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 variancesPetroleum 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