Leverage effect and dynamics correlation between international crude oil and China’s precious metals

Physica A 534 (2019) 122319

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Physica A journal homepage: www.elsevier.com/locate/physa

Leverage effect and dynamics correlation between international crude oil and China’s precious metals ∗

Yufeng Chen a,b,c , , Fang Qu a,c a

School of Economics, Zhejiang Gongshang University, Hangzhou, 310018, China College of Business Administration, Capital University of Economics and Business, Beijing, 100070, China c Center for Studies of Modern Business, Zhejiang Gongshang University, Hangzhou, 310018, China b

article

info

Article history: Received 12 April 2019 Received in revised form 28 May 2019 Available online 8 August 2019 Keywords: Dynamic correlation Precious metals Oil price Copula-DCC-GARCH Structural breaks

a b s t r a c t This paper examines the leverage effect and dynamic correlation between the international crude oil and China’s precious metals (gold, silver, and platinum) over the period 2006 to 2018. The model links the univariate volatilities with the dynamic correlations via combining Copula method and DCC model, which provide us with a way to analyze the multivariate joint distribution correlation while exploring the marginal distribution. The result indicates that the volatility of international crude oil and China’s precious metals has leverage effect. Specifically, gold and silver are more sensitive to good news, and crude oil is opposite of them, indicating that information shocks may have diverse asymmetric effects on the volatility of asset. Moreover, the dynamic correlation between international crude oil and China’s precious metals is generally positive, and when the financial and economic climate slowdown, there also be a negative correlation on them, which is confirmed by the test of structural break. © 2019 Elsevier B.V. All rights reserved.

1. Introduction In fact, some commodities such as oil and precious metals have long been a hot asset for portfolio investors, just like stocks and bonds. Based on this, many countries have actively promoted and established their own commodity trading markets in order to stabilize commodity prices and maintain financial security. In recent years, however, the volatility of commodity prices has drastically increased especially the crude oil and precious metals. This has led to extensive and unremitting studies by scholars from various countries on the impact of volatility both in crude oil prices and precious metals price on economy [1–6]. The reasons of this volatility are not only the impact of excess liquidity in the global capital, macroeconomic shock in supply and demand and seasonal demand adjustment, but also the production of speculative capital promotion after the financialization of commodities and the result of changes in spillover effect between markets in the context of financial globalization. After the financialization, commodities such as oil and precious metals have become an essential investment tool. The investment demand of financial capital has replaced the supply and demand of the real economy as the mainly impact factor of price fluctuation [7,8]. Especially in the context of financial globalization, the frequent trading of global financial capital has intensified commodity price volatility and even distorted the true relationship between supply and demand. Consequently, it is crucial for China to understand the investment value after financialization of commodities and to study the spillover effect and dynamic correlations between transnational markets after financial globalization, which plays a vital role to maintain economic security and financial stability. ∗ Correspondence to: No.18, Xuezheng Street, Jianggan District, Hangzhou, Zhejiang, 310018, China. E-mail address: [email protected] (Y. Chen). https://doi.org/10.1016/j.physa.2019.122319 0378-4371/© 2019 Elsevier B.V. All rights reserved.

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Y. Chen and F. Qu / Physica A 534 (2019) 122319

China is the central consumer and importer of commodities such as crude oil and precious metals. In 2017, China’s total crude oil importation ranked top in the world and the crude oil external dependence was 72.3%. According to the report from International Energy Agency (IEA), the crude oil external dependence in China will steady at 80% in 2040. In addition, China is also the largest gold producer in the world, accounting for 14% of global gold production in 2017, ranking top in the world for 11 consecutive years. China is still the unique gold consumer in the world, with gold consumption accounting for about 15% of the worlds in 2017. Consequently, the financialization and globalization on crude oil and China’s precious metals is an irresistible trend. In April 2001, China announced the abolition of the nearly 50-year-old system of unified procurement and allocation of gold. In October 2002, the Shanghai Gold Exchange (SGE) officially opened, which may indicate the beginning of the financialization of precious metals in China. However, it was not until March 26, 2018 that the crude oil futures in China were finally released on the Shanghai Futures Exchange (SFE). Prior to this, the China’s precious metals have been mainly affected by international crude oil due to the lack of crude oil trading market in China. It is well known that crude oil and precious metals are crucial strategic resources. In this sense, the volatility and the dynamic correlation of crude oil and precious metals have become pivotal reference indicators for financial crisis and even macroeconomic shock, and have caused economists and policymakers to pay great attention to it. Consequently, this paper will study the volatility of the respective prices of international crude oil and China’s precious metals from the perspective of empirical analysis, and explore their the spillover effects and dynamic correlation in the context of financial globalization. The study may help the stakeholder to further excavate the understanding of volatility and correlation after the financial globalization [9,10], and also have significant reference implication for market investment, financial reform, and energy economic security. Compared with the previous literature, the potential contributions of this paper are concentrated in the following aspects: Firstly, this paper employ a combination method of Copula and DCC to study the leverage effect (asymmetric effect of shock) of each series (oil, gold, silver and platinum) and from the perspective of the macro-economy to explore the dynamic correlation between international crude oil and China’s precious metals (oil–gold, oil–silver, oil–platinum). Thus, this combination method makes it possible to model the volatilities of each series (oil, gold, silver and platinum) using univariate GARCH models with different standardized residual distribution, which provide a greater flexibility in modeling and estimating the volatility and volatility spillover than while adopting the typical multivariate GARCH model. Secondly, the method proposed by Bai and Perron [11,12] is employed to investigate the structural breaks of dynamic correlation coefficient between international crude oil and China’s precious metals, rather than just using the time of occurrence of an economic event to speculate the fluctuation of correlation on the period. This paper is organized as follows. Section 2 provides the related literature and the comments. Section 3 describes the methodology. In Section 4, the data source and filters are explained. Section 5 is about empirical results and discussions. Finally, the conclusion in Section 6 has been shown. 2. Literature review Crude oil and precious metals are special commodities in which commodity attributes and financial attributes coexist. With the improvement of the financialization of commodities, financial attributes have become the foremost factors affecting price and volatility [13]. Thus, most of past studies of them can essentially be divided into two categories. The first category has been concerned with the volatility and information transmission between crude oil and precious metals. For example, Watkins [14] studied the volatility of the price of major metals (including gold, silver, aluminum, copper, lead, nickel, tin, zinc,) agricultural products (wheat) and two crude oil futures (WTI, Brent) between 1985 and 1994. They found the volatility of oil prices does not appear to be separated far from the volatilities of other commodities, and believed that the information transmission between commodities is relatively stable during this period. Baffes [13] is the most representative of the study. He researches the effect of crude oil on 35 internationally traded primary commodities prices and found evidence that crude oil has different information shocks to commodities and the precious metals reacted strongly to crude oil price from 1960 to 2005. Hammoudeh and Yuan [15] employed the GARCH-type model to believe the crude oil price as a determinant of the univariate volatility of three important metals (gold, silver and copper) in the US. They account for interest rate changes and the results indicate that gold and silver have similar volatility feature globally. Based on 40 years of data between 1968 and 2008, Shafiee and Topal [16] concluded that there is a fixed price-ratio correlation between gold and oil, although this ratio will fluctuation over time, the information shocks between them has not changed. Batten et al. [17] found that the volatility of precious metals is sensitive to macroeconomic shocks, but the sensitivity is quite different. They believe that the fluctuation of the macroeconomic can explained the volatility of gold, but it is not real to silver. Le and Chang [18] employ structural vector autoregressive (SVAR) approach to examine the impact of volatility of crude oil prices on gold market returns. They found that oil price was positively related to gold during the period 1994–2011. Moreover, Zhu et al. [19] believe that international crude oil prices played a vital role in the volatility of China’s precious metals, both in the long run and the short run. Recently, research results based on the autoregressive conditional jump intensity (ARJI) model have been shown that discrete jumps existed on the volatility of crude oil market, and the effect of this jump on precious metals was significantly negative [20]. The second category of research goes a step further by studying the mean and volatility spillover effects and dynamic correlations of precious metals, crude oil and other commodities. The significant spillover effect implies that the shock increases the correlation of returns not just in the own market but also in other market. Sari et al. [21] employed the

Y. Chen and F. Qu / Physica A 534 (2019) 122319

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ARDL model to examine the co-movements and spillover effects among the precious metals (gold, silver, platinum and palladium), the crude oil price and the spot price of the US dollar/euro exchange rate, and found evidence that the correlations in them are weak in the long run and stronger in the short run. Charlot and Marimoutou [22] also studied the volatility and dynamic correlation among exchange rates, stock indexes, crude oil prices and precious metal prices. Different from traditional econometric methods, they chose the Hidden Markov Decision Tree (HMDT) model. Their results shown that the correlation will increase in the bear market, while in other times the correlations are uncertain. It may indicate that the correlation may be related to the economic shocks. Meanwhile, Kang et al. [23] employed the multivariate DECO-GARCH model and constructed the spillover index to study the spillover effects among gold, silver, crude oil and some agricultural commodities (wheat and rice), and concluded that the correlation will increase sharply during the economic crisis. And the leverage effect caused by the asymmetry of information shock and risk is also the research focus. Tiwari and Sahadudheen [6] discussed the dynamic correlation between crude oil price and gold price from 1990 to 2013. Their study employed the EGARCH model and found that the impact of crude oil price on gold price is asymmetric, which means that positive and negative shocks of oil have different affects. Reboredo and Ugolini [24] reached a similar conclusion, they employed the Copula function to explain the asymmetric response of metal prices to oil price, and found the fact that spillover effect for upward oil price was larger than downward. In addition, according to recent research, the impact of macroeconomic shocks (global financial crisis, European sovereign debt crisis) and structural breaks on volatility is significant, which further implies that both volatility spillover effect and correlations persistently move together over time [10,25,26]. To sum up, the second category of research goes further on the basis of the first category of research, which is not only examining the volatility of a single series and the information transmission of them, but also considering the spillover effects and correlation between crude oil and precious metals. In some studies, the crude oil and precious metals were not discussed separately. Instead, they were considered as general commodities just as agricultural commodities, food, raw materials and exchange rates [13,14,23], and that, they were found to have similar price trend and volatility, and did not explain the crude oil and precious metals have special financial attributes in detail. Subsequently, many literatures focus on the crude oil and gold, less on other precious metals commodities, and believed that oil and gold are both important strategic materials and traded in US dollars, so there may be some correlation between them. Undoubtedly, these literatures make little of the particularities of other precious metal commodities [17,21], such as silver and platinum, and pay attention to the volatility of individual commodities [15,20]. With the improvement of modeling and estimation methods, the dynamic correlation and spillover effect between crude oil and precious metals has gradually become the hot topic of the discussion [21,22]. After that, some scholars maintain that the spillover effect may be asymmetric [6,24]. Nevertheless, the above literatures are mainly based on financial markets in developed countries, and there are relatively few studies on the facts of China [19,20]. In summary, both the feature on volatility of crude oil and precious metals themselves and the correlation between them should be given high attention. Meanwhile, from the perspective of research methods, most of the previous studies used financial time series methods (GARCH-type model, multivariate GARCH, SVAR, cointegration analysis and causality test) to explain the issues of volatility, spillover effects and correlations on crude oil [27,28] and other financial markets such as precious metal. Certain studies also employed other methods (Copula function, HMDT, spillover index and Quantile approach) to analyze such issues [29]. All of these research methods provide the powerful empirical support for subsequent research. 3. Methodology The volatility with the univariate GARCH of the returns shows the unique function of the asset, especially the leverage effect of volatility. When discussion the portfolio, it is necessary to consider the overall risk of the portfolio, which forces us to consider the volatility, spillover and correlation, and this correlation needs to be explored in combination with the volatility of individual asset returns. Many empirical researches have found that the correlation of financial time series is often time-varying, it called dynamic correlation. Multivariate GARCH (MGARCH) is a powerful weapon for studying the volatility and dynamic correlation, and its essence is modeling the conditional covariance matrix. The DCC model is a typical MGARCH method that allows the correlation matrix to be dynamic over time while retaining few parameters. Therefore, based on the DCC model proposed by Engle [30], combined with the Copula method, the volatility and dynamic correlation between the international crude oil price and China’s precious metal are investigated. Finally, the Bai and Perron test is used to further explore the impact of major economic events on the dynamic correlation. 3.1. The GJR-GARCH and DCC model The purpose of this paper is to examine the leverage effect and dynamic correlation between international crude oil and China’s precious metals through exploring current market trading activities. Firstly, the GJR-GARCH model is employed to discuss the leverage effect of international crude oil, gold, silver, and platinum, which indicates the asymmetric effect of asset price volatility and external information shocks. Secondly, this paper discussed the dynamic correlation between the international crude oil and the China’s precious metals in combination with the Copula method and the DCC model, since the Copula method can connect independent marginal distributions (regardless of correlation), which provide us with a way to analyze the multivariate joint distribution correlation while studying the marginal distribution. This method

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Y. Chen and F. Qu / Physica A 534 (2019) 122319

can not only study individual volatility feature, but also explore the dynamic correlation by combination the DCC model. Therefore, this combination method provides more individual information than only use the DCC model. To study individual volatility while get marginal distribution, the following GJR-GARCH(1,1) model is employed: ri,t = 100 × ln Pi,t /Pi,t −1

(

)

(1)

ri,t = µi + φi ri,t −1 + εi,t + ϕi εi,t −1 , i = 1, 2, . . . , k; t = 1, 2, . . . , T

(2)

εi,t =

(3)

hi,t ei,t , ei,t ∼ sstd (νi , λi )

√

+ βi hi,t −1 + f γ ε

hi,t = ωi + α ε

2 i i,t −1

(

2 i i,t −1

)

(εi,t −1 < 0)

(4)

√ ei,t = εi,t / hi,t

(5)

Eq. (2) is the mean equation of the returns series with autoregressive moving average (ARMA) process. µ, φ and ϕ denote the coefficients of the autoregressive (AR) and moving average (MA), respectively. Eqs. (3) and (5) show that standardized residuals with a skewed student-t distribution (sstd/SK-t). And in this study, we will consider diverse distributions for the residuals term ε (shock or innovation), including the normal, student-t and skewed student-t distribution. The reason for selecting the skewed student-t distribution in Table 3 is given. Eq. (4) is the variance equation, where f (•) is an indicator function, when εi,t −1 ⩽ 0, the f (•) = 1, else f (•) = 0. For sustaining stationarity of the volatility process to be guaranteed, coefficients are assumed to satisfy the following constraints, α > 0, β > 0, α + β + γ /2 < 1. γ represents a leverage effect or asymmetric effect, so when εi,t −1 > 0, it means good news or positive shock, and εi,t −1 ⩽ 0 means bad news or negative shock. The effect of good news on conditional variance is α , while the effect of bad news is α + γ . Therefore, when γ > 0, it can be considered as a leverage effect and increase the volatility, when γ < 0, the market price is more sensitive to positive news and has a higher level of response, when γ = 0, the model is reduced to a standard GARCH(1,1) model. Hence, Eqs. (2) to (5) constitutes the GJR-GARCH(1,1) model. So far, the leverage effect and volatility of each series can be examined. From Eqs. (2) to (5), the standardized residuals for each returns series can be calculated by GJR-GARCH(1,1) model. Therefore, the standardized residuals can be added into the following DCC model: Qt = qij,t , Q ∗ = diag qij,t

(

)

(

) ∗ −1

Rt = Qt

(

(

)

(6)

) ∗ −1

Qt Qt

(7)

where

)

(

(

qij,t = qij,t + a ei,t −1 ej,t −1 − qij,t + b qij,t −1 − qij,t

)

= (1 − a − b) qij,t + aei,t −1 ej,t −1 + bqij,t −1

(8)

In Eq. (8) the a and b are the coefficients of the DCC (1,1) model, satisfying a > 0, b > 0, a + b < 1, qij,t is the unconditional covariance matrix of standardized residuals ei,t and ej,t . Therefore, Qt represents the covariance matrix of the standardized residuals, the dimension (N × N ), the symmetric and positive definite. Finally, Rt represents the dynamic correlation coefficients matrix. 3.2. The Copula-DCC-GARCH model At present, the combination of Copula and GARCH-type model is widely employed in the analysis of financial time series [31–36]. In this(paper, in order to) combine the Copula method with the GARCH model, the)standardized residuals ( vector is assumed as e1,t , e2,t , . . . , eN ,t , and the joint distribution function of e1,t , e2,t , . . . , eN ,t is F , the joint density function is f , the marginal distribution functions are F1 , F2 , . . . FN , and the marginal density functions are f1 , f2 . . . fN , respectively. Hence, there is a multi-dimension Copula function C so that the following equation can be showed: F e1,t , e2,t , . . . , eN ,t = C F1 e1,t , F2 e2,t , . . . , FN eN ,t

(

)

( (

)

(

)

(

))

(9)

Assuming that the density function of the Copula function C is c, then the partial derivative of Eq. (9) is available: f e1,t , e2,t , . . . , eN ,t = c F1 e1,t , F2 e2,t , . . . , FN eN ,t

(

)

( (

)

(

)

(

))

×

N ∏ (

fi ei,t

)

(10)

i=1

There are about two types of Copula functions: static and time-varying Copulas. Static Copula function assumes that the dependence structure between parameters is time-invariant, so the time-varying dependence structure between international crude oil and China’s precious metals is employed by us, i.e., time-varying Copula function. However, there are many specific forms of the Copula function [37], and this article uses Normal-Copula, t-Copula, Frank-Copula, Gumbel-Copula and Clayton-Copula to estimate the dependence structure of international crude oil and China’s precious metals.

Y. Chen and F. Qu / Physica A 534 (2019) 122319

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Table 1 GOF test results of various Copula function. Gaussian

Student-t

Frank

Gumbel

Clayton

WTI-AU

LL GOF

7.287 0.0282

13.01 0.0533∗∗∗

8.685 0.0204

5.789 0.0624∗∗∗

3.042 0.1217∗∗∗

WTI-AG

LL GOF

11.90 0.0273

18.05 0.0591∗∗∗

10.62 0.0272∗

10.81 0.0665∗∗∗

7.02 0.1315∗∗∗

WTI-PT

LL GOF

14.59 0.0310∗

20.46 0.0512∗∗∗

12.42 0.0336∗

12.35 0.0636∗∗∗

7.65 0.1287∗∗∗

Notes: *, **, *** indicate statistical significance at the 10%, 5% and 1% level, respectively. LL denotes the LogLikelihood.

After estimating the Copula function, the Goodness-Of-Fit test (GOF) is required. The effective GOF test is based on the comparison between empirical Copula and the hypothesized Copula [38], and this method is based on measuring the squared euclidean distance between them. Hence, the smaller the GOF value, the better the model estimating effect where

√ GOF =

N (CN − C )

(11)

The CN indicates the corresponding empirical Copula, C is the hypothesized Copula, N is the number of marginal distribution functions. Table 1 shows the calculation results of GOF. The t-Copula has the best estimating effect on the condition of significant coefficients, and this empirical result is consistent with the studies of Kole et al. [39]. So, the t-Copula function is applied to explain new light on the dynamic correlation between international crude oil and China’s precious metals. Thus, the standardized residuals vector joint distribution function can be expressed as: F e1,t , e2,t , . . . , eN ,t = CRt ,v F1 e1,t , F2 e2,t , . . . , FN eN ,t

(

)

( (

)

(

)

(

))

(12)

where R denotes the correlation coefficient matrix of t-Copula, v is degree of freedom (DOF). To combine the t-Copula and the DCC-GARCH model, the dynamic correlation coefficient matrix Rt of the DCC-GARCH model is employed to replace the R matrix [36] in Eq. (12), as follows: F e1,t , e2,t , . . . , eN ,t = CRt t ,v F1 e1,t , F2 e2,t , . . . , FN eN ,t

(

)

( (

)

(

)

(

))

(13)

Finally, the Copula-DCC-GARCH model can be estimated by the following two-step methods are usually employed [33,35]. Step 1: this paper use the univariate GJR-GARCH) model to estimate the volatility of each returns series to ( obtain the standardized residuals vector e1,t , e2,t , . . . , eN ,t and maximum of marginal distribution ( likelihood estimate ) parameters for them. Step 2: transform the standardized residuals vector e1,t , e2,t , . . . , eN ,t into the uniform distribution vector of [0, 1] via a probability integral transform (PIT), and then estimate the dynamic correlation coefficient through the log-likelihood function of the Copula-DCC-GARCH model. Hence, the log-likelihood function of this model is defined as:

( ) T 1 Γ (v+N/2) Γ (v+1/2) v+N ∑ τt ′ R− t τt − NT log − log 1 + Γ (v/2) Γ (v/2) 2 v t =1 ( ) T T N ∑ τ2 v + 1 ∑∑ − log |Rt | + log 1 + it (14) 2 v t =1 t =1 i=1 ( ( ) ( ) ( )) where ut = F1 τ1,t , F2 τ2,t , . . . , FN τN ,t , the vector τt is the vector of the (transformed standardized ( ) ( )) residuals which depends on the copula specification. For the t-Copula it maintains that: τt = tv−1 τ1,t , . . . , tv−1 τN ,t , tv−1 is the inverse student-t distribution with ν DOF. Rt denotes the dynamic correlation coefficient matrix of τit (in the DCC model estimation, this paper replace eit in Eq. (8) to τit ). In general, two-step estimators provide computational tractability at LLt −Copula (Rt , v; ut ) = −T log

the expense of loss of efficiency. 3.3. Bai and Perron test In order to reveal in detail the linkage between the international crude oil and China’s precious metals, this paper uses the method proposed by Bai and Perron [11] to detect the structural breaks of dynamic correlation coefficient. The purpose of Bai and Perron test is to estimate whether there has been structural change in the way two or more time series are related over time. The specific method is as follows: Let yt be the dynamic correlation coefficient. Suppose yt has m variable structural breakpoints, so there are m + 1 phases. The linear regression equation can be defined as: yt = ci + ut , t = Ti−1 + 1, Ti−1 + 2, . . . , Ti

(15)

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Y. Chen and F. Qu / Physica A 534 (2019) 122319

Fig. 1. Daily spot price on WTI, AU, AG and PT from November 2006 to April 2018.

where, i = 1, 2, . . . , m + 1, ci is the mean of the dynamic correlation coefficient, and the value of variable structural breakpoints (T1 , T2 , . . . , Tm ) is unknown. Let T0 = 1, Tm+1 = T , T denote the observed number of) dynamic correlation ( coefficients, and the goal in this paper is to find the variable structural breakpoints T1∗ , T2∗ , . . . , Tm∗ so that: T1∗ , T2∗ , . . . , Tm∗ = arg min RSST (T1 , T2 , . . . , Tm )

(

)

T1 ,T2 ,...,Tm

(16)

Bai and Perron point out that M = 5 is sufficient in most economic empirical studies. Therefore, the number of maximum variable structural breakpoints is set to 5 in this paper. If the maximum number of variable structural breakpoints is equal to 5, it will adjust the maximum number of M. Finally, all possible variable structural breakpoints can be detected. More details on this test can be found in [11,12]. 4. Data description In general, precious metals refer to gold, silver and platinum group metals. Consequently, the dataset consists of the gold, silver and platinum commodities with the largest trading on the SGE, the market indices utilized are: AU(t + d)(AU), AG(t + d)(AG) and Pt9995(PT). Moreover, the NYMEX crude oil price (WTI) is used to represent international crude oil. Considering the availability of data while excluding data onto inconsistent transaction dates, the sample period was extended from November 2006 to April 2018. After eliminating the mismatching transaction days, we finally obtain 2687 log-returns for each series. The starting date of our analysis is November 2006 in order to include possible distortions in the linkage between crude oil price returns and commodity returns caused by the turbulence in financial markets occurred in the context of the Global Financial Crisis (GFC) during the second half of 2007. All data series have been collected from Wind Information Financial Database (Wind). Returns series were defined as Eq. (1), where Pi,t use the closing price for each series. Fig. 1 presents the tendency between WTI daily price and the AU, AG and PT daily price movements on the SGE. The indexes of AU, AG, PT, and WTI refer to different ranges. This article employs the price of WTI as the standardized range and converts the price index of AU, AG and PT into this range to explore their movement trends. From 2008 to 2009, the change of WTI oil price was relatively large. After 2009, the change slowed, and the shocks followed. Until 2014, the trend of it showed a downward trend. Both AG and PT had the same downward trend as WTI in 2008, but the downward trend of AU was not significant. This may indicate that there may be a substitution effect between gold and crude oil in financial markets. Fig. 2 presents the volatility cluster of the returns series. The volatility of returns series is great fluctuation during the GFC in 2008–2009 can be found, and the volatility cluster of returns to WTI is drastic, while AU, AG and PT are relatively stable. Table 2 shows the descriptive statistical properties of the returns series (WTI, AU, AG and PT). During the full sample period, the mean value of returns to AU, AG and WTI are positive, and AU had the highest value (0.0214%). Moreover, the PT had the negative mean value (−0.0128%), may suggest that investment in platinum during this period is not as good as other precious metals commodities. The widest gap between the maximum and minimum of the WTI series shows that the international crude oil price fluctuation most acutely during this period, which is consistent with the information shown in Fig. 2. While all returns series were skewed and had high values of the kurtosis statistic, only the WTI returns have skewness close to zero. Consequently, this fact may imply that there was a higher probability of a large decrease in returns with

Y. Chen and F. Qu / Physica A 534 (2019) 122319

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Fig. 2. Daily returns on WTI, AU, AG and PT from November 2006 to April 2018. Table 2 Descriptive statistics of returns. Mean Maximum Minimum Std.Dev Skewness Kurtosis Jarque–Bera ADF PP Q(20) Q2 (20) ARCH(20)

AU

AG

PT

WTI

0.0214 5.8503 −9.4959 1.0973 −0.5754 9.1632 4407.371∗∗∗ −52.349∗∗∗ −52.346∗∗∗ 44.5541∗∗∗ 681.3796∗∗∗ 236.654∗∗∗

0.0031 8.2518 −12.9242 1.7202 −0.5730 9.8546 5415.101∗∗∗ −50.716∗∗∗ −50.766∗∗∗ 30.4970∗ 581.2981∗∗∗ 266.316∗∗∗

−0.0128

0.0055 16.4087 −19.6625 2.5286 −0.0803 8.6537 3586.993∗∗∗ −55.770∗∗∗ −55.852∗∗∗ 59.2349∗∗∗ 2365.5349∗∗∗ 625.271∗∗∗

7.4097

−16.0028 1.4331

−0.8065 13.1235 11780.97∗∗∗ −52.089∗∗∗ −52.144∗∗∗ 52.3154∗∗∗ 837.7184∗∗∗ 321.543∗∗∗

Notes: The table displays summary statistics of daily returns over the period from November 2006 to April 2018. ARCH is the Lagrange Multiplier test for autoregressive conditional heteroscedasticity. *, **, *** indicate statistical significance at the 10%, 5% and 1% level, respectively.

the precious metals market, as suggested by the negative value of the AU, AG and PT skewness. Jarque–Bera tests statistic is based on skewness and kurtosis, which further examines the non-normality of the returns series. The article examines the stationarity of the returns series, since the mean value of each series very closing to zero, the Augmented Dickey– Fuller (ADF) test is employed that does not include the constant term and the time trend term. The results of ADF tests from Table 2 show that all series are stationary, and the Phillips and Perron (PP) test also proves this. The Ljung–Box statistics Q(20) and Q2 (20) indicate that AU, PT and WTI exhibit significant serial autocorrelation. Finally, the Lagrange Multiplier test statistics confirm the presence of significant ARCH effects in all returning series, thus supporting the use of the GARCH-type model. 5. Empirical results This paper first examines the leverage effect of each returns series (WTI, AU, AG and PT), and secondly employ the Copula-DCC-GARCH model to explore the spillover and dynamic correlation of international crude oil to the China’s precious metals. This is consistent with the interpretation of existing Copula-based multivariate GARCH models [33,35,36]. Finally, Bai and Perron test is used to analyze the structural breaks of dynamic correlation coefficients.

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Y. Chen and F. Qu / Physica A 534 (2019) 122319

Table 3 Comparison between GARCH and GJR-GARCH model. GARCH(1,1)

GJR-GARCH(1,1)

norm

std

sstd

norm

std

sstd

AU

LL AIC

−3759.374

−3639.498

−3637.568

−3759.343

−3637.166

−3635.287

2.8009

2.7124

2.7117

2.8016

2.7114

2.7108

AG

LL AIC

−4927.752

−4601.055

−4601.055

−4925.262

−4596.130

3.6709

3.4286

3.4294

3.6698

3.4257

−4596.129 3.4264

PT

LL AIC

−4381.952

−4298.315 3.2037

−4297.469 3.2035

−4381.159 3.2635

−4298.287

WTI

LL AIC

−5810.557

−5757.308 4.2889

−5752.343 4.2860

−5789.255 4.3127

−5747.278

3.2648 4.3278

3.2062 4.2822

−4297.461 3.2027 −5741.797 4.2789

Notes: LL denotes the LogLikelihood. Table 4 Result of estimation of ARMA-GJR-GARCH model.

µ φ ϕ ω α β γ λ υ α + β + γ /2

AU

AG

PT

0.0165 −0.0425∗∗∗ – 0.0064∗∗∗ 0.0580∗∗∗ 0.9495∗∗∗ −0.0231∗∗ 0.9507∗∗∗ 5.1090∗∗∗ 0.996

0.0121 – – 0.0485∗∗∗ 0.1328∗∗∗ 0.8957∗∗∗ −0.0589∗∗∗ 1.0010∗∗∗ 3.0800∗∗∗ 0.999

−0.0144

WTI 0.0069

0.8498∗∗∗ −0.8758∗∗∗ 0.0177∗∗∗ 0.0528∗∗∗ 0.9343∗∗∗ 0.0066 0.9655∗∗∗ 6.0911∗∗∗ 0.990

−0.8061∗∗∗ 0.7670∗∗∗ 0.0206∗∗ 0.0225∗∗ 0.9437∗∗∗ 0.0622∗∗∗ 0.9136∗∗∗ 8.1248∗∗∗ 0.997

Notes: *, **, *** indicate statistical significance at the 10%, 5% and 1% level, respectively.

5.1. Leverage effect of international crude oil and China’s precious metals In view of the non-normal distribution features such as fat tail, kurtosis, autocorrelation, and asymmetry in financial returns series. Consequently, the ARMA-GJR-GARCH model is employed to describe the returns series. By the Akaike Information Criterion (AIC), the optimal lag order of the mean equation can be found. Most financial studies indicate that the volatility in many financial markets is leveraged or asymmetric. The bad news of the same intensity is more volatile than good news, and there is a negative correlation between volatility caused by information shocks and risk transfer which is called leverage effect. It reflects an asymmetry effect come from instability of asset prices and information shocks and also mirrors the risk aversion of investors. This paper compared the estimating results of variance equation (GARCH(1,1) model and GJR-GARCH(1,1)) under different distribution (Normal, Student-t and Skewed Student-t), and selected the optimal model to estimate the returns series according to the LogLikelihood and AIC. The results in Table 3 show that for the AU, AG, PT and WTI, when the standardized residual follow the Skewed Student-t distribution, the AIC of the model is smaller and the log likelihood of the model is larger, so it can be found that the GJR-GARCH(1,1)-sstd model is the better of choice. Table 4 reports the estimation results of the univariate ARMA-GJR-GARCH(1,1) model, coefficients (φ , ϕ ) of the mean equation of the returns series are significant at the 1% level (As shown in Table 2, the AG has no autocorrelation, so its mean equation contains only constant terms µ). The coefficients (ω, α , β ) of the variance equation are all significant at both the 1% and 5% level, which indicate that all series has a significant GARCH effect. However, the leverage effect coefficient γ between the various returns shows diverse feature. Firstly, the leverage effect coefficient of AU is negative, which means that a bad news can only bring 0.0349 (α + γ in AU) times shock in short term. In other words, gold is more sensitive to good news. For silver the leverage effect similar to gold can be found. Secondly, bad news for WTI will bring a 0.0847 (α + γ in WTI) times shock, making the volatility increase, which means that the international crude oil is more sensitive to bad news. Therefore, it is easy to find there is a potential hedging function between international crude oil and China’s precious metals such as gold and silver. Finally, due to gold, silver and oil are widely used, but platinum is mostly used for decoration, so the investment value of gold and silver is higher than platinum. Therefore, the asymmetric effect (leverage effect) with platinum is not significant. In general, China’s precious metals can serve as hedge assets for international crude oil during this period (2006–2018) because of the diverse leverage effect. In this paper, the autocorrelation and heteroscedasticity tests are performed on the standardized residuals because there are specific requirements for standardized residuals employing the Copula function. The Kolmogorov–Smirnov (K– S) test is performed on the standardized residuals after the PIT. As shown in Table 5, the Ljung–Box Q statistics and the Lagrange Multiplier test denote that the standardized residuals with 10 lags of the series are not significant, which indicates that there is no serial autocorrelation and heteroscedasticity on standardized residuals. Consequently, the model

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Table 5 Test of standardized residuals on GJR-GARCH model. Q(10) ARCH(10) K–S

AU

AG

PT

WTI

13.3161 12.733 0.9745

4.1929 4.104 0.9893

5.8085 5.505 0.9985

12.8271 12.632 0.9824

Notes: This table presents the p-values of the Kolmogorov–Smirnov test. ARCH is the Lagrange Multiplier test for autoregressive conditional heteroscedasticity.

Fig. 3. Dynamic correlation between the WTI and China’s precious metals on AU, AG and PT.

of GJR-GARCH is efficient and appropriate. Using the K–S test, it can be judged whether the standardized residuals after the PIT follow the uniform distribution of [0, 1] so that the t-Copula function can be employed to explore the dependence structure and dynamic correlation. 5.2. Dynamic correlation between international crude oil and China’s precious metals China’s precious metal is affected by volatility in international crude oil, which is the reflection of the volatility spillover effect of international crude oil. From the perspective of dynamic correlation, the impact of volatility spillover effects can be intuitively understood. According to the Copula-DCC-GARCH model, dynamic correlations between the international crude oil and China’s precious metals in this marked are presented in Fig. 3. There is generally a stable positive correlation between them. It is because that the mean value of the correlation coefficients between international crude oil and China’s precious metals (gold, silver, and platinum) is positive, and a similar conclusion can be drawn from Table 6. The reasons for this positive correlation can be explained in terms of both commodity attributes and financial attributes of oil and precious metals. Firstly, oil and precious metals are important industrial raw materials from the perspective of commodity attributes, and in general they are complementary relationship, and one of the rising demands drives another demand to rise, which leads to an increase in prices. Secondly, in the financial market, oil and precious metals are substitutes for each other from the perspective of financial attributes and investment, when the price of oil rises, the returns rise, and the precious metals as an investment alternative for oil, the expectation of rising precious metals returns will also be raised, thus lead to precious metals investment growth. Their commodity attributes and financial attributes create this positive correlation together. However, these correlations show a negative feature in 2007 and 2009, and this negative correlation appeared more frequently after 2011, especially in 2014 and 2016. Specifically, the correlation between WTI and AU to increase in 2007 and 2008, but it rapid to decline in the early of 2009, and eventually it was negatively correlated, while AU and AG also

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Y. Chen and F. Qu / Physica A 534 (2019) 122319 Table 6 Descriptive statistics of dynamic correlation coefficients. Mean Maximum Minimum

WTI-AU

WTI-AG

WTI-PT

0.0719 0.3558 −0.2755

0.0957 0.3645 −0.1563

0.1074 0.3710 −0.1554

Table 7 Result of Bai and Perron test. Date and correlation corresponding to the structural breakpoints WTI-AU

Date Correlation

2009-03–30 0.1037

2011-06–14 0.0954

2013-03–01 0.0891

2015-08-03 0.0333

WTI-AG

Date Correlation

2009-06–01 0.3645

2011-07–11 0.0971

2013-04–03 0.2381

−0.0099

WTI-PT

Date Correlation

2009-06–01 0.2716

2011-02–15 −0.0981

2013-05–29 0.0782

2016-01-10 0.0828

2016-06-13

Table 8 Mean value of dynamic correlation coefficients on each phase. WTI-AU WTI-AG WTI-PT

Phase I

Phase II

Phase III

Phase IV

Phase V

0.0639 0.0872 0.1042

0.1237 0.1586 0.1640

0.0559 0.0736 0.1161

0.0753 0.0902 0.0731

0.0430 0.0655 0.0920

have the similar dynamic correlation. This negative correlation may be due to the sharp drop in international crude oil that occurred between July 2008 and early 2009, forcing investors to switch investing in other commodities, which led to the higher price of other commodities just like gold and silver. After May 2011, this negative correlation feature appeared more frequently. Meanwhile, WTI oil price has re-entered the upward channel since early 2009, and fell sharply again in August 2014. In fact, the negative correlation of international crude oil price after major economic events such as the GFC over 2007–2009, and the European sovereign debt crisis in 2011, which indicate the hedging function between crude oil and precious metals will emerge when the economic climate is uncertain. Consequently, the macroeconomic shock is one of the vital reasons for the negative correlation is believed. And the negative correlation can be seen as a sign that the precious metals financial attributes have increased, which may indicate that precious metals may be more investment value during this period. It can be seen that the transform of positive and negative in correlation is the reflection of the time-varying feature of the volatility spillover effects between international crude oil and China’s precious metals. 5.3. Bai and Perron test on dynamic correlation coefficient Here, this paper employs the Bai and Perron test [11,12] to explore how international crude oil and China’s precious metals are affected by macroeconomic shocks. As shown in Table 7, there are four structural breakpoints in the dynamic correlation coefficients between them (WTI-AU, WTI-AG, and WTI-PT). Most of the time the structural breakpoints occurred is concentrated in the years of 2009, 2011, 2013 and 2016. This is consistent with the times when the international crude oil has volatility. From Table 8 and Fig. 4, the evidence that after the GFC, the confidence of the financial market has increased and the dynamic correlation coefficient between them (WTI-AU, WTI-AG, and WTI-PT) has increased can be shown. Specifically, the mean value of the correlation coefficient of WTI-AU increased from 0.0872 in phase I to 0.1586 in phase II. After the European sovereign debt crisis in 2011, the mean value of the correlation coefficient fell again to 0.0736 in phase III. And the crisis in 2013 eased, the mean value of the correlation coefficient rebounds to 0.0902 in phase IV. The mean value of the correlation coefficients of WTI-AG, WTI-PT have the similar trends, which may indicates that the dynamic correlation between international crude oil and China’s precious metals will fluctuation with the uncertain of economic climate (macroeconomic shock), and when the economic situation is positive, the correlation will be stronger, and the economic situation is bad, the correlation will be weak. It is may be that when the economic situation for better, the hedging function between crude oil and precious metals may be weakened, which may be because both investment in crude oil or precious metals can bring similar returns. Hence, when there is bad news such as negative political events and economic deterioration, the hedging function of precious metals is extremely significant. In addition, it can be further found from Table 7 that the structural breaks of the dynamic correlation coefficient between WTI and AU occurs before WTI-AG and WTI-PT, indicating that international oil price will affect gold first, and further affect the correlation. This means that within the precious metals market, gold price may be as guiding as wind vanes, while silver and platinum may be subordinate.

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Fig. 4. Dynamic correlation coefficients with structural breaks.

6. Conclusion The study employ the GJR-GARCH model to discuss the leverage effect of each returns series of international crude oil, gold, silver and platinum, which indicates the asymmetry effect of volatility on asset price and external information shocks. Secondly, based on the Copula-DCC-GARCH model, the dynamic correlation between international crude oil and China’s precious metals are studied, and the reasons of fluctuation for this dynamic correlation are discussed. Finally, Bai and Perron test is employed to explore the structural breaks of dynamic correlation coefficients. The study found that (1) both the volatility of international crude oil and China’s precious metals have leverage effect (asymmetric effect), but their feature of leverage effects is divergent. Gold and silver are more sensitive to good news, while the crude oil is sensitive to bad news. (2) The positive dynamic correlation between international crude oil and China’s precious metals has been found, and this positive correlation has not continued to increase. (3) There is also a negative correlation between crude oil and China’s precious metals, and the occurrence of the negative correlations is closely related to the macroeconomic shock, which has been proved from Bai and Perron test. That is to say, when the economic climate is improving, the correlation will be stronger. Oppositely, the correlation will be weakened or even become negative. In other words, from the perspective of financial markets, there is a substitution relationship between crude oil and China’s precious metals only when the economy in a downturn. Within the precious metals market in China, gold price has a guiding function, and other precious metals (silver, platinum) are subordinate. These conclusions further excavate the understanding of financialization of commodities and financial globalization. The crude oil and precious metals are vital strategic resources, so they may have special investment value and functions such as leverage effect. And the fluctuation of correlations between crude oil and precious metals are still closely related to the actual economic climate [8]. The correlation of international commodities markets (agricultural, metals and fossil energy) are becoming more integrated due to financial globalization [40,41]. This has prompted a large amount of financial capital to intervene in the commodity market, exacerbating the volatility between different categories of commodities, which has led to special effects such as the leverage effect of crude oil and gold, and the price leadership of gold within the precious metals market. In the volatility of commodity prices such as crude oil and gold, the China demand factor cannot be ignored. In particular, it is worth noting that, in the context of the pricing of most commodities dominated by overseas markets, although China is an important consumer of commodities such as crude oil and gold, but the loss of the pricing power of the commodity is caused by the lack of some commodity trading markets and insufficient financialization. Eventually, the international speculators will have a potential impact on the Chinese economy through domestic and international market linkages. Only when China has established and perfected its own commodity markets (e.g. oil and precious metals) can blunt this affect. At present, the pace of financial reform and innovation in China is accelerating. More commodities are being released into relevant financial markets such as crude oil futures that began trading in March, 2018 on Shanghai Futures Exchange,

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Y. Chen and F. Qu / Physica A 534 (2019) 122319

which indicates the increasing financialization trend of China’s commodities. Exploring the leverage effect and dynamic correlation between international crude oil and precious metals in China is beneficial to further explore the doubleedged sword features come from the China’s commodity financialization. On the one hard, it will vigorously promote the development of futures, options and other commodity derivatives markets and help the pricing power competition, achieving positive interaction between China’s demand factors and the volatility of commodity prices, avoiding the potential adverse effects of financialization of commodity and financial globalization. On the other hand, it is necessary to strengthen supervision to prevent excessive speculative funds from entering the commodity market and avoid excessive financialization of commodities. 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