavy crude oil prices from 1994-2001 for Europe 1Te:+441752585705. and the US,using an error correction model.Lin and Tamvakis(2001) 2 http://www.eia.gov/countries/cab.cfm?fips-CH. investigate volatility spillover effects between NYMEX and International http://dx.doi.org/10.1016/j.econmod.201407.013 0264-99930 2014 Elsevier B.V.All rights reserved

Return and volatility spillovers between china and world oil markets Bing Zhang a, ⁎, Peijie Wang b,1 a Department of Finance and Insurance, Nanjing University, PR China b School of Management, University of Plymouth, UK article info abstract Article history: Accepted 3 July 2014 Available online 8 August 2014 Keywords: China World oil market Spillover index Financial crisis Volatility We examine return and volatility spillovers between China and world oil markets. This topic is of great importance because China is the world's second-largest oil importer and has exhibited substantial growth in oil consumption. Extending Diebold and Yilmaz's (2012) method of catching spillover dynamics, it is found that return and volatility spillovers between China and world oil markets are bi-directional and asymmetric. The Chinese oil market is highly affected by world oil markets and exerts an influence on world oil markets, although to a lesser extent. Moreover, the volatility spillover index has increased significantly since the peak of the last financial crisis in September 2008. Although the US oil market impacts China's market most in terms of spillover, the influence of China's oil market on the world oil market has intensified in recent years. © 2014 Elsevier B.V. All rights reserved. 1. Introduction A deep understanding of return and volatility spillovers between China and world oil markets is of great importance. First, China is the world's second-largest oil consumer behind the US. The increasing demand for and greater dependence on imported crude oil in China could lead to closer connections between Chinese and international oil markets. China's oil import reached 305.9 million tons in 2011 and was ranked second in the world. However, China uses only one tenth of the per capita oil consumption of the US, so there is plenty of room for the country's consumption to (attempt to) grow. This phenomenon promises to maintain strong pressure on energy prices for the foresee￾able future (BP, 2011). According to the International Energy Agency, China's oil consumption growth represented over a third of the world's oil consumption growth in 2010. IEA forecasts that China's oil consump￾tion will continue to grow during 2012 and 2013 at a moderate pace. Even so, the anticipated oil growth of over 0.8 million barrels per day between 2011 and 2013 would represent 64% of the projected growth in world oil demand during the 2-year forecast period.2 Since 1998, the market mechanism of oil pricing has gradually been established in China, and crude oil in the Chinese domestic market has been priced at levels referenced to those of international markets to maintain the incentive for the exploration and production of crude oil within China. Consequently, the sharp fluctuations in world oil prices may have a great impact on China's institutions, individuals and even entire econo￾my. Second, the 2008 subprime crisis in the US heavily influenced the world economy, including the Chinese economy. After the financial crisis, an enormous drop in world oil prices made the co-movement between China and world oil prices even more tightly linked. This development has reignited the researcher's interest in the return and volatility spillover effect between China and world oil markets. It is of importance to know whether international market linkages have strengthened after the financial crisis. Third, understanding return and volatility spillovers between China and world oil prices is helpful for in￾stitutional and individual investors to engage in effective risk manage￾ment and superior asset allocation. For policy makers and regulators, more information about spillover characteristics of China and the world oil markets they obtain will enable better energy policies. During the crisis, the world witnessed increasing volatility spillovers across markets. There exists great practical value in measuring and monitoring such spillovers—both to provide “early warning systems” for emergent crisis and to track the progress of potential crises. Finally, the impact of China's increased oil demand on oil prices has become a hot topic of debate in recent financial press, these debates prompt us to conduct a further investigation. The spillover effect among different markets is a hot topic that has recently attracted a large volume of empirical research. Lanza et al. (2005) examine heavy crude oil prices from 1994–2001 for Europe and the US, using an error correction model. Lin and Tamvakis (2001) investigate volatility spillover effects between NYMEX and International Economic Modelling 42 (2014) 413–420 ⁎ Corresponding author at: Department of Finance and Insurance, Business School, Nanjing University, 210093, PR China. Tel.: +86 25 83621102. E-mail address: zhangbing@nju.edu.cn (B. Zhang). 1 Tel.: +44 1752 585705. 2 http://www.eia.gov/countries/cab.cfm?fips=CH. http://dx.doi.org/10.1016/j.econmod.2014.07.013 0264-9993/© 2014 Elsevier B.V. All rights reserved. Contents lists available at ScienceDirect Economic Modelling journal homepage: www.elsevier.com/locate/ecmod

414 B.Zhang.P.Wang Economic Modelling 42 (2014)413-420 Petroleum Exchange(IPE)crude oil contracts in both non-overlapping effects between China and the world oil markets.Jiao et al.(2007) and simultaneous trading hours.The authors find that substantial spill- find that oil prices in China have been increasingly affected by interna- over effects do exist when both markets are trading simultaneously. tional oil prices.Chen et al.(2009)examine China's influence on the vol- Sadorsky(2012)tests the volatility dynamics between oil prices and atilities of crude oil prices in international markets in the 11-year period the stock prices of clean energy and technology companies and finds between 1997 and 2007.The authors find that fluctuations in oil prices that the dynamic conditional correlation MGARCH model fits the data in China have little impact on the volatilities of the world crude oil mar- the best.Chang et al.(2010)present evidence of volatility spillovers kets,whereas the reverse impact is relatively slow and weak.However and asymmetric effects on conditional variances for most international these papers use the earlier data,setting the applicability of the results oil markets.Liu and Tu(2012)investigate jump spillover effects of five to the new era covering the recent financial crisis in doubt.It is impera- energy (petroleum)futures and their implications for diversification tive to understand what types of connections exist between China and benefits.Furio and Chulia(2012)observe that Brent crude oil and world oil markets in recent years.In addition,the present paper covers Zeebrugge natural gas forward prices play a prominent role in the both return and volatility spillover effects between China and interna- Spanish electricity price formation process.Furthermore,the authors tional oil markets. find that causations run from Brent crude oil and natural gas forward The rest of the paper is organized as follows:Section 2 briefly intro markets to the Spanish electricity forward market in both price and duces the spillover index method.Section 3 provides the empirical anal- volatility spillovers. ysis of return spillovers.Section 4 provides the empirical analysis of Studies covering the relationship between China and world oil volatility spillovers.Section 5 concludes this study,advancing a number markets,there generally hold one of two views.On the one hand. of suggestions and recommendations. Li and Leung(2011)find that China is now an active participant in the world oil market.On the other hand,Du et al.(2010)find that China's 2.Methodology economic activity fails to affect the world oil prices,indicating that the world oil price remains exogenous with respect to China's macro- The original measure of return and volatility spillover index by economy in a time series sense,and China has not yet possessed oil Diebold and Yilmaz(2009)is based on forecast-error variance de- pricing power in the world oil markets. compositions in a vector autoregressive framework.Consider first To investigate return and volatility spillovers in international stock the simple example of a covariance stationary first-order two-variable markets more effectively,Diebold and Yilmaz(2009)propose a novel VAR measure based on forecast error variance decompositions in a vector autoregressive framework,which is abbreviated as DY2009 in the X:DX -1+8 (1) paper.Diebold and Yilmaz(2011)apply this new method to analyze re- turn and volatility spillovers among four South American countries. where Xr =(XitX2t)',which represents either a vector of asset returns Diebold and Yilmaz(2012)have recently developed a new method, or a vector of asset return volatilities.is a 2 x 2 parameter matrix,and designated DY2012 in the paper.The authors employ this upgraded Er is a residual vector.By covariance stationary,the moving average model,DY2012,to explore the spillovers among major US financial as- representation of the VAR exists and is given by: sets including stocks,bonds,foreign currencies,and commodities from 1999 to 2009,focusing on volatility interaction during the subprime X:(L)Et (2) mortgage crisis.Zhou et al.(2012)adopt this method to study volatility spillovers between China and world equity markets and finds that the where (L)=(1 -L).We may rewrite the moving average US market exerted dominant volatility impacts on other markets during representation as: the subprime mortgage crisis.Whereas the other markets were also very volatile and driven by bad news,their massive volatilities were X,=A(L)ut (3) transmitted back to the US market as well. The purpose of the current paper is to examine return and volatility with ur =Q E.Q,is the unique lower-triangular Cholesky factor of spillovers between China and the world oil markets.Our study contrib- the covariance matrix of Er.The one-step-ahead forecasting error is then: utes to the existing literature in two aspects.First,our paper differs from those in the previous literature in that we are the first to adopt and then extend the DY2012 method to examine return and volatility spillovers e+1=X:+1-Xt+14 Aout+1= C0,11 00.12 山1+1 between the Chinese and world oil markets.We extend the DY2012 0C0.21 00.22 u2.r+1 (4) method to catch the dynamic patterns in spillovers and make the E(et+1e+1)=AoAo extended method more pertinent to the present study.The DY2012 method has several advantages over the other models.This method does not depend on the Cholesky factor identification of VAR.Therefore, Therefore,in particular,the variance of the one-step-ahead error in the results of variance decomposition do not hinge on the sequence of forecasting Xit is ao.n1+a6.12.and in forecasting X2t is a621+a622. the variables.In addition,DY2012 may be used to indicate the direction The spillover index may be expressed as: of the spillover as well.That is,it may provide the value of directional spillovers between any two markets.DY2012 avoids the controversial issues associated with the definition and existence of episodes of conta- S= 62+a62.100 (5 gion.To our best knowledge,this is the first study to apply this method trace(AoA) to address the spillover effect in world oil markets.In particular,we introduce rolling window techniques to further enhance the power of the DY2012 method.This augmentation is particularly helpful for ana- Furthermore,Diebold and Yilmaz (2012)work with the generalized lyzing the dynamic linkages between the world and China oil markets, VAR framework and produce a variance decomposition invariant to which may provide a more vivid and insightful picture of the position ordering,thus overcoming pitfalls generally found in identification and power of the Chinese oil market in the world arena. schemes of variance decompositions.Diebold and Yilmaz(2012)define Second,the paper explores the role of China in world oil markets "own variance shares"as the fraction of the H-step ahead error vari- using recent crude oil data.Due to the relatively late development of ances in forecasting X due to shocks to X for i 1,2....N and "cross the Chinese oil market,little is known about the volatility spillover variance shares"as the fractions of the H-step-ahead error variances

Petroleum Exchange (IPE) crude oil contracts in both non-overlapping and simultaneous trading hours. The authors find that substantial spill￾over effects do exist when both markets are trading simultaneously. Sadorsky (2012) tests the volatility dynamics between oil prices and the stock prices of clean energy and technology companies and finds that the dynamic conditional correlation MGARCH model fits the data the best. Chang et al. (2010) present evidence of volatility spillovers and asymmetric effects on conditional variances for most international oil markets. Liu and Tu (2012) investigate jump spillover effects of five energy (petroleum) futures and their implications for diversification benefits. Furió and Chuliá (2012) observe that Brent crude oil and Zeebrugge natural gas forward prices play a prominent role in the Spanish electricity price formation process. Furthermore, the authors find that causations run from Brent crude oil and natural gas forward markets to the Spanish electricity forward market in both price and volatility spillovers. Studies covering the relationship between China and world oil markets, there generally hold one of two views. On the one hand, Li and Leung (2011) find that China is now an active participant in the world oil market. On the other hand, Du et al. (2010) find that China's economic activity fails to affect the world oil prices, indicating that the world oil price remains exogenous with respect to China's macro￾economy in a time series sense, and China has not yet possessed oil pricing power in the world oil markets. To investigate return and volatility spillovers in international stock markets more effectively, Diebold and Yilmaz (2009) propose a novel measure based on forecast error variance decompositions in a vector autoregressive framework, which is abbreviated as DY2009 in the paper. Diebold and Yilmaz (2011) apply this new method to analyze re￾turn and volatility spillovers among four South American countries. Diebold and Yilmaz (2012) have recently developed a new method, designated DY2012 in the paper. The authors employ this upgraded model, DY2012, to explore the spillovers among major US financial as￾sets including stocks, bonds, foreign currencies, and commodities from 1999 to 2009, focusing on volatility interaction during the subprime mortgage crisis. Zhou et al. (2012) adopt this method to study volatility spillovers between China and world equity markets and finds that the US market exerted dominant volatility impacts on other markets during the subprime mortgage crisis. Whereas the other markets were also very volatile and driven by bad news, their massive volatilities were transmitted back to the US market as well. The purpose of the current paper is to examine return and volatility spillovers between China and the world oil markets. Our study contrib￾utes to the existing literature in two aspects. First, our paper differs from those in the previous literature in that we are the first to adopt and then extend the DY2012 method to examine return and volatility spillovers between the Chinese and world oil markets. We extend the DY2012 method to catch the dynamic patterns in spillovers and make the extended method more pertinent to the present study. The DY2012 method has several advantages over the other models. This method does not depend on the Cholesky factor identification of VAR. Therefore, the results of variance decomposition do not hinge on the sequence of the variables. In addition, DY2012 may be used to indicate the direction of the spillover as well. That is, it may provide the value of directional spillovers between any two markets. DY2012 avoids the controversial issues associated with the definition and existence of episodes of conta￾gion. To our best knowledge, this is the first study to apply this method to address the spillover effect in world oil markets. In particular, we introduce rolling window techniques to further enhance the power of the DY2012 method. This augmentation is particularly helpful for ana￾lyzing the dynamic linkages between the world and China oil markets, which may provide a more vivid and insightful picture of the position and power of the Chinese oil market in the world arena. Second, the paper explores the role of China in world oil markets using recent crude oil data. Due to the relatively late development of the Chinese oil market, little is known about the volatility spillover effects between China and the world oil markets. Jiao et al. (2007) find that oil prices in China have been increasingly affected by interna￾tional oil prices. Chen et al. (2009) examine China's influence on the vol￾atilities of crude oil prices in international markets in the 11-year period between 1997 and 2007. The authors find that fluctuations in oil prices in China have little impact on the volatilities of the world crude oil mar￾kets, whereas the reverse impact is relatively slow and weak. However, these papers use the earlier data, setting the applicability of the results to the new era covering the recent financial crisis in doubt. It is impera￾tive to understand what types of connections exist between China and world oil markets in recent years. In addition, the present paper covers both return and volatility spillover effects between China and interna￾tional oil markets. The rest of the paper is organized as follows: Section 2 briefly intro￾duces the spillover index method. Section 3 provides the empirical anal￾ysis of return spillovers. Section 4 provides the empirical analysis of volatility spillovers. Section 5 concludes this study, advancing a number of suggestions and recommendations. 2. Methodology The original measure of return and volatility spillover index by Diebold and Yilmaz (2009) is based on forecast-error variance de￾compositions in a vector autoregressive framework. Consider first the simple example of a covariance stationary first-order two-variable VAR: Xt ¼ ΦXt−1 þ εt ð1Þ where Xt = (X1t, X2t)′, which represents either a vector of asset returns or a vector of asset return volatilities. Φ is a 2 × 2 parameter matrix, and εt is a residual vector. By covariance stationary, the moving average representation of the VAR exists and is given by: Xt ¼ Φð ÞL εt ð2Þ where Φ(L) = (1 − ΦL)−1 . We may rewrite the moving average representation as: Xt ¼ A Lð Þut ð3Þ with ut = Qtεt. Qt −1 is the unique lower-triangular Cholesky factor of the covariance matrix of εt. The one-step-ahead forecasting error is then: etþ1;t ¼ Xtþ1−Xtþ1;t ¼ A0utþ1 ¼ α0;11 α0;12 α0;21 α0;22
u1;tþ1 u2;tþ1
E etþ1;te 0 tþ1;t   ¼ A0A0 0 ð4Þ Therefore, in particular, the variance of the one-step-ahead error in forecasting X1t is α0,11 2 + α0,12 2 , and in forecasting X2t is α0,21 2 + α0,22 2 . The spillover index may be expressed as: S ¼ α2 0;12 þ α2 0;21 trace A0A0 0   100 ð5Þ Furthermore, Diebold and Yilmaz (2012) work with the generalized VAR framework and produce a variance decomposition invariant to ordering, thus overcoming pitfalls generally found in identification schemes of variance decompositions. Diebold and Yilmaz (2012) define “own variance shares” as the fraction of the H-step ahead error vari￾ances in forecasting Xi due to shocks to Xi for i = 1,2,..,N and “cross variance shares” as the fractions of the H-step-ahead error variances 414 B. Zhang, P. Wang / Economic Modelling 42 (2014) 413–420

B.Zhang,P.Wang Economic Modelling 42 (2014)413-420 415 160 Table 2 Return spillover index of three oil markets. 120 US CH UK From others US 49.5 26.6 23.9 CH 27.1 49.6 23.2 50 UK 247 24.7 50.7 49 w Contnbution to others 52 51 47 Contribution including own 101 101 98 50.1% Brent 40 we may calculate the directional spillover index using the normalized elements of the variance decomposition matrix. We present the directional spillovers received by market i from all 2002-12-26 001-12-26 2004-12-26 200312-26 200512-26 207-12-26 2006-12-26 209-12-26 2008-12-26 202-12-26 2011-12-26 2010-12-26 2013-1226 other markets j as follows: N N (H) Fig.1.The prices of three oil markets H i=1 in forecast X due to shocks to Xj.for i.j=1.2.....N,such that i j.The (H) j≠i 100 ≠i 100 (9) KPPS H-step ahead forecast error variance decomposition is: H- 听(eg)2 Likewise,we may calculate the directional volatility spillovers (H= =0 i,j=1,,n (6) transmitted by market i to all other markets j as: h=0 (H) 疏(H) where E is the variance matrix for the error vector st.ou is the standard i= deviation of the error term for the ith equation,and e,is the selection j≠i j≠i S(H) 100= ,100 (10) vector with 1 as the ith element,and 0 otherwise.According to the char- N (H) acteristics of generalized VAR,we have:(H)1.We normalize each entry of the variance decomposition matrix by the row sum as: We may also obtain the net volatility spillover from market i to all other markets j by calculating the difference between Eqs.(10)and 醋(H= H (7 (9)as: ∑H S(H)=S(H)-S (H). (11) Based on KPSS variance decomposition,we may construct a total The net directional spillover (11)provides summary information spillover index as follows: about the net magnitude of each market's contribution to volatility in other markets.It is also of interest for us to examine the net pairwise volatility spillovers,which we define as: H (H） i,j=1 i.j=1 S(H= 100= i≠j ,100 (8) 丽 N (H)= 100 (12) H) Ok(H) （ i.j-1 =1 The index is used to measure the contributions from the spillovers of Given the background of the world oil market evolution and return and volatility shocks across various markets to the total forecast turbulence,especially after the collapse of Lehman Brothers,it seems error variance.Because the KPSS framework solves the ordering prob- impossible that any single parameter model would apply over the entire lem (the generalized VAR procedure accounts for contemporaneous in- sample.Although the full sample spillover table and spillover index novations with the observed historical distribution of errors,which is provide a useful summary of "average"return and volatility spillover different from the former method used to orthogonalize innovations) behavior,they might miss potentially important secular and cyclical Table 1 Summary statistics of crude oil retums () Table 3 wn DAQING BRENT Return spillover index of three oil markets before Dec 24,2008. Mean 0.0232 0.0257 0.0271 Median 0.0541 0.0344 0.0431 US CH UK From others Maximum 13.1611 53979 7.8736 US 44.3 21.2 34.5 56 Minimum -6.5970 -5.7400 -7.3100 CH 252 51.9 22.9 Std.Dev. 1.0721 0.9258 0.9554 UK 35.3 19.9 44.8 Skewness 0.4311 -02672 -0.1270 Contribution to others 61 41 57 159 Kurtosis 11.8589 42083 5.0643 Contribution including own 105 93 102 53.0%

in forecast Xi due to shocks to Xj, for i, j = 1, 2,…, N, such that i ≠ j. The KPPS H-step ahead forecast error variance decomposition is: θ g ijð Þ¼ H σ−1 jj H X−1 h¼0 e 0 iAhej  2 H X−1 h¼0 e 0 iAh XA0 hej  ; i; j ¼ 1; …; n ð6Þ where Σ is the variance matrix for the error vector εt, σii is the standard deviation of the error term for the ith equation, and ei is the selection vector with 1 as the ith element, and 0 otherwise. According to the char￾acteristics of generalized VAR, we have: ∑ N j¼1 θ g ijð Þ H ≠1. We normalize each entry of the variance decomposition matrix by the row sum as: eθ g ijð Þ¼ H θ g ijð Þ H XN j¼1 θ g ijð Þ H ð7Þ Based on KPSS variance decomposition, we may construct a total spillover index as follows: S g ð Þ¼ H XN i; j ¼ 1 i≠j eθ g ijð Þ H XN i; j¼1 eθ g ijð Þ H 100 ¼ XN i; j ¼ 1 i≠j eθ g ijð Þ H N 100: ð8Þ The index is used to measure the contributions from the spillovers of return and volatility shocks across various markets to the total forecast error variance. Because the KPSS framework solves the ordering prob￾lem (the generalized VAR procedure accounts for contemporaneous in￾novations with the observed historical distribution of errors, which is different from the former method used to orthogonalize innovations), we may calculate the directional spillover index using the normalized elements of the variance decomposition matrix. We present the directional spillovers received by market i from all other markets j as follows: S g i ð Þ¼ H XN j ¼ 1 j≠i eθ g ijð Þ H XN j¼1 eθ g ijð Þ H 100 ¼ XN j ¼ 1 j≠i eθ g ijð Þ H N 100: ð9Þ Likewise, we may calculate the directional volatility spillovers transmitted by market i to all other markets j as: S g i ð Þ H ¼ XN j ¼ 1 j≠i eθ g jið Þ H XN j¼1 eθ g jið Þ H 100 ¼ XN j ¼ 1 j≠i eθ g jið Þ H N 100: ð10Þ We may also obtain the net volatility spillover from market i to all other markets j by calculating the difference between Eqs. (10) and (9) as: S g i ð Þ¼ H S g i ð Þ H −S g i ð Þ H : ð11Þ The net directional spillover (11) provides summary information about the net magnitude of each market's contribution to volatility in other markets. It is also of interest for us to examine the net pairwise volatility spillovers, which we define as: S g ijð Þ¼ H eθ g ijð Þ H XN k¼1 eθ g ikð Þ H − eθ g jið Þ H XN k¼1 eθ g jkð Þ H 0 BBBB@ 1 CCCCA 100: ð12Þ Given the background of the world oil market evolution and turbulence, especially after the collapse of Lehman Brothers, it seems impossible that any single parameter model would apply over the entire sample. Although the full sample spillover table and spillover index provide a useful summary of “average” return and volatility spillover behavior, they might miss potentially important secular and cyclical 0 20 40 60 80 100 120 140 160 WTI Daqing Brent Fig. 1. The prices of three oil markets. Table 1 Summary statistics of crude oil returns (%). WTI DAQING BRENT Mean 0.0232 0.0257 0.0271 Median 0.0541 0.0344 0.0431 Maximum 13.1611 5.3979 7.8736 Minimum −6.5970 −5.7400 −7.3100 Std. Dev. 1.0721 0.9258 0.9554 Skewness 0.4311 −0.2672 −0.1270 Kurtosis 11.8589 4.2083 5.0643 Table 2 Return spillover index of three oil markets. US CH UK From others US 49.5 26.6 23.9 51 CH 27.1 49.6 23.2 50 UK 24.7 24.7 50.7 49 Contribution to others 52 51 47 150 Contribution including own 101 101 98 50.1% Table 3 Return spillover index of three oil markets before Dec 24, 2008. US CH UK From others US 44.3 21.2 34.5 56 CH 25.2 51.9 22.9 48 UK 35.3 19.9 44.8 55 Contribution to others 61 41 57 159 Contribution including own 105 93 102 53.0% B. Zhang, P. Wang / Economic Modelling 42 (2014) 413–420 415

416 B.Zhang.P.Wang Economic Modelling 42 (2014)413-420 Table4 yield meaningful estimation results without a serious small sample Return spillover index of three oil markets after Dec 24.2008. bias issue.We focus on this recent 10-year history to make our study 你 CH UK From others topical.We collect all the data from Wind database US 51.7 23.2 25.1 48 Fig.1 presents a graphical illustration of our data.As shown,there CH 19.9 45.9 34.2 54 are three distinct characteristics:1)the oil prices of WTI,Brent and UK 21.6 33.5 448 55 Daqing are highly correlated:2)there is a general upward trend Contribution to others 41 57 59 158 throughout the sample period until August 2008.Since then,the Contribution including own 93 103 104 52.5% financial crisis had a heavy influence on the entire world,with oil prices suddenly dropping and then gradually rising again;and 3)the price dif- ference between various oil markets has broadened in recent months. movements in spillovers.In addition,according to Du et al.(2010),the Table 1 provides summary statistics of crude oil returns in three structural stability tests indicate a structural break in China's oil VAR countries.As shown,the US has the lowest average oil returns and the model because of the reforms of China's oil pricing mechanism;there- largest standard deviations over the sample period.The US oil market fore,it is more appropriate to break the entire sample into different has positive skewness,indicating that it has undergone huge price sub-samples for the estimation of the model. hikes.The fluctuation of the Chinese Daqing price is less than that of To address this issue,we will estimate return spillovers using rolling international crude oil price. samples.Rolling window techniques are effective robustness test It is obvious that trading hours of various oil markets are different. methods (Swanson,1998).The paper employs a fixed rolling window We must consider this non-synchronous trading problem prior to technique,which indicates that after determining a sample size,the examining any further results.Such being the case,we use a simple start and end dates move forward at the same time.Let (x1....xT)be a method that is similar to the method of Cai et al.(2009)to solve this sequence of the stock returns.When using the Moving Window non-synchronous trading problem.The daily returns of the US and UK method,one makes T-w 1 sub samples (x -w+1.....x)for oil markets are lagged one day in estimation of the VAR model together =w.....T with sub sample size w.called a window width,and with the current volatilities of the Chinese Daging oil markets.In our then derives the spillover index value for each sub sample.A 250-day paper,we mainly present the empirical results with this adjustment (50-week)window is chosen for it is one calendar year,and we find and discuss the economic implications based on them that the fluctuations of return spillovers in the 100-day rolling sample are too strong for us to detect any meaningful patterns.We assess the extent and nature of spillover variations over time via the correspond- 3.2.The full-sample return spillover table ing time series of spillover indices. We calculate (H)in Eq.(6)with the full sample and obtain the results reported in Table 2.Its ijth entry is the estimated contributions 3.Data and empirical analysis of return spillovers to the forecast error variance of market i coming from innovations to market j.Therefore,the off-diagonal column sums(labeled contributions 3.1.Data to others)or row sums(labeled contributions from others),are the "to" and "from"directional spillovers,and the "from minus to"differences are The Daging oil field is the largest in China,and its crude oil output ac- the net directional volatility spillovers.Moreover,owing to row normal- counts for approximately 25%of national production.Because its price ization,the sum of the variances in a row is 100%.The last row in the basically represents the level of crude oil prices in China,the paper table represents the contribution to the volatilities of all markets from chooses Daqing crude oil spot prices as representative of the Chinese this particular market.The total return spillover index,which appears crude oil price.There currently are two major benchmarks for world in the lower right-hand corner of the table,is computed as the sum of oil prices:West Texas Intermediate (WTl)crude oil and Brent crude all variances in the 3 x 3 matrix minus the sum of the diagonal variances. oil.The sample period covers 12 years from December 27,2001 through The return spillover table may be viewed as the "input-output"decom- December 24,2013,and,after deleting non-match data,we have a total position of the total return spillover index. of 2871 observations.From the econometric point of view,12 years of In the ijth entry in the 3 x 3 matrix is the estimated contribution to daily data (a total of 2871 return observations)are long enough to the forecast error variance of market i resulting from innovations to 65 SPILLRETURNS 60 55 50 45 40 35 30 T1111111111111111111111111111 2003 2004”200520062007200820092010201120122013 time Spillover of all the market plot.Retums.50 week window.10 step horizon Fig.2.Total retumn spillovers of three oil markets(50-week windows)

movements in spillovers. In addition, according to Du et al. (2010), the structural stability tests indicate a structural break in China's oil VAR model because of the reforms of China's oil pricing mechanism; there￾fore, it is more appropriate to break the entire sample into different sub-samples for the estimation of the model. To address this issue, we will estimate return spillovers using rolling samples. Rolling window techniques are effective robustness test methods (Swanson, 1998). The paper employs a fixed rolling window technique, which indicates that after determining a sample size, the start and end dates move forward at the same time. Let (x1,…,xτ) be a sequence of the stock returns. When using the Moving Window method, one makes τ − w + 1 sub samples (xτ − w+1,…, xτ) for τ = w,…, τ with sub sample size w, called a window width, and then derives the spillover index value for each sub sample. A 250-day (50-week) window is chosen for it is one calendar year, and we find that the fluctuations of return spillovers in the 100-day rolling sample are too strong for us to detect any meaningful patterns. We assess the extent and nature of spillover variations over time via the correspond￾ing time series of spillover indices. 3. Data and empirical analysis of return spillovers 3.1. Data The Daqing oil field is the largest in China, and its crude oil output ac￾counts for approximately 25% of national production. Because its price basically represents the level of crude oil prices in China, the paper chooses Daqing crude oil spot prices as representative of the Chinese crude oil price. There currently are two major benchmarks for world oil prices: West Texas Intermediate (WTI) crude oil and Brent crude oil. The sample period covers 12 years from December 27, 2001 through December 24, 2013, and, after deleting non-match data, we have a total of 2871 observations. From the econometric point of view, 12 years of daily data (a total of 2871 return observations) are long enough to yield meaningful estimation results without a serious small sample bias issue. We focus on this recent 10-year history to make our study topical. We collect all the data from Wind database. Fig. 1 presents a graphical illustration of our data. As shown, there are three distinct characteristics: 1) the oil prices of WTI, Brent and Daqing are highly correlated; 2) there is a general upward trend throughout the sample period until August 2008. Since then, the financial crisis had a heavy influence on the entire world, with oil prices suddenly dropping and then gradually rising again; and 3) the price dif￾ference between various oil markets has broadened in recent months. Table 1 provides summary statistics of crude oil returns in three countries. As shown, the US has the lowest average oil returns and the largest standard deviations over the sample period. The US oil market has positive skewness, indicating that it has undergone huge price hikes. The fluctuation of the Chinese Daqing price is less than that of international crude oil price. It is obvious that trading hours of various oil markets are different. We must consider this non-synchronous trading problem prior to examining any further results. Such being the case, we use a simple method that is similar to the method of Cai et al. (2009) to solve this non-synchronous trading problem. The daily returns of the US and UK oil markets are lagged one day in estimation of the VAR model together with the current volatilities of the Chinese Daqing oil markets. In our paper, we mainly present the empirical results with this adjustment and discuss the economic implications based on them. 3.2. The full-sample return spillover table We calculate θij g (H) in Eq. (6) with the full sample and obtain the results reported in Table 2. Its ijth entry is the estimated contributions to the forecast error variance of market i coming from innovations to market j. Therefore, the off-diagonal column sums (labeled contributions to others) or row sums (labeled contributions from others), are the “to” and “from” directional spillovers, and the “from minus to” differences are the net directional volatility spillovers. Moreover, owing to row normal￾ization, the sum of the variances in a row is 100%. The last row in the table represents the contribution to the volatilities of all markets from this particular market. The total return spillover index, which appears in the lower right-hand corner of the table, is computed as the sum of all variances in the 3 × 3 matrix minus the sum of the diagonal variances. The return spillover table may be viewed as the “input–output” decom￾position of the total return spillover index. In the ijth entry in the 3 × 3 matrix is the estimated contribution to the forecast error variance of market i resulting from innovations to Table 4 Return spillover index of three oil markets after Dec 24, 2008. US CH UK From others US 51.7 23.2 25.1 48 CH 19.9 45.9 34.2 54 UK 21.6 33.5 44.8 55 Contribution to others 41 57 59 158 Contribution including own 93 103 104 52.5% Spillover of all the market plot. Returns. 50 week window. 10 step horizon time The spillover index (%) 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 30 35 40 45 50 55 60 65 SPILLRETURNS Fig. 2. Total return spillovers of three oil markets (50-week windows). 416 B. Zhang, P. Wang / Economic Modelling 42 (2014) 413–420

B.Zhang,P.Wang Economic Modelling 42 (2014)413-420 417 62.5 SPILLRETURNS 60.0 8 575 apu 55.0 52.5 JaAolllds 50.0 47.5 45.0 425 11111111111111111111111111111111111 2004 2005 2006 2007 2008 200920102011 2012 2013 time Spillover of all the market plot.Retums.100 week window.10 step horizon Fig.3.Total return spillovers of three oil markets (100-week windows). market j.For example,the element in row 2,column 3 is the volatility contribution of the Chinese oil market to other markets has increased contribution from the UK market to the variance of the China market from-7%to 3%. (23.2%).The sum of the variances in column 3 is the total contribution We inspect spillover variations over time via the corresponding time from the UK market to all other markets in terms of return spillover series of spillover indices,which are exhibited graphically in the total (47%).The total return spillover index is 50.1%.This finding indicates spillover plots of Figs.2 and 3. that in the full sample,approximately 50.1%of the forecast error variance is due to return spillovers among different markets. As Table 2 shows,we find that the oil market that affects others most 3.3.Rolling test results strongly is the US oil market;it is the most affected oil market as the same.The contribution of the Chinese oil market to other markets is 3.3.1.Spillover index The total return spillover among the three oil markets during the 51%,and the effect of the other markets on the Chinese market is 50% the net spillover index of Chinese Daging oil market is 1%,which sample period is presented in Fig.2(50-week window)and Fig.3 demonstrated that the Daging oil market is a weak influencer of (100-week window). international oil market returns.As mentioned before,the end of the We highlight some major events in these plots as follows: 2008 global financial crisis may strongly influence the link between 1.From 2003 to 2013,the spillover index changes from 31%to 63%in China and the world oil market,which should be considered carefully. the 250-day chart and from 42%to 61%in the 500-day chart,reveal- Therefore,we use December 24,2008 as a break point to separate the ing an overall upward trend in the spillover index among the three entire samples into two parts,the two sub-samples'return spillover markets. tables are shown in Tables 3 and 4,respectively.It may be observed 2.The second spike of the spillover index in October 2008 indicates the that the Chinese oil market's influence on the world has become more strong influence of the global financial crisis on the world oil markets. pronounced following the world financial crisis.The total spillover The period featuring the highest spillover index of the global oil 75 SPRLLRETURNS_CHO SPLLRETURNS_CH 50 25 olllds 25 1111111厂111111厂111111厂11 2003200420052006200720082009201020112012 2013 time net Spillover of CH plot.Retums.50 week window.10 step horizon Fig.4.Return spillovers between the Chinese and other oil markets

market j. For example, the element in row 2, column 3 is the volatility contribution from the UK market to the variance of the China market (23.2%). The sum of the variances in column 3 is the total contribution from the UK market to all other markets in terms of return spillover (47%). The total return spillover index is 50.1%. This finding indicates that in the full sample, approximately 50.1% of the forecast error variance is due to return spillovers among different markets. As Table 2 shows, we find that the oil market that affects others most strongly is the US oil market; it is the most affected oil market as the same. The contribution of the Chinese oil market to other markets is 51%, and the effect of the other markets on the Chinese market is 50%, the net spillover index of Chinese Daqing oil market is 1%, which demonstrated that the Daqing oil market is a weak influencer of international oil market returns. As mentioned before, the end of the 2008 global financial crisis may strongly influence the link between China and the world oil market, which should be considered carefully. Therefore, we use December 24, 2008 as a break point to separate the entire samples into two parts, the two sub-samples' return spillover tables are shown in Tables 3 and 4, respectively. It may be observed that the Chinese oil market's influence on the world has become more pronounced following the world financial crisis. The total spillover contribution of the Chinese oil market to other markets has increased from −7% to 3%. We inspect spillover variations over time via the corresponding time series of spillover indices, which are exhibited graphically in the total spillover plots of Figs. 2 and 3. 3.3. Rolling test results 3.3.1. Spillover index The total return spillover among the three oil markets during the sample period is presented in Fig. 2 (50-week window) and Fig. 3 (100-week window). We highlight some major events in these plots as follows: 1. From 2003 to 2013, the spillover index changes from 31% to 63% in the 250-day chart and from 42% to 61% in the 500-day chart, reveal￾ing an overall upward trend in the spillover index among the three markets. 2. The second spike of the spillover index in October 2008 indicates the strong influence of the global financial crisis on the world oil markets. The period featuring the highest spillover index of the global oil time The spillover index (%) 200 4 200 5 200 6 200 7 200 8 200 9 201 0 201 1 201 2 201 3 42.5 45.0 47.5 50.0 52.5 55.0 57.5 60.0 62.5 SPILLRETURNS Spillover of all the market plot. Returns. 100 week window. 10 step horizon Fig. 3. Total return spillovers of three oil markets (100-week windows). time The spillover index (%) 200 3 200 4 200 5 200 6 200 7 200 8 2009 201 0 2011 201 2 201 3 -25 0 25 50 75 net Spillover of CH plot. Returns. 50 week window. 10 step horizon SPILLRETURNS_CHO SPILLRETURNS_OTH SPILLRETURNS_CH Fig. 4. Return spillovers between the Chinese and other oil markets. B. Zhang, P. Wang / Economic Modelling 42 (2014) 413–420 417