Price Influence and Volatility Risk Transmission of NonFerrous Metals Futures: Situation in China ()
1. Introduction
As an important industrial raw material, nonferrous metals play an important role in the development of the national economy, and in recent decades, the development of the nonferrous metal industry has strongly promoted the rapid development of China’s economy.
With the establishment and development of China’s futures market, nonferrous metal futures have been launched on the Shanghai Futures Exchange (SHFE), and copper and aluminum futures, as the earliest futures varieties of nonferrous metal futures, were listed and traded on the Shanghai Metal Futures Exchange, the predecessor of the Shanghai Futures Exchange, in 1993. Subsequently, the third nonferrous metal futures product, zinc futures, was listed on the Shanghai Futures Exchange on March 26, 2007. The fourth nonferrous metal futures product, lead futures, was listed on the Shanghai Futures Exchange on March 24, 2011. The fifth and sixth varieties of nonferrous metal futures, nickel and tin futures, were listed and traded on the Shanghai Futures Exchange on March 27, 2015, so far, the Shanghai Futures Exchange has listed six basic futures varieties of nonferrous metals. With the development of the internationalization of the futures market, the Shanghai International Energy Exchange, a subsidiary of the Shanghai Futures Exchange, launched the first international copper futures variety of domestic nonferrous metals on November 19, 2020. The Shanghai Futures Exchange has made strict designs for nonferrous metal futures in terms of trading, delivery and risk control, and has continuously optimized various rules and systems with the development of the market, which has effectively guaranteed the healthy development of the nonferrous metal futures market.
Since the launch of the nonferrous metal futures market, the market has been running steadily, and the nonferrous metal futures varieties have shown different activity, and the following nonferrous metal futures six varieties of trend chart can be seen that before 2015, the turnover of copper and zinc futures was outstanding, and after 2015, after the launch of nickel futures, the turnover of nickel once exceeded the turnover of copper and zinc, and after 2020, copper, nickel, zinc, aluminum, and tin performed well, and the turnover of lead was at the bottom (Figure 1).
After years of development, the nonferrous metal futures market has become
Source: Shanghai futures exchange website.
Figure 1. Trend chart of the turnover of six nonferrous metal futures varieties.
the most mature futures market in the domestic futures market, and the futures market has achieved remarkable results in serving entity enterprises, and most of the domestic nonferrous metal enterprises have participated in the hedging of the nonferrous metal futures market. The price of nonferrous metal futures has a certain international influence, and the healthy development of the nonferrous metal industry has laid a solid foundation for the international pricing power of nonferrous metal futures. Further research on the discovery function of nonferrous metal futures prices, the influence of international pricing and the transmission of volatility risks, provide theoretical support for the further development of the nonferrous metal futures market, and provide technical support for market participants, so as to further promote the healthy development of the nonferrous metal industry.
The article is organized as follows: Part I: Introduction. Part II: Literature Review. Part III: research methods and models; Part IV: Empirical Analysis; Part V: Conclusions.
2. Literature Review
There is a lot of research literature on nonferrous metal futures, and in recent years, there have been many studies on the price discovery, price influence and volatility of the nonferrous metal futures market in China.
2.1. Domestic Literatures on the Relationship between NonFerrous Metal Futures and Spot Prices and the Price Discovery Function
For example, Zhang and Liu (2006) found that there is a longterm equilibrium relationship between aluminum and copper futures prices and spot prices in China. Wang et al. (2011) found that the futures prices of copper, aluminum, and zinc listed on the Shanghai Futures Exchange can guide the spot price, and the futures market is in a dominant position in price discovery and has a stronger ability than the spot market. Xu and Li (2012) found that there is a significant twoway price guidance relationship between China’s metal futures and spot market by using the information transfer effect model and the GS model. Yu (2018) used the Johansen cointegration test and wavelet coherence analysis method to study the correlation between the prices and spot prices of six nonferrous metal futures traded on the Shanghai Futures Exchange of copper, aluminum, zinc, nickel, lead and tin, and analyzed their leading relationship in the timefrequency domain. The results show that, except for aluminum, there is a cointegration relationship between the futures prices and spot prices of the other five nonferrous metals. The futures prices of the six nonferrous metals, including aluminum, can guide the spot prices to a certain extent, but the price discovery efficiency of copper and nickel futures is higher, followed by the price discovery efficiency of lead, tin and zinc futures, and the price discovery efficiency of aluminum futures is significantly lower than that of the other five nonferrous metals. Li (2018) studied the guiding relationship between the spot prices of copper, aluminum, zinc, lead, nickel and tin in China’s nonferrous metal market through the vector error correction model. The results show that the spot prices of copper, zinc, lead, nickel and tin guide each other, and the price of aluminum futures guides the changes of spot prices in one direction. Song and Xing (2020) used the GARCH family model and the state space model to explore the various functions of the domestic copper futures spot market, and concluded that domestic copper futures have a strong price discovery function, a good hedging function, and a strong volatility spillover to the spot market. Wang and Yu (2021) established the Vector error correction model (VECM) and studied the relationship between domestic copper futures and spot prices, and concluded that there is a longterm cointegration relationship between the two, and the price guidance of futures is more advantageous, but on the whole, the copper price discovery function in China is not efficient. Jiang (2022) studied the linkage relationship between the spot prices of nonferrous metals in China based on the VAR model, and explored the longterm equilibrium relationship and price guidance relationship between the domestic copper spot, aluminum spot, zinc spot, lead spot, nickel spot, and tin spot prices.
2.2. Domestic Literatures on the Relationship between Domestic and Foreign Futures Prices and Volatility Spillover of NonFerrous Metals
For example, Zhou et al. (2012) conducted a study on the copper futures varieties in domestic metal futures trading, analyzed the spillover of domestic aluminum futures and foreign London copper futures on the research object, and found that domestic copper futures are more likely to be affected by London copper futures, while although there is a twoway spillover between domestic copper futures and aluminum futures, the spillover of copper futures is significantly stronger. Wang and Shao (2012) used the twostate threshold vector error correction model to study the longterm equilibrium relationship and shortterm dynamic adjustment mechanism of Chinese and international nonferrous metal futures prices in different states, and found that there is a significant threshold cointegration relationship between copper and aluminum futures on the London Futures Exchange and the Shanghai Futures Exchange, and the adjustment strength of Chinese and international nonferrous metal futures prices to the longterm equilibrium state is asymmetrical. Shen and He (2014) used an independent component analysis method to study the risk spillovers of three different futures varieties between domestic and foreign futures markets, and found that there were significant differences in the risk spillover intensity of major futures products at home and abroad before and after the outbreak of the financial crisis. Xu and Wang (2014) constructed the VAR model and GS model to study the price guidance relationship of the domestic copper futures and spot market and concluded that the domestic copper futures market is weak and effective. And it is believed that the Shanghai copper and London copper futures markets affect each other, but the impact of London copper on the price change of Shanghai copper is more significant. Jiang and Shen (2015) analyzed the correlation between China and the international futures market and the price discovery function by using cointegration theory, VECM and various price discovery models. The study concludes that there is a longterm equilibrium relationship between China and international copper, aluminum and zinc futures prices. The London market has a strong guiding role in the Shanghai market, has a strong impact on the prices of copper, aluminum and zinc in the Shanghai market, and has a weak impact on Shanghai lead. LME has a larger market share, and SHFE has a stronger price discovery function for aluminum and zinc. Liu et al. (2018) examined the degree of spillover between the London copper and Shanghai copper futures markets, and the results showed that there was a positive mutual spillover effect between the London copper and Shanghai copper futures markets. Li (2018) found that there is a longterm equilibrium relationship between the Shanghai and London metal futures markets through the Granger causality test. There will also be crossinfluences and transmission effects between different metal futures commodity markets. Liu (2022) starts from the perspective of price discovery function and fluctuation spillover effect, verifies the effectiveness of the domestic pricing center and the influence of international pricing power in China’s copper futures market. The model analysis results of the longterm market show that there is an obvious Autoregressive Conditional Heteroskedasticity (ARCH) effect and a strong GARCH effect between the LME and SHFE copper markets, and the price formation process of the two markets is independent, and there are shock spillover effects and fluctuation spillover effects between them, and the overall trend is closely linked. The results of shortterm data construction model show that there is only a oneway fluctuation spillover from SHFE to LME, and there is no fluctuation spillover from LME to SHFE.
2.3. Foreign Literatures on the Relationship between NonFerrous Metal Futures and Spot Prices, Price Discovery and Volatility Spillover Effects
For example, Liu and Wang (2014) selected the 3month contract, 15month contract and 27month futures contract of the main nonferrous metals of copper, aluminum, zinc and nickel in the LME to crosscorrelate with their spot prices, and verified the interaction between spot yield and volatility through the VECM model and the binary BEKKGARCH model. It is concluded that the volatility spillover effect has a significant effect on the nonlinear correlation of spot prices. Yue et al. (2015) used the VARDCCGARCH model to study the relationship between China’s nonferrous metal market price and London metal futures price, and found that there is a linkage between the London futures market price and the Chinese nonferrous metal market price, and the LME nonferrous metal price still has a great impact on China’s nonferrous metal price. However, with the exception of lead, the impact of Chinese nonferrous metal prices on LME nonferrous metal prices is still weak. Fernandez (2016) studied the correlation between spot and futures prices for aluminium, copper, lead, nickel, tin, and zinc on the London Metal Exchange. Isabel FiguerolaFerretti and Gonzalo (2016) analyzed the correlation between the spot prices and futures prices of LME copper and other base metals from January 1989 to October 2006, verified the effectiveness of the longterm equilibrium and shortterm correction of the futures market through cointegration relationship and nonlinear VECM model, and analyzed the quantitative level of price contribution between the futures and spot prices by using PT decomposition. It is concluded that there is an effective price spillover from the futures market to the spot market, and the effectiveness of the price discovery function is verified. Kang et al. (2017), Kang & Yoon’s (2019) study found that LME nonferrous metal futures have a greater impact on SHFE nonferrous metal futures. Shi et al. (2018) conducted an indepth study of the relationship between China’s copper and aluminum futures markets by using a volatility decomposition method. Kang et al. (2017) used the weekly data of LME and SHFE copper, aluminum, and zinc varieties to construct a volatility aggregation analysis of time series, and found that the longterm (more than 64 weeks) linkage phenomenon was significant, while the shortterm (less than 16 weeks) showed a weak or even negative correlation, arguing that the shortterm deviation was caused by shortterm investors’ diversification in order to reduce risk, and the longterm LME market still dominated. Sang Hoon Kang and Yoon (2019) used the prices of four futures products, including the CSI 300 Index and the Shanghai Futures Exchange Copper from April 2005 to March 2019, and discussed the transmission direction and intensity of yield and volatility spillovers during the global financial crisis and the European debt crisis through the multivariate DECOGARCH model and the spillover index model, and concluded that there is a longterm and obvious positive correlation between the CSI 300 Index and commodity futures in the postfinancial crisis period, the spillover effects of returns and volatility between markets are more significant.
To sum up, a large number of studies at home and abroad on relationship of nonferrous metal futures and spot prices, the relationship between domestic and foreign prices and the relationship between fluctuation spillovers are mainly focused on some nonferrous metal futures and spot varieties, and the price influence of nonferrous metal futures copper, aluminum, zinc, lead, nickel and tin and the volatility risk transmission of all varieties of nonferrous metal futures at home and abroad are still relatively lacking. Conduct a comprehensive study on the price discovery and international influence of nonferrous metal futures and the transmission of volatility risks, hoping to obtain valuable conclusions and provide valuable suggestions for the development of the nonferrous metal futures market.
3. Research Methods and Models
3.1. Cointegration Test and ECM Model of Domestic and Foreign NonFerrous Metal Futures Price Yields
If it can be inferred that the logarithmic series of domestic and foreign nonferrous metal futures prices is a firstorder single integer, the possible cointegration relationship between them can be further analyzed. The stable sequence of domestic and foreign nonferrous metals (copper, aluminum, zinc, lead, nickel, tin) futures prices and yields is as follows: ${R}_{11t}$
, ${R}_{12t}$
, ${R}_{13t}$
, ${R}_{14t}$
, ${R}_{15t}$
, ${R}_{16t}$
, ${R}_{21t}$
, ${R}_{22t}$
, ${R}_{23t}$
, ${R}_{24t}$
, ${R}_{25t}$
, ${R}_{26t}$
, The binary error correction model (ECM)can be expressed as:
$\begin{array}{c}{R}_{1jt}={\gamma}_{j}\left(LN{P}_{1jt1}{\beta}_{i}LN{P}_{2jt1}+C\right)+{\alpha}_{1}{R}_{1jt1}+{\alpha}_{2}{R}_{1jt2}\\ \text{\hspace{0.17em}}+{\varphi}_{j1}{R}_{2jt1}+{\varphi}_{j2}{R}_{2jt2}+{\epsilon}_{jt}\end{array}$
(1)
${\gamma}_{j}$
is the adjustment parameter for error correction. ${\epsilon}_{jt}$
is the uncorrelated white noise error sequence, where J = 1, 2, 3, 4, 5, 6. If the above ECM model is true, it shows that the price yield of nonferrous metal futures at home and abroad is affected by the same error correction process, but with different adjustment speeds, and the return to longterm equilibrium has a common trend component and similar cycle characteristics, which may lead to different shortterm fluctuation patterns due to the different error correction coefficients. In ECM, the longterm correction relationship can be expressed as follows:
$LN{P}_{\text{1j}t}{\beta}_{j}LN{P}_{2jt}+C={u}_{jt}$
(2)
where ${u}_{jt}$
is a stationary time series of zero mean, j = 1, 2, 3, 4, 5, 6. The above relationship represents the cointegration relationship between domestic nonferrous metal futures prices (copper, aluminum, zinc, lead, nickel, tin) and foreign nonferrous metal futures prices (copper, aluminum, zinc, lead, nickel, tin), and the standardized cointegration vectors are ${\left(1,{\beta}_{j}\right)}^{\prime}$
.
There are many methods for testing and estimating cointegration relations, including the Engle and Granger (1987) twostep method and Johansen (1988) maximum likelihood method (MLE), and the Johansen test is superior to the Engle & Granger method for multivariate cointegration tests. In this paper, the Johansen test is used. According to Engle and Granger (1987) expression theorem, there are three equivalent expressions of cointegration systems: vector autoregressive VAR, moving average MA and ECM, among which ECM can best describe the synthesis of shortterm fluctuations and longterm equilibrium, and is the most widely used. Engle and Granger (1987) demonstrated that cointegration sequences can necessarily be represented as errorcorrected representations. Therefore, when the variable sequence is cointegrated, an error correction model should be established.
3.2. GARCHM Model of Domestic and Foreign NonFerrous Metal Futures Price Returns
The Autoregressive conditional heteroskedasticity model (ARCH) can effectively characterize the volatility of risk and return, and make these volatility and risk measures timevarying in nature, reflecting the dynamic impact of new information acquisition and new shocks. Engle (1982) proposed the Generalized Autoregressive Conditional Heteroskedasticity (GARCH)model, which can be generalized to allow the conditional variance to have an impact on the rate of return, therefore, the GARCHM (p, q) model of the futures price yield of nonferrous metals (copper, aluminum, zinc, lead, nickel, tin) at home and abroad is set as follows:
${R}_{t}=\alpha +\lambda {\sigma}_{t}^{2}+{\displaystyle \sum _{i=1}^{m}{\theta}_{i}}{R}_{ti}+{\displaystyle \sum _{j=1}^{n}{\eta}_{j}}{\epsilon}_{tj}$
(3)
Among them, ${R}_{t}$
is the futures price yield of nonferrous metals (copper, aluminum, zinc, lead, nickel, tin) at home and abroad. ${\sigma}_{t}^{2}$
is the conditional variance, $\epsilon $
is the residual, and $\lambda $
, $\theta $
, $\eta $
are the parameter. When the risk (volatility) increases, the return level of the domestic and foreign nonferrous metal futures markets increases, and the coefficient of the corresponding conditional variance in the equation $\lambda >0$
. When the risk increases and the return level of the domestic and foreign nonferrous metal futures markets decreases, the corresponding conditional variance coefficient $\lambda <0$
3.3. Asymmetric Leverage Effect Model of Domestic and Foreign NonFerrous Metal Futures Price Returns
The leverage effect reflects the unidirectionality of volatility conduction, or a certain degree of risk attitude difference, and the leverage effect can be achieved by introducing a certain asymmetry into the GARCH model, or it can be achieved through threshold regression, which is called the Threshold Autoregressive Conditional Heteroskedasticity Model (TARCH) model at this time. The TARCH or Threshold ARCH model was independently introduced by Zakoian (1994) and Glosten et al. (1993). The variance equation for the price returns of domestic and foreign nonferrous metals (copper, aluminum, zinc, lead, and nickel, tin) futures is set as:
${\sigma}_{t}^{2}=\beta +{\displaystyle \sum _{i=1}^{q}{\varphi}_{i}}{\epsilon}_{ti}^{2}+{\displaystyle \sum _{j=1}^{p}{\phi}_{j}}{\sigma}_{tj}^{2}+\omega {D}_{t1}{\epsilon}_{t1}^{2}$
(4)
${D}_{t1}$
is dummy variable that represents the direction of change in the absolute residuals,if ${\epsilon}_{t1}<0$
, then ${D}_{t1}=1$
.otherwise,${D}_{t1}=0$
. In the model, good news $\left({\epsilon}_{t1}>0\right)$
and bad news $\left({\epsilon}_{t1}<0\right)$
have different effects on conditional variance, good news has one $\sum {\varphi}_{i}$
shock, the bad news has a $\sum {\varphi}_{i}}+\omega $
shock. If $\omega \ne 0$
, the information is asymmetrical, if $\omega >0$
, there is a leverage effect, the main effect of the asymmetric effect is to make the fluctuation increase, if $\omega <0$
, the main effect of the asymmetric effect is to make the fluctuation decrease.
Due to the asymmetry of market fluctuations and reactions, there are a variety of structural forms and representations, and there are also some generalized forms of GARCH model, such as Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) Model, which are widely used. According to the EGARCH model proposed by Nelson (1991), we set the conditional variance equation for the price return of domestic and foreign nonferrous metals (copper, aluminum, zinc, lead, nickel, tin) futures as follows:
$\mathrm{ln}{\sigma}_{t}^{2}=\omega +\beta \mathrm{ln}{\sigma}_{t1}^{2}+\alpha \left\frac{{\epsilon}_{t1}}{{\sigma}_{t1}}\right+\gamma \frac{{\epsilon}_{t1}}{{\sigma}_{t1}}$
(5)
If $\gamma <0$
, Bullish and bearish news have different impacts, the bullish news has an $\alpha \gamma $
impact on the shock, bearish news has an $\alpha +\gamma $
impact on the shock, if $\gamma \ne 0$
, Then there is asymmetry in the shock reaction, then,
$f\left(\frac{{\epsilon}_{t}}{{\sigma}_{t}}\right)=\alpha \left\frac{{\epsilon}_{t1}}{{\sigma}_{t1}}\right+\gamma \frac{{\epsilon}_{t1}}{{\sigma}_{t1}}$
(6)
$f(\u2022)$
is the information impact curve.
3.4. Volatility Spillover Effect Model of Domestic and Foreign NonFerrous Metal Futures Prices Yields
When there is a large fluctuation in the foreign (domestic) nonferrous metal futures market, it will cause investors to change their investment behavior in the domestic (foreign) nonferrous metal futures market, and transmit this fluctuation to other futures markets, that is, the “spillover effect” of the nonferrous metal futures market. In order to describe the correlation between the volatility of domestic and foreign nonferrous metal futures markets, we use the volatility spillover model proposed by Hamao et al. (1990) to analyze the shortterm dependence and interaction between the volatility of domestic and foreign nonferrous metal futures markets, then,
${\sigma}_{At}^{2}=\beta +{\displaystyle \sum _{i=1}^{q}{\varphi}_{i}}{\epsilon}_{Ati}^{2}+{\displaystyle \sum _{j=1}^{p}{\phi}_{j}}{\sigma}_{Atj}^{2}+{\displaystyle \sum _{l=1}^{r}{\varsigma}_{l}{\epsilon}_{Btl}^{2}}$
(7)
${\epsilon}_{Btl}^{2}$
means that the yield shock or disturbance in market B in the previous L period is the absolute volatility degree that has been realized in reality, and if the coefficient of these perturbation terms is statistically significantly positive, it indicates that there is a significant spillover effect.
4. Empirical Analysis
4.1. Variable and Data
4.1.1. Variable Selection
At present, the main varieties of nonferrous metal commodity futures listed in China are copper, aluminum, zinc, lead, nickel, tin, alumina and international copper, etc., according to the needs of research, we select the basic varieties of nonferrous metal futures copper, aluminum, zinc, lead, nickel, tin futures, therefore, we select the domestic and foreign basic nonferrous metal futures prices and the domestic spot prices of the corresponding varieties as research variables.
The domestic nonferrous metal commodity futures prices are selected as the research targets of copper, aluminum, zinc, lead, nickel and tin futures listed on the Shanghai Futures Exchange. The futures prices of foreign nonferrous metal commodities are selected as the research targets of copper, aluminum, zinc, lead, nickel and tin futures prices with 3month expiring’s on the LME in London, United Kingdom. The spot prices of domestic nonferrous metals are selected as the average spot prices of copper, aluminum, zinc, lead, nickel and tin in the domestic nonferrous metals market as the research objects.
4.1.2. Data
Due to the existence of different holidays at home and abroad, such as “May Day”, “Eleventh”, Spring Festival and other holidays in China, and Christmas and other holidays abroad, the data does not match part of the time, and the mismatched data will be deleted in the specific processing process. In addition, the moving average method is used to make up for the missing data.
In order to eliminate the possibility of heteroskedasticity in the data, we use a logarithmic processing method for the selected data. Data source: Shanghai Futures Exchange website, Wind information terminal.
We define the nonferrous metal futures price yield ${R}_{t}$
as the firstorder difference of the logarithm of the nonferrous metal futures price, then
${R}_{t}=LN{P}_{t}LN{P}_{t1}$
(8)
${P}_{t}$
is the price of nonferrous metal futures. When the price fluctuation of nonferrous metal futures is not very drastic, it is approximately equal to the daily rate of change of nonferrous metal futures price, corresponding to the overall income level of the nonferrous metal futures market.
Since there is no unified qualitative conclusion on the statistical nature of the nonferrous metal futures price yield series, there are still different views on whether the nonferrous metal futures price yield is strong, weakly effective, or invalid, therefore, we investigate the changes in the daily rate of return series ${R}_{t}$
, absolute daily rate of return series $\left{R}_{t}\right$
and daily average square rate of return series ${R}_{t}^{2}$
of nonferrous metal futures prices. When the sample size is relatively large, according to the large number theorem and the weak effective market, it can be seen that the average price return of the overall nonferrous metal futures in the sample interval is as follows:
${\overline{R}}_{t}=\frac{1}{T}{\displaystyle \sum _{t=1}^{T}{R}_{t}}\approx 0$
(9)
where T is the sample size. Assuming that the deviation of the daily return of the nonferrous metal futures price from the sample mean is described as ${\epsilon}_{t}$
, then,
${\epsilon}_{t}={R}_{t}{\overline{R}}_{t}\approx {R}_{t}$
(10)
$\left{\epsilon}_{t}\right=\left{R}_{t}{\overline{R}}_{t}\right\approx \left{R}_{t}\right$
(11)
${\epsilon}_{t}^{2}={\left({R}_{t}{\overline{R}}_{t}\right)}^{2}\approx {R}_{t}^{2}$
(12)
Therefore, the daily yield ${R}_{t}$
, daily absolute yield $\left{R}_{t}\right$
, and daily average square yield ${R}_{t}^{2}$
of nonferrous metal futures prices respectively indicate the twoway movement, absolute change, and mean square fluctuation of nonferrous metal futures prices around the mean, and the fluctuations they reflect are gradually increasing. In particular, the mean square rate of return actually represents the variance of the current fluctuation of the daily return series of nonferrous metal futures prices, which is a measure of current risk.
4.1.3. Descriptive Statistical Analysis
The following is a descriptive statistics on the futures and spot prices of various nonferrous metal, and the specific results are shown in Table 1 & Table 2 below.
Table 1. Descriptive statistics of futures and spot prices of copper, aluminum, and zinc at home and abroad.

LNFP1 
LNLP1 
LNSP1 
LNFP2 
LNLP2 
LNSP2 
LNFP3 
LNLP3 
LNSP3 
Mean 
10.819 
8.743 
10.829 
9.666 
7.643 
9.664 
9.808 
7.743 
9.834 
Median 
10.854 
8.832 
10.858 
9.658 
7.623 
9.650 
9.812 
7.745 
9.831 
Maximum 
11.381 
9.302 
11.378 
10.114 
8.256 
10.097 
10.263 
8.415 
10.268 
Minimum 
9.773 
7.458 
9.763 
9.181 
7.160 
9.179 
9.065 
6.975 
9.117 
Std. Dev. 
0.299 
0.355 
0.290 
0.172 
0.189 
0.172 
0.217 
0.235 
0.212 
Skewness 
−0.998 
−1.294 
−1.006 
−0.034 
0.225 
0.021 
−0.365 
−0.315 
−0.320 
Kurtosis 
3.779 
4.478 
3.995 
2.368 
2.570 
2.389 
2.902 
3.625 
2.796 
JarqueBera 
932.485 
1801.913 
1022.866 
77.560 
74.343 
72.143 
88.720 
128.755 
73.721 
Probability 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
Sum 
52678.92 
42568.16 
52725.92 
44579.98 
35248.34 
44572.10 
38478.50 
30374.47 
38577.79 
Sum Sq. Dev. 
435.887 
612.340 
408.141 
136.549 
164.937 
136.877 
184.586 
217.365 
176.358 
Observations 
4869 
4869 
4869 
4612 
4612 
4612 
3923 
3923 
3923 
Note: FP1 represents the Shanghai copper futures price, LP1 represents the LME copper futures price, SP1 represents the domestic copper spot price, FP2 represents the Shanghai aluminum futures price, LP2 represents the LME aluminum futures price, SP2 represents the domestic aluminum spot price, FP3 represents the Shanghai zinc futures price, LP3 represents the LME zinc futures price, SP3 represents the domestic Shanghai zinc spot price, and LN represents the logarithm.
Table 2. Descriptive statistics of futures and spot prices of lead, nickel and tin at home and abroad.

LNFP4 
LNLP4 
LNSP4 
LNFP5 
LNLP5 
LNSP5 
LNFP6 
LNLP6 
LNSP6 
Mean 
9.648 
7.640 
9.650 
11.648 
9.595 
11.659 
11.987 
9.974 
11.992 
Median 
9.635 
7.644 
9.638 
11.602 
9.539 
11.610 
11.895 
9.913 
11.890 
Maximum 
10.014 
7.955 
9.995 
12.497 
10.781 
12.738 
12.877 
10.7924 
12.817 
Minimum 
9.380 
7.359 
9.419 
11.082 
9.001 
11.074 
11.305 
9.492 
11.336 
Std. Dev. 
0.118 
0.107 
0.115 
0.312 
0.338 
0.325 
0.302 
0.272 
0.303 
Skewness 
0.449 
−0.109 
0.506 
0.324 
0.438 
0.332 
0.523 
0.803 
0.581 
Kurtosis 
2.802 
2.832 
2.887 
2.312 
2.683 
2.320 
2.866 
3.083 
2.908 
JarqueBera 
109.828 
9.894 
134.691 
80.922 
78.754 
81.889 
100.383 
233.489 
123.007 
Probability 
0.000 
0.007 
0.000 
0.000 
0.0000 
0.000 
0.000 
0.000 
0.000 
Sum 
30093.14 
23828.94 
30098.48 
25347.20 
20878.29 
25370.99 
25999.57 
21634.51 
26010.18 
Sum Sq. Dev. 
43.349 
35.658 
41.302 
211.446 
248.571 
229.634 
197.423 
160.920 
199.541 
Observations 
3119 
3119 
3119 
2176 
2176 
2176 
2169 
2169 
2169 
Note: FP4 represents the Shanghai lead futures price, LP4 represents the LME lead futures price, SP4 represents the domestic lead spot price, FP5 represents the Shanghai nickel futures price, LP5 represents the LME nickel futures price, SP5 represents the domestic nickel spot price, FP6 represents the Shanghai tin futures price, LP6 represents the LME tin futures price, SP6 represents the domestic Shanghai tin spot price, and LN represents the logarithm.
4.1.4. NonFerrous Metals Domestic and Foreign Futures and Spot Price Chart
The following is a time series chart of nonferrous metal futures and spot prices, as follows:
As can be seen in the above Figure 2, the futures and spot price series of nonferrous metal futures at home and abroad are all nonstationary series.
4.1.5. Domestic and Foreign NonFerrous Metal Futures Price Yield Chart
In the following, we make a time series chart of each time series of domestic and foreign nonferrous metal futures and spots, and make a basic judgment on the price yield and volatility of domestic and foreign nonferrous metal futures.
It can be seen from Figures 320 that there are multiple abnormal peaks in the futures and spot price yield series of nonferrous metals (copper, aluminum, zinc, lead, nickel, tin) at home and abroad, and the fluctuations show obvious volatility clustering phenomenon, indicating that the daily fluctuation of the price yield series of nonferrous metals (copper, aluminum, zinc, lead, nickel, tin)futures and spot markets at home and abroad is sudden and significant, and the volatility has the phenomenon of conditional heteroskedasticity. It can be speculated that the disturbance in the sequence of futures and spot prices yields in the domestic and foreign markets of nonferrous metals is not a white noise process.
From the comparison of various yield series of domestic and foreign nonferrous metal futures and spot prices, it is found that there are similar fluctuation patterns when there are abnormal fluctuation values and volatility clustering intervals, indicating that there may be a certain degree of correlation between them and the spillover effect of volatility. In the following, we use the daily yield series of futures prices to build a time series model to analyze the twoway fluctuation of the yield series and its impact.
Figure 2. Nonferrous metal futures and spot price trends at home and abroad.
Figure 3. Futures and Spot price daily yield of copper at home and abroad.
Figure 4. The daily absolute yield chart of copper futures and spot prices at home and abroad.
Figure 5. The daily average square yield chart of copper futures and spot prices at home and abroad.
Figure 6. The daily yield chart of aluminum futures and spot prices at home and abroad.
Figure 7. The daily absolute rate of return chart of aluminum futures and spot prices at home and abroad.
Figure 8. The daily average square yield chart of aluminum futures and spot prices at home and abroad.
Figure 9. The Daily yield chart of zinc futures and spot prices at home and abroad.
Figure 10. The Daily absolute yield chart of zinc futures and spot prices at home and abroad.
Figure 11. The daily average square yield chart of zinc futures and spot prices at home and abroad.
Figure 12. The daily yield chart of the futures and spot price of lead at home and abroad.
Figure 13. The daily absolute yield chart of the futures and spot price of lead at home and abroad.
Figure 14. The daily mean square yield chart of lead futures and spot prices at home and abroad.
Figure 15. The Daily yield chart of nickel futures and spot prices at home and abroad.
Figure 16. The Absolute daily yield chart of nickel futures and spot prices at home and abroad.
Figure 17. The Daily average square yield chart of nickel futures and spot prices at home and abroad.
Figure 18. The Daily yield chart of futures and spot price of tin at home and abroad.
Figure 19. The daily absolute yield chart of tin futures and spot prices at home and abroad.
Figure 20. The daily average square yield chart of nickel futures and spot prices at home and abroad.
4.2. NonFerrous Metal Futures Cointegration Correlation Test and ECM Model Empirical Analysis
Data Stationarity Test
There are many methods for unit root testing, generally including DF, ADF testing and PP testing. The most commonly used ADF test is used here. On the premise of ensuring that the residual terms are not correlated in the test, we use the AIC criterion and the SC criterion to determine that the hysteresis order is the best lag order when both values are the minimum. The specific test results are as follows Table 3.
Table 3. ADF unit root test results.
Variable 
Augmented DickeyFuller test statistic 
Test type (c, t, n) 
1% level 
5% level 
10% level 
DurbinWatson stat 
whether or not stable 
lnfp1 
−3.039 
(c, t, 2) 
−3.960 
−3.411 
−3.127 
2.004 
No 
lnlp1 
−3.179 
(c, t, 1) 
−3.960 
−3.411 
−3.127 
2.000 
No* 
lnsp1 
−3.376 
(c, t, 22) 
−3.960 
−3.411 
−3.127 
1.999 
No* 
Lnfp2 
−1.924 
(c, t, 10) 
−3.960 
−3.411 
−3.127 
1.999 
No 
Lnlp2 
−2.446 
(c, t, 2) 
−3.960 
−3.411 
−3.127 
1.997 
No 
Lnsp2 
−1.828 
(c, t, 29) 
−3.960 
−3.411 
−3.127 
1.998 
No 
Lnfp3 
−0.034 
(0, 0, 2) 
−2.566 
−1.941 
−1.617 
2.004 
No 
Lnlp3 
−2.206 
(c, 0, 18) 
−3.432 
−2.862 
−2.567 
2.001 
No 
Lnsp3 
−2.109 
(c, 0, 1) 
−3.432 
−2.862 
−2.567 
1.991 
No 
Lnfp4 
−2.318 
(c, 0, 21) 
−3.432 
−2.862 
−2.567 
1.998 
No 
Lnlp4 
−0.274 
(0, 0, 4) 
−2.566 
−1.941 
−1.617 
1.998 
No 
Lnsp4 
−2.108 
(c, 0, 1) 
−3.432 
−2.862 
−2.567 
1.999 
No 
Lnfp5 
−1.183 
(c, 0, 9) 
−3.433 
−2.863 
−2.567 
1.998 
No 
Lnlp5 
−1.359 
(c, 0, 13) 
−3.433 
−2.863 
−2.567 
1.998 
No 
Lnsp5 
−1.115 
(c, 0, 12) 
−3.433 
−2.863 
−2.567 
2.003 
No 
Lnfp6 
−1.110 
(c, 0, 18) 
−3.433 
−2.863 
−2.567 
1.997 
No 
Lnlp6 
−1.298 
(c, 0, 8) 
−3.433 
−2.863 
−2.567 
1.999 
No 
Lnsp6 
−1.824 
(c, t, 0) 
−3.962 
−3.412 
−3.128 
1.955 
No 
D (lnfp1) 
−10.990 
(0, 0, 31) 
−2.565 
−1.941 
−1.617 
2.001 
Yes 
D (lnlp1) 
−11.920 
(0, 0, 26) 
−2.565 
−1.941 
−1.617 
1.998 
Yes 
D (lnsp1) 
−14.546 
(0, 0, 21) 
−2.565 
−1.941 
−1.617 
1.999 
Yes 
D (lnfp2) 
−70.730 
(0, 0, 0) 
−2.565 
−1.941 
−1.617 
1.998 
Yes 
D (lnlp2) 
−47.443 
(0, 0, 1) 
−2.565 
−1.941 
−1.617 
1.997 
Yes 
D (lnsp2) 
−13.205 
(0, 0, 28) 
−2.565 
−1.941 
−1.617 
1.998 
Yes 
D (lnfp3) 
−43.371 
(0, 0, 1) 
−2.566 
−1.941 
−1.617 
2.004 
Yes 
D (lnlp3) 
−15.133 
(0, 0, 17) 
−2.566 
−1.941 
−1.617 
2.001 
Yes 
D (lnsp3) 
−63.829 
(0, 0, 0) 
−2.566 
−1.941 
−1.617 
1.991 
Yes 
D (lnfp4) 
−12.574 
(0, 0, 23) 
−2.566 
−1.941 
−1.617 
2.005 
Yes 
D (lnlp4) 
−27.714 
(0, 0, 3) 
−2.566 
−1.941 
−1.617 
1.998 
Yes 
D (lnsp4) 
−54.440 
(0, 0, 0) 
−2.566 
−1.941 
−1.617 
1.999 
Yes 
D (lnfp5) 
−17.144 
(0, 0, 8) 
−2.566 
−1.941 
−1.617 
1.998 
Yes 
D (lnlp5) 
−14.098 
(0, 0, 12) 
−2.566 
−1.941 
−1.617 
1.998 
Yes 
D (lnsp5) 
−13.849 
(0, 0, 11) 
−2.566 
−1.941 
−1.617 
2.003 
Yes 
D (lnfp6) 
−9.468 
(0, 0, 17) 
−2.566 
−1.941 
−1.617 
1.997 
Yes 
D (lnlp6) 
−15.859 
(0, 0, 7) 
−2.566 
−1.941 
−1.617 
1.999 
Yes 
D (lnsp6) 
−45.530 
(0, 0, 0) 
−2.566 
−1.941 
−1.617 
1.999 
Yes 
Note: D denotes the firstorder difference. C is the intercept, t is the temporal trend, n is the lag order, and * is significant at the significance level of 1% and 5%.
From the above unit root test results, it can be seen that the logarithm of domestic and foreign nonferrous metal futures and spot prices is nonstationary at the significance levels of 1%, 5% and 10%, except for the LME copper futures price and the domestic copper spot price, which are nonstationary at the significance level of 1%, 5% and 5%. The firstorder difference of each variable is stationary at the significance levels of 1%, 5%, and 10%.
4.3. Causality Test Analysis
4.3.1. Causality Test of Domestic NonFerrous Metal Futures and Spot Prices
We conduct a Granger causality test on the futures and spot prices of domestic nonferrous metal, and study the guidance of domestic nonferrous metal futures prices on domestic nonferrous metal spot price variables. Since the causality test is sensitive to the lag order, in the actual test, according to the AIC and SC criteria, the best lag order is when the two values are the smallest. The specific test results are as follows Table 4.
Table 4. Granger causality test results for each variable.
Null Hypothesis 
Sample 
FStatistic 
Prob. 
LNSP1 does not Granger Cause LNFP1 
4868 
5.173 
0.023 
LNFP1 does not Granger Cause LNSP1 

118.717 
2.E−27 
LNSP2 does not Granger Cause LNFP2 
4602 
2.066 
0.024 
LNFP2 does not Granger Cause LNSP2 

89.063 
2E−168 
LNSP3 does not Granger Cause LNFP3 
3915 
2.215 
0.019 
LNFP3 does not Granger Cause LNSP3 

89.800 
2E−152 
LNSP4 does not Granger Cause LNFP4 
3110 
2.264 
0.016 
LNFP4 does not Granger Cause LNSP4 

57.925 
4.E−98 
LNSP5 does not Granger Cause LNFP5 
2174 
21.537 
4.E−06 
LNFP5 does not Granger Cause LNSP5 

150.810 
1.E−33 
LNSP6 does not Granger Cause LNFP6 
2167 
7.350 
0.001 
LNFP6 does not Granger Cause LNSP6 

173.374 
1.E−70 
From the above test results, it can be seen that at the significance level of 1%, the domestic nonferrous metal copper, aluminum, zinc, lead, nickel and tin futures prices are the Granger reasons for their spot prices. At the significance level of 5%, the spot prices of domestic nonferrous metals copper, aluminum, zinc, lead, nickel and tin are the Granger reasons for their futures prices. The domestic nonferrous metal copper, aluminum, zinc, lead, nickel and tin futures prices have a stronger guiding effect on their spot prices than the spot prices on their futures prices.
4.3.2. Causality Test between Domestic and Foreign NonFerrous Metal Futures Prices
We conduct a Granger causality test on domestic and foreign nonferrous metal futures prices, and study the guidance of foreign nonferrous metal futures prices on domestic nonferrous metal futures price variables. Since the causality test is sensitive to the lag order, in the actual test, according to the AIC and SC criteria, the best lag order is when the two values are the smallest. The specific test results are as follows Table 5.
Table 5. Causality test results of domestic and foreign nonferrous metal futures prices
Null Hypothesis 
Sample 
FStatistic 
Prob. 
LNLP1 does not Granger Cause LNFP1 
4868 
35.419 
3.E−09 
LNFP1 does not Granger Cause LNLP1 

8.918 
0.003 
LNLP2 does not Granger Cause LNFP2 
4603 
113.310 
1E−192 
LNFP2 does not Granger Cause LNLP2 

3.003 
0.001 
LNLP3 does not Granger Cause LNFP3 
3907 
197.966 
9E−282 
LNFP3 does not Granger Cause LNLP3 

1.905 
0.055 
LNLP4 does not Granger Cause LNFP4 
3116 
247.295 
7E−144 
LNFP4 does not Granger Cause LNLP4 

1.178 
0.317 
LNLP5 does not Granger Cause LNFP5 
2174 
166.492 
9.E−37 
LNFP5 does not Granger Cause LNLP5 

1.479 
0.224 
LNLP6 does not Granger Cause LNFP6 
2165 
106.595 
6.E−83 
LNFP6 does not Granger Cause LNLP6 

0.296 
0.881 
From the above causality test, it can be seen that at the significance level of 1%, there is a twoway Granger causal relationship between the domestic Shanghai copper and aluminum futures prices and LME copper and aluminum futures prices. At the significance level of 5%, there is a twoway Granger causal relationship between domestic Shanghai zinc and LME zinc futures prices. At the significance levels of 1%, 5% and 10%, the LME lead, nickel and tin futures prices are the oneway Granger causality of domestic Shanghai lead, Shanghai nickel and Shanghai tin. Therefore, the futures prices of copper, aluminum and zinc in domestic nonferrous metal futures have a strong guiding effect on LME copper, aluminum and zinc futures prices, while the lead, nickel and tin futures prices in domestic nonferrous metal futures have no obvious guiding effect on LME lead, nickel and tin futures prices. So in domestic nonferrous metal futures, copper, aluminum, and zinc have strong international pricing influence, while lead, nickel, and tin have weak international pricing influence.
4.4. LongTerm Cointegration Relationship Test Analysis
We make Johansen’s maximum likelihood estimation test for domestic nonferrous metal (copper, aluminum, zinc, lead, nickel, tin) futures prices and foreign (copper, aluminum, zinc, lead, nickel, tin) futures prices. In the test, the case containing constants is considered, and the equation form of the optimal lag order is determined according to the SC criterion and the AIC criterion, and the lag order is selected 4 except for the lead 1, and the results are as follows Table 6.
Table 6. Johanson cointegration test results between domestic and foreign nonferrous metal futures prices.
Cointegration relation 
Eigenvalue 
Trace Statistic 
0.05 Critical Value 
Prob. 
The number of cointegration relationships 
Domestic Shanghai copper futures prices and LME copper futures prices 
0.004 
26.172 
15.495 
0.001 
None* 
0.002 
8.970 
3.841 
0.003 
At most 1* 
Domestic Shanghai aluminum futures price and LME aluminum futures price 
0.006 
31.623 
15.495 
0.000 
None* 
0.001 
5.186 
3.841 
0.023 
At most 1* 
Domestic Shanghai zinc futures prices and LME zinc futures prices 
0.006 
26.497 
15.495 
0.001 
None* 
0.001 
4.564 
3.841 
0.033 
At most 1* 
Domestic Shanghai lead futures price and LME lead futures price 
0.006 
24.226 
15.495 
0.002 
None* 
0.001 
4.625 
3.841 
0.032 
At most1 
Domestic Shanghai nickel futures prices and LME nickel futures prices 
0.024 
53.993 
15.495 
0.000 
None* 
0.001 
1.755 
3.841 
0.185 
At most 1 
Domestic Shanghai nickel futures prices and LME nickel futures prices 
0.011 
28.705 
25.872 
0.022 
None* 
0.002 
4.763 
12.518 
0.631 
At most 1 
Note: “*” indicates rejection of the null hypothesis at the 5% significance level.
The cointegration test results show that there is a cointegration relationship, so the cointegration relationship between the domestic nonferrous metals (copper, aluminum, zinc, lead, nickel, tin) futures prices and the LME nonferrous metals (copper, aluminum, zinc, lead, nickel, tin) futures prices is estimated as follows:
${\mu}_{1t}=LN{P}_{11t}0.965LN{P}_{21t}2.285$
(13)
${u}_{2t}=LN{P}_{12t}0.986LN{P}_{22t}2.128$
(14)
${u}_{3t}=LN{P}_{13t}0.959LN{P}_{23t}2.383$
(15)
${u}_{4t}=LN{P}_{14t}3.510LN{P}_{24t}+17.164$
(16)
${u}_{5t}=LN{P}_{15t}0.934LN{P}_{25t}2.691$
(17)
${u}_{6t}=LN{P}_{16t}0.854LN{P}_{26t}0.0001@\text{TREND}3.312$
(18)
Then the cointegration equations corresponding to the maximized eigenroots are as follows (the values in parentheses are the standard deviations, and the following are similar)
$LN{P}_{11t}=0.965LN{P}_{21t}+2.285$
(19)
(0.059)
$LN{P}_{12t}=0.986LN{P}_{22t}+2.128$
(20)
(0.084)
$LLN{P}_{13t}=0.959LN{P}_{23t}+2.383$
(21)
(0.046)
$LN{P}_{14t}=3.510LN{P}_{24t}17.164$
(22)
(0.660)
$LN{P}_{15t}=0.934LN{P}_{25t}+2.691$
(23)
(0.017)
$LN{P}_{16t}=0.854LN{P}_{26t}+0.0001@\text{TREND}+3.312$
(24)
(0.055) (2.4E−05)
From the cointegration equation, we can see that there is a significant longterm codirectional change relationship between domestic nonferrous metals (copper, aluminum, zinc, lead, nickel, tin) futures and LME nonferrous metals (copper, aluminum, zinc, lead, nickel, tin) futures market, except for lead, there is little difference in the range of changes of copper, aluminum, zinc and nickel (0.965, 0.986, 0.959, 0.934, 0.854), and the lead futures in the domestic and LME markets have the strongest codirectional change relationship (2.765).
4.5. ECM Model Estimation of NonFerrous Metals Futures Price Yield at Home and Abroad
From the above cointegration test, it can be seen that there is a cointegration relationship between domestic and foreign nonferrous metal (copper, aluminum, zinc, lead, nickel, tin) futures prices. Therefore, we establish an ECM between the price yield of domestic nonferrous metals (copper, aluminum, zinc, lead, nickel, tin) futures and the price yield of LME (copper, aluminum, zinc, lead, nickel and tin) futures and the results are shown in Table 7 below.
Table 7. Error correction model estimation results.
ECM 
R11 
R21 

R12 
R22 

R13 
R23 
EC 
−0.0002 
0.010 

0.001 
0.013 

−0.008 
0.016 

(0.002) 
(0.003) 

(0.002) 
(0.003) 

(0.004) 
(0.006) 
R11 (−1) 
−0.459 
0.095 
R12 (−1) 
−0.211 
0.017 
R13 (−1) 
−0.406 
0.038 

(0.016) 
(0.023) 

(0.015) 
(0.022) 

(0.019) 
(0.027) 
R11 (−2) 
−0.206 
0.041 
R12 (−2) 
−0.044 
0.024 
R13 (−2) 
−0.173 
−0.012 

(0.018) 
(0.026) 

(0.016) 
(0.023) 

(0.020) 
(0.029) 
R11 (−3) 
−0.095 
−0.008 
R12 (−3) 
−0.023 
0.026 
R13 (−3) 
−0.094 
0.007 

(0.017) 
(0.024) 

(0.016) 
(0.023) 

(0.019) 
(0.028) 
R11 (−4) 
−0.022 
−0.031 
R1 (−4) 
−0.009 
−0.013 
R13 (−4) 
−0.055 
−0.066 

(0.013) 
(0.018) 

(0.014) 
(0.020) 

(0.015) 
(0.022) 
R21 (−1) 
0.592 
−0.104 
R22 (−1) 
0.347 
−0.023 
R23 (−1) 
0.495 
−0.037 

(0.012) 
(0.016) 

(0.011) 
(0.016) 

(0.013) 
(0.019) 
R21 (−2) 
0.349 
−0.058 
R22 (−2) 
0.072 
0.012 
R23 (−2) 
0.243 
0.014 

(0.015) 
(0.022) 

(0.012) 
(0.017) 

(0.016) 
(0.023) 
R21 (−3) 
0.186 
−0.012 
R22 (−3) 
0.003 
−0.028 
R23 (−3) 
0.118 
−0.004 

(0.016) 
(0.023) 

(0.012) 
(0.018) 

(0.016) 
(0.025) 
R21 (−4) 
0.110 
0.065 
R22 (−4) 
0.033 
0.005 
R23 (−4) 
0.068 
0.062 

(0.014) 
(0.020) 

(0.012) 
(0.017) 

(0.015) 
(0.022) 
C 
0.0001 
0.0004 

3.49E−05 
8.84E−05 
C 
2.25E−06 
9.95E−06 

(0.0002) 
(0.0003) 

(0.0002) 
(0.0002) 

(0.0002) 
(0.0003) 
R^{2} 
0.363 
0.016 

0.181 
0.008 

0.289 
0.009 
Rsquared 
0.361 
0.015 

0.180 
0.006 

0.287 
0.007 
Adjusted Rsquared 
0.698 
1.432 

0.450 
0.915 

0.623 
1.3179 
S.E. of regression 
0.012 
0.017 

0.010 
0.014 

0.013 
0.0184 
Sum squared resid 
306.749 
9.005 

113.168 
4.135 

176.248 
4.091 
Log likelihood 
14620.59 
12872.46 

14732.03 
13099.34 

11557.95 
10091.94 
DurbinWatson stat 
−6.008 
−5.289 

−6.391 
−5.682 

−5.902 
−5.153 
Mean dependent var 
−5.9948 
−5.276 

−6.377 
−5.668 

−5.886 
−5.137 
S.D. dependent var 
0.0004 
0.0004 

6.15E−05 
8.80E−05 

1.14E−05 
1.11E−05 
Akaike info criterion 
0.0158 
0.017 

0.011 
0.014 

0.015 
0.018 
ECM 
R14 
R24 

R15 
R25 

R16 
R26 
EC 
0.001 
0.004 

−0.043 
0.032 

−0.027 
−0.006 

(0.001) 
(0.001) 

(0.009) 
(0.012) 

(0.006) 
(0.007) 
R14 (−1) 
−0.213 
0.022 
R15 (−1) 
−0.310 
−0.085 
R16 (−1 
−0.280 
0.008 

(0.019) 
(0.027) 

(0.024) 
(0.034) 

(0.025) 
(0.028) 
R14 (−2) 
−0.033 
0.049 
R15 (−2) 
−0.183 
0.002 
R16 (−2) 
−0.101 
0.014 

(0.019) 
(0.027) 

(0.025) 
(0.035) 

(0.026) 
(0.029) 
R14 (−3) 
−0.017 
0.044 
R15 (−3) 
−0.063 
−0.0133 
R16 (−3) 
−0.024 
0.020 

(0.019) 
(0.027) 

(0.024) 
(0.035) 

(0.026) 
(0.028) 
R14 (−4) 
0.011 
0.021 
R15 (−4) 
−0.023 
−0.003 
R16 (−4) 
−0.039 
−0.007 

(0.017) 
(0.024) 

(0.021) 
(0.029) 

(0.023) 
(0.025) 
R24 (−1)) 
0.357 
−0.006 
R25 (−1) 
0.442 
0.104 
R26 (−1) 
0.438 
0.023 

(0.013) 
(0.019) 

(0.018) 
(0.026) 

(0.023) 
(0.025) 
R24 (−2)) 
0.060 
−0.022 
R25 (−2) 
0.193 
0.011 
R26 (−2) 
0.104 
0.020 

(0.015) 
(0.021) 

(0.021) 
(0.029) 

(0.025) 
(0.028) 
R24 (−3)) 
−0.004 
−0.055 
R25 (−3) 
0.071 
0.011 
R26 (−3) 
0.063 
0.007 

(0.015) 
(0.021) 

(0.021) 
(0.029) 

(0.025) 
(0.028) 
R24 (−4)) 
0.012 
0.027 
R25 (−4) 
−0.059 
−0.006 
R26 (−4) 
−0.025 
0.004 

(0.015) 
(0.021) 

(0.020) 
(0.028) 

(0.024) 
(0.027) 
C 
2.46E−05 
−5.96E−05 

0.0002 
0.0002 

0.0004 
0.0003 

(0.0002) 
(0.0003) 

(0.0004) 
(0.0005) 

(0.0003) 
(0.0004) 
Rsquared 
0.198 
0.011 

0.295 
0.0106 

0.176 
0.003 
Adjusted Rsquared 
0.196 
0.008 

0.291 
0.005 

0.172 
−0.001 
S.E. of regression 
0.334 
0.676 

0.623 
1.246 

0.453 
0.557 
Sum squared resid 
0.010 
0.015 

0.017 
0.024 

0.015 
0.016 
Log likelihood 
85.136 
3.947 

99.543 
2.318 

51.062 
0.720 
DurbinWatson stat 
9811.563 
8715.066 

5757.849 
5006.400 

6095.057 
5872.893 
Mean dependent var 
−6.295 
−5.591 

−5.307 
−4.613 

−5.624 
−5.419 
S.D. dependent var 
−6.276 
−5.572 

−5.281 
−4.587 

−5.598 
−5.392 
Akaike info criterion 
−6.0E−07 
−5.67E−05 

0.0002 
0.0002 

0.0004 
0.0003 
Schwarz criterion 
0.012 
0.015 

0.020 
0.024 

0.016 
0.016 
Note: Among them, R11, R21, R12, R22, R13, R23, R14, R24, R15, R25, R16 and R26 respectively represent the price yield of Shanghai copper, LME copper, Shanghai aluminum, LME aluminum, Shanghai zinc, LME zinc, Shanghai lead, LME lead, Shanghai nickel, LME nickel, Shanghai tin, LME tin futures respectively, where a positive number in parentheses indicates the standard deviation and a negative number indicates the lag order. EC stands for Error Correction Item, which is similar to the following.
According to the above error correction equation calculation, solving the unconditional mathematical expectation of the yield series, the longterm equilibrium futures price return levels of domestic and foreign nonferrous metals (copper, aluminum, zinc, lead, nickel, tin) futures markets can be obtained as follows:
$\overline{{R}_{11}}=0.03\%$
, $\overline{{R}_{21}}=0.04\%$
, $\overline{{R}_{12}}=0.004\%$
, $\overline{{R}_{22}}=0.007\%$
, $\overline{{R}_{13}}=0.002\%$
,
$\overline{{R}_{23}}=0.00\%$
, $\overline{{R}_{14}}=0.00\%$
, $\overline{{R}_{24}}=0.00\%$
, $\overline{{R}_{15}}=0.00\%$
, $\overline{{R}_{25}}=0.02\%$
,
$\overline{{R}_{16}}=0.04\%$
, $\overline{{R}_{26}}=0.03\%$
.
According to the calculation results, there is no significant difference between the longterm price yield of domestic nonferrous metals (copper, lead, nickel, tin) and LME nonferrous metals (copper, lead, nickel, tin) futures, and there is a significant difference between the longterm futures price yield of the domestic nonferrous metals (aluminum, zinc) futures market and the LME nonferrous metals (aluminum, zinc) futures market, and the longterm price yield of the LME nonferrous metals (copper, aluminum, zinc, nickel) futures market is stronger than that of the domestic nonferrous metals (copper, aluminum, zinc, nickel) futures market. Only the domestic tin futures price yield is stronger than that of the LME tin futures, except for the domestic Shanghai zinc futures price yield is negative, the other domestic nonferrous metal futures price yields are positive. The price yield of nonferrous metal futures at home and abroad is affected by the longterm equilibrium relationship, and the correction item is a negative marginal contribution to the price yield of Shanghai copper, Shanghai zinc, Shanghai nickel, Shanghai tin and LME tin, and a positive marginal contribution to the price yield of other domestic and foreign nonferrous metal futures. In the ECM model, due to the partial and insignificant hysteresis coefficients, it indicates that there is an interaction between the corresponding futures price returns of domestic nonferrous metals (copper, aluminum, zinc, lead, nickel, tin) and LME (copper, aluminum, zinc, lead, nickel, tin) and shortterm fluctuations. Therefore, the ECM model shows that although there are different shortterm fluctuation patterns between the corresponding futures price returns of domestic nonferrous metals (copper, aluminum, zinc, lead, nickel, tin) and LME (copper, aluminum, zinc, lead, nickel, tin), there is also a longterm cointegration trend.
4.6. The GARCH Model Family Analysis of Domestic and Foreign NonFerrous Metal Futures Markets
We use the GARCH model to test the conditional heteroscedasticity of domestic and foreign nonferrous metals (copper, aluminum, zinc, lead, and nickel, tin) futures price return series. First, the partial autocorrelation function (PACF) and the autocorrelation function (ACF) are used to determine the order of the AR process and the MA process in the mean equation, and then according to the characteristics of the absolute residual sequence, the order of the ARCH term and the GARCH term in the variance equation is determined, and the domestic nonferrous metals (copper, aluminum, zinc, lead, nickel, tin) are finally determined after analysis and comparison The mean equation for the futures price return series is ARMA (1, 1), ARMA (1, 1), ARMA (4, 4), ARMA (2, 2), ARMA (2, 2), ARMA (5, 5), and the variance equation is GARCH (1, 1). The mean equations of the foreign LME nonferrous metals (copper, aluminum, zinc, lead, nickel, tin) futures price return series are ARMA (8, 8), ARMA (9, 9), ARMA (10, 10), ARMA (8, 8), ARMA (14, 14), ARMA (4, 4), and the variance equation are all GARCH (1, 1). Due to space limitations, the overall estimate and significance results are omitted. The GARCHM model, leverage effect model and spillover effect model for estimating the price returns of nonferrous metal futures at home and abroad are as follows:
4.6.1. GARCHM Model Estimation of the Price Yield of NonFerrous Metal Futures at Home and Abroad
Our empirical estimates of the GARCHM model of futures prices returns for domestic and foreign nonferrous metals (copper, aluminum, zinc, lead, nickel, tin) are shown in Table 8 below (the estimates of nonmajor parameters are omitted, and the values in parentheses are standard deviations, which are similar as follows):
From the above estimation results, it can be seen that the coefficient estimates of the conditional variance term GARCH of domestic and foreign nonferrous metals (copper, aluminum, zinc, lead, nickel, tin) futures price returns are 0.022,
Table 8. GARCHM estimation results.
variable 
R11 
R21 
R12 
R22 
R13 
R23 
R14 
R24 
R15 
R25 
R16 
R26 
@SQRT (GARCH) 
0.022 (0.131) 
0.034* (0.017) 
−0.008 (0.583) 
0.006 (0.677) 
0.003 (0.842) 
0.008 (0.590) 
−0.009 (0.427) 
0.005 (0.741) 
0.0001 (0.990) 
0.008 (0.625) 
0.030* (0.091) 
0.024 (0.272) 
AR (1) 
−0.615 (0.002) 

−0.582 (0.001) 









AR (2) 






0.946 (0.000) 

−0.677 (0.000) 



AR (4) 




0.649 (0.000) 






0.928 (0.000) 
AR (5) 










0.852 (0.000) 

AR (8) 

−0.992 (0.000) 





0.76 (0.000) 




AR (9) 



0.878 (0.000) 








AR (10) 





0.644 (0.000) 






AR (14) 









0.964 (0.000) 


MA (1) 
0.577 (0.006) 

0.531 (0.002) 









MA (2) 






−0.967 (0.000) 

0.674 (0.002) 



MA (4) 




−0.651 (0.000) 






−0.934 (0.000) 
MA (5) 










−0.880 (0.000) 

MA (8) 

0.994 (0.000) 





−0.810 (0.000) 




MA (9) 



−0.876 (0.000) 








MA (10) 





−0.651 (0.000) 






MA (14) 









−0.978 (0.000) 


Rsquared 
0.002 
0.005 
0.001 
0.001 
0.003 
0.008 
0.003 
0.011 
0.002 
0.012 
0.012 
0.003 
Adjusted
Rsquared 
0.001 
0.004 
0.001 
0.0007 
0.003 
0.007 
0.002 
0.0101 
0.001 
0.011 
0.011 
0.002 
S.E. of regression 
0.015 
0.017 
0.011 
0.014 
0.015 
0.018 
0.012 
0.015 
0.020 
0.024 
0.024 
0.016 
Sum squared resid 
1.093 
1.448 
0.552 
0.920 
0.874 
1.318 
0.416 
0.675 
0.884 
1.243 
1.243 
0.557 
Log likelihood 
14263.93 
13508.61 
15103.35 
13384.82 
11357.63 
10462.99 
9843.369 
8805.539 
5636.302 
5314.661 
5314.661 
6147.480 
DurbinWatson stat 
1.972 
2.142 
1.981 
2.046 
2.056 
2.071 
2.138 
2.020 
1.962 
1.883 
1.883 
1.938 
Mean dependent var 
0.0003 
0.0004 
4.1E−05 
8.7E−05 
8.0E−06 
1.2E−05 
2.1E−06 
−7.5E−05 
0.0002 
0.0002 
0.0002 
0.0003 
S.D. dependent var 
0.015 
0.017 
0.011 
0.014 
0.015 
0.018 
0.012 
0.015 
0.020 
0.024 
0.024 
0.016 
Akaike info criterion 
−5.859 
−5.557 
−6.550 
−5.810 
−5.793 
−5.345 
−6.314 
−5.659 
−5.177 
−4.913 
−4.913 
−5.676 
Schwarz criterion 
−5.851 
−5.549 
−6.541 
−5.806 
−5.784 
−5.335 
−6.302 
−5.647 
−5.164 
−4.897 
−4.897 
−5.660 
HannanQuinn criter. 
−5.856 
−5.554 
−6.547 
−5.811 
−5.790 
−5.341 
−6.310 
−5.655 
−5.174 
−4.907 
−4.907 
−5.670 
0.034, −0.008, 0.003, 0.008, −0.009, 0.005, 0.0001, 0.008, 0.030 and 0.024, respectively. The conditional variance coefficient of nonferrous metal futures price yield at home and abroad is significant for London copper and Shanghai nickel, while the others are not significant. The conditional variance coefficient of domestic and foreign nonferrous metal futures price yields is positive except for Shanghai Aluminum and Shanghai Lead, which reflects the negative correlation between the returns and risks of Shanghai Aluminum and Shanghai Lead futures markets, and the negative risk premium of returns.
There is a positive correlation between the returns and risks of the domestic copper, zinc, nickel and tin futures markets and LME copper, aluminum, zinc, lead, nickel and tin futures markets. There is a positive risk premium for returns, there is a certain risk reward in the market, and volatility increases the current rate of return. In addition to the Shanghai nickel futures market, the risk premium of the LME copper, aluminum, zinc, lead and tin futures markets is higher than that of the domestic futures market, indicating that foreign nonferrous metal market investors have a stronger risk appetite than domestic investors, and the risk appetite of domestic and foreign nickel futures market investors is relatively strong, and the risk appetite of domestic investors is slightly stronger than that of foreign investors. Therefore, there is a difference in the risk premium of returns between the domestic nonferrous metal futures market and the LME metal futures market, so there are theoretical arbitrage opportunities in the domestic and foreign metal futures markets.
4.6.2. EGARCH Model Estimation of Domestic and Foreign NonFerrous Metal Futures Price Yields
The following estimates the EGARCH model of the price yield of nonferrous metals (copper, aluminum, zinc, lead, nickel, tin) futures at home and abroad, and the estimation models are EGARCH (2, 2), EGARCH (1, 1), EGARCH (2, 2), EGARCH (2, 2), EGARCH (2, 2), EGARCH (2, 1), EGARCH (2, 1), EGARCH (2, 2), EGARCH (1, 1), EGARCH (2, 2), EGARCH (2, 2), and the results of the variance equation for specific estimates are shown in Table 9.
From the above estimation results, it can be seen that the estimated value of the asymmetric term coefficient is not equal to zero, indicating that the impact of the
Table 9. EGARCH model estimation results.
variable 
$\mathrm{ln}{\sigma}_{1}^{2}$

$\mathrm{ln}{\sigma}_{2}^{2}$

$\mathrm{ln}{\sigma}_{3}^{2}$

$\mathrm{ln}{\sigma}_{4}^{2}$

$\mathrm{ln}{\sigma}_{5}^{2}$

$\mathrm{ln}{\sigma}_{6}^{2}$

$\mathrm{ln}{\sigma}_{7}^{2}$

$\mathrm{ln}{\sigma}_{8}^{2}$

$\mathrm{ln}{\sigma}_{9}^{2}$

$\mathrm{ln}{\sigma}_{10}^{2}$

$\mathrm{ln}{\sigma}_{11}^{2}$

$\mathrm{ln}{\sigma}_{12}^{2}$

C 
−0.654 (0.000) 
−0.260 (0.000) 
−0.811 (0.000) 
−0.040 (0.000) 
−0.504 (0.000) 
−0.139 (0.000) 
−0.340 (0.000) 
−0.135 (0.000) 
−0.019 (0.040) 
−0.950 (0.000) 
−0.630 (0.000) 
−1.173 (0.000) 
$\left{\epsilon}_{t}\left(1\right)/{\sigma}_{t}\left(1\right)\right$

0.217 (0.000) 
0.157 (0.000) 
0.274 (0.000) 
0.220 (0.000) 
0.169 (0.000) 
0.172 (0.000) 
0.296 (0.000) 
0.199 (0.000) 
0.190 (0.000) 
0.359 (0.000) 
0.219 (0.000) 
0.297 (0.000) 
$\left{\epsilon}_{t}\left(2\right)/{\sigma}_{t}\left(2\right)\right$

0.167 (0.000) 

0.237 (0.000) 
−0.192 (0.000) 
0.172 (0.000) 
−0.067 (0.000) 
−0.104 (0.000) 
−0.134 (0.000) 
−0.177 (0.000) 

0.187 (0.000) 
0.255 (0.000) 
${\epsilon}_{t}\left(1\right)/{\sigma}_{t}\left(1\right)$

−0.023 (0.000) 
−0.030 (0.000) 
0.038 (0.000) 
0.005 (0.006) 
−0.005 (0.030) 
0.006 (0.002) 
0.022 (0.001) 
−0.023 (0.000) 
0.008 (0.004) 
0.074 (0.000) 
0.042 (0.000) 
−0.041 (0.000) 
$\mathrm{ln}{\sigma}_{t}^{2}\left(1\right)$

0.052 (0.163) 
0.983 (0.000) 
0.046 (0.010) 
1.592 (0.000) 
−0.015 (0.000) 
0.993 (0.000) 
0.978 (0.000) 
0.990 (0.000) 
1.785 (0.000) 
0.911 (0.000) 
0.027 (0.050) 
−0.018 (0.143) 
$\mathrm{ln}{\sigma}_{t}^{2}\left(2\right)$

0.905 (0.000) 

0.907 (0.000) 
−0.594 (0.000) 
0.986 (0.000) 



−0.786 (0.000) 

0.933 (0.000) 
0.926 (0.000) 
Rsquared 
0.002 
0.001 
0.001 
0.001 
0.003 
0.007 
0.003 
0.005 
0.002 
0.0002 
0.001 
0.005 
Adjusted
Rsquared 
0.001 
0.001 
0.001 
0.001 
0.003 
0.007 
0.002 
0.005 
0.001 
−0.001 
−0.0003 
0.004 
S.E. of regression 
0.015 
0.017 
0.011 
0.0141 
0.015 
0.018 
0.012 
0.015 
0.020 
0.024 
0.016 
0.016 
Sum squared resid 
1.093 
1.454 
0.552 
0.921 
0.874 
1.318 
0.416 
0.679 
0.884 
1.258 
0.550 
0.555 
Log likelihood 
14257.07 
13508.28 
15110.12 
13385.79 
11360.98 
10465.38 
9854.916 
8818.152 
5637.689 
5295.307 
6213.473 
6167.578 
Durbin
Watson stat 
1.978 
2.148 
1.985 
2.048 
2.056 
2.071 
2.139 
2.017 
1.962 
1.887 
2.082 
1.933 
Mean dependent var 
0.0003 
0.0004 
4.1E−05 
8.7E−05 
8.0E−06 
1.2E−05 
2.1E−06 
−7.5E−05 
0.0002 
0.0002 
0.0004 
0.0003 
S.D. dependent var 
0.015 
0.017 
0.011 
0.014 
0.015 
0.018 
0.012 
0.015 
0.020 
0.024 
0.016 
0.0160 
Akaike info criterion 
−5.855 
−5.556 
−6.551 
−5.813 
−5.793 
−5.345 
−6.320 
−5.666 
−5.178 
−4.894 
−5.737 
−5.692 
Schwarz criterion 
−5.843 
−5.547 
−6.539 
−5.801 
−5.779 
−5.332 
−6.305 
−5.650 
−5.155 
−4.876 
−5.713 
−5.668 
HannanQuinn criter. 
−5.851 
−5.553 
−6.547 
−5.810 
−5.788 
−5.340 
−6.315 
−5.660 
−5.170 
−4.888 
−5.728 
−5.683 
Note: ${\sigma}_{1}^{2}$
, ${\sigma}_{2}^{2}$
, ${\sigma}_{3}^{2}$
, ${\sigma}_{4}^{2}$
, ${\sigma}_{5}^{2}$
, ${\sigma}_{6}^{2}$
, ${\sigma}_{7}^{2}$
, ${\sigma}_{8}^{2}$
, ${\sigma}_{9}^{2}$
, ${\sigma}_{10}^{2}$
, ${\sigma}_{11}^{2}$
, ${\sigma}_{12}^{2}$
represent the variance of Shanghai copper, London copper, Shanghai aluminum, London aluminum, Shanghai zinc, London zinc, Shanghai lead, London lead, Shanghai nickel, London nickel, Shanghai tin, and London tin futures.${\epsilon}_{t}$
represent residuals, ${\sigma}_{t}$
stands for standard deviation. The negative number in parentheses is the lag order, t = 1.212.
news shock is asymmetrical, and the asymmetric coefficient in the variance equation of the price return of Shanghai copper, London copper, Shanghai zinc, London lead, and London tin futures is negative and significant, indicating that there is asymmetry and leverage effect in the Shanghai copper, London copper, Shanghai zinc, London lead, and London tin futures markets, and when the impact of bullish news, the Shanghai copper, London copper, Shanghai zinc, London lead, and London tin futures markets are 0.361, 0.127, and 0.336, 0.042, 0.511 times the shock impact respectively.
When the negative news hits, it will have an impact of 0.407, 0.187, 0.346, 0.088 and 0.593 times on the Shanghai copper, London copper, Shanghai zinc, London lead and London tin futures markets respectively. The impact of negative news is greater than the impact of bullish news, among which the leverage effect of LME tin is the strongest, and the leverage effect of Shanghai Zinc is the weakest. The asymmetry coefficient in the variance equation of other nonferrous metals Shanghai aluminum, London aluminum, London zinc, Shanghai lead, Shanghai nickel, London nickel and Shanghai tin price yield is positive, indicating that the impact of bullish in these markets is greater than the impact of bearishness, when the impact of bullish news, Shanghai aluminum, London aluminum, London zinc, Shanghai lead, Shanghai nickel, London nickel, Shanghai tin market has a 0.549, 0.033, 0.111, 0.214, 0.021, 0.433, 0.448 times shock impact, when the impact of negative news, Shanghai aluminum, The London aluminum, London zinc, Shanghai lead, Shanghai nickel, London nickel and Shanghai tin markets had an impact of 0.473, 0.023, 0.099, 0.170, 0.005, 0.285 and 0.364 times. The following is the shock response curve of domestic and foreign nonferrous metals (copper, aluminum, zinc, lead, nickel, tin) futures market information as follows:
From Figures 2132 below, we can see the asymmetric impact of market news on volatility, the impact of negative news in Shanghai copper and London copper futures markets is greater than the impact of bullish news, but the impact of negative news in London copper market is greater than that of Shanghai copper negative news. The impact of the bullish news in the Shanghai aluminum and London aluminum markets is slightly greater than the impact of the negative news, and the impact of the bullish and negative news on the two markets is relatively close. There are obvious differences in the negative and bullish impact of the Shanghai zinc and London zinc futures markets, the impact of the bullish news in the Shanghai zinc market is greater than the impact of the bearish news, and the impact of the negative news in the London zinc futures market is significantly greater than the impact of the bullish news. There are also obvious differences
Figure 21. The information shock curve of Shanghai copper futures markets.
Figure 22. The information shock curve of London copper futures markets.
Figure 23. The information shock curve of Shanghai aluminum futures markets.
Figure 24. The information shock curve of Londonaluminum futures markets.
Figure 25. The information shock curve of Shanghai zinc futures markets.
Figure 26. The information shock curve of London zinc futures markets.
Figure 27. The information shock curve of Shanghai lead futures markets.
Figure 28. The information shock curve of London lead futures markets.
Figure 29. The information shock curve of Shanghai nickel futures markets.
Figure 30. The information shock curve of London nickel futures markets.
Figure 31. The information shock curve of Shanghai tin futures markets.
Figure 32. The information shock curve of London tin futures markets.
in the impact of negative news in the Shanghai lead and London lead futures markets, the impact of the positive news in the Shanghai lead futures market is greater than the impact of the negative news, and the negative news in the London lead futures market is slightly greater than the impact of the positive news. The impact of bullish news is greater than that of bearish news in the Shanghai nickel futures market, but the impact of bullish news is greater than that of bearish news in the London nickel futures market than that of the Shanghai nickel market. There are obvious differences in the impact of negative news in the Shanghai tin and London tin futures markets, the impact of the positive news in the Shanghai tin futures market is slightly greater than the impact of the negative news, and the impact of the negative news in the London tin futures market is greater than the impact of the positive news.
The enlightenment from the gap in the impact of the news of the nonferrous metal futures market at home and abroad is that in addition to the domestic and foreign aluminum futures, from the comparison of the domestic and foreign futures markets of copper, zinc, lead, nickel and tin, the risk of the foreign market is greater than the risk of the domestic market. For investors, arbitrage is carried out in accordance with the normal domestic and foreign futures price comparison relationship, due to the different degrees of influence of bullish and negative news at home and abroad, the normal price comparison relationship is often distorted, therefore, there is a greater risk of crossmarket arbitrage through the copper, zinc, lead, nickel and tin futures markets.
4.6.3. Spillover Effect Model Estimation of Domestic and Foreign NonFerrous Metal Futures Price Yields
Firstly, the conditional variance of the GARCHM model of domestic and foreign nonferrous metal futures price returns is tested for the Granger causality test, and the best lag order is selected, and the test results are shown in Table 10 & Table 11 below.
Table 10. The Granger causality test results of conditional variance of domestic and foreign nonferrous metal futures prices yields.
Null Hypothesis 
Sample 
FStatistic 
Prob. 
H2 does not Granger Cause H1 
4858 
153.149 
3.E−65 
H1 does not Granger Cause H2 

2.575 
0.076 
H4 does not Granger Cause H3 
4600 
15.446 
2.E−07 
H3 does not Granger Cause H4 

123.631 
5.E−53 
H6 does not Granger Cause H5 
3911 
22.482 
2.E−10 
H5 does not Granger Cause H6 

142.257 
2.E−60 
H8 does not Granger Cause H7 
3108 
30.766 
6.E−14 
H7 does not Granger Cause H8 

96.619 
2.E−41 
H10 does not Granger Cause H9 
2153 
2.450 
0.012 
H9 does not Granger Cause H10 

213.809 
3E−266 
H12 does not Granger Cause H11 
2161 
2.193 
0.112 
H11 does not Granger Cause H12 

44.502 
1.E−19 
Note: Among them, H1, H2, H3, H4, H5, H6, H7, H8, H9, H10, H11, and H12 are the conditional variances of the GarchM model of Shanghai copper, London copper, Shanghai aluminum, London aluminum, Shanghai zinc, London zinc, Shanghai lead, London lead, Shanghai nickel, London nickel, Shanghai tin, and London tin futures price returns.
From the results of the above Granger causality test, it can be seen that at the significance level of 10%, the volatility of Shanghai copper and London copper futures price returns is causal with each other, and at the significance level of 1% and 5%, London copper has a oneway guiding relationship with Shanghai copper, indicating that the influence of London copper on Shanghai copper is greater than that of Shanghai copper on London copper. At the significance levels of 1%, 5% and 10%, there is a twoway guiding relationship between the price return volatility of Shanghai Aluminum and London Aluminum, Shanghai Zinc and London Zinc, and Shanghai Lead and London Lead futures. At the 1% significance level, Shanghai Nickel has a oneway guiding relationship with the price return volatility of London nickel futures, and at the 5% and 10% significance levels, there is a twoway guiding relationship between the price return volatility of Shanghai Nickel and London Nickel futures, indicating that the impact of Shanghai Nickel on London Nickel is greater than that of London Nickel on Shanghai Nickel. At the significance levels of 1%, 5% and 10%, there is a oneway guiding relationship Shanghai tin futures price returns volatility on London tin futures price returns volatility, and there is no guidance relationship London tin futures price returns volatility on Shanghai tin futures price returns volatility, indicating that the impact of Shanghai tin on London tin is significantly greater than that of London tin on Shanghai tin.
In short, the price return volatility of London copper, Shanghai nickel and Shanghai tin futures has a stronger guiding effect on the price return volatility of Shanghai copper, London nickel and London tin than the price yield fluctuation of Shanghai copper, London nickel and London tin futures on the price return volatility of London copper, Shanghai nickel and Shanghai tin futures. There is a strong mutual guiding effect between the price yields fluctuations of aluminum, zinc and lead futures of domestic nonferrous metal futures and the price yields fluctuations of foreign aluminum, zinc and lead futures, and there is little difference in mutual guidance.
It shows that the risks of domestic and foreign nonferrous metal futures markets have strong mutual influences, and the impact of the London copper, Shanghai nickel and Shanghai tin futures market on the Shanghai copper, London nickel and Shanghai tin futures markets is stronger than that of the Shanghai copper, London nickel and Shanghai tin futures markets on London copper, Shanghai nickel and Shanghai tin futures market. Therefore, the risk transmission of copper, nickel and tin futures prices at home and abroad has obvious asymmetry.
The following are the specific estimates of the spillover effect models of domestic and foreign nonferrous metals (copper, aluminum, zinc, lead, nickel, tin) futures markets, as shown in Table 11 below.
The above conditional variance model shows that the early absolute disturbance of the yield of the London copper futures price has a negative impact on the fluctuation of the current yield of the Shanghai copper futures price, and the absolute disturbance of the early absolute disturbance of the Shanghai copper futures price yield has a positive impact on the fluctuation of the current yield of the London copper futures price. The early absolute disturbance of the price yield of London aluminum futures has a positive impact on the fluctuation of the current yield of Shanghai aluminum futures price, and the early absolute disturbance of the price yield of Shanghai aluminum futures has a negative impact on
Table 11. Estimation results of spillover effect model in domestic and foreign nonferrous metal futures markets.
variable 
${\sigma}_{1}^{2}$

${\sigma}_{2}^{2}$

${\sigma}_{3}^{2}$

${\sigma}_{4}^{2}$

${\sigma}_{5}^{2}$

${\sigma}_{6}^{2}$

${\sigma}_{7}^{2}$

${\sigma}_{8}^{2}$

${\sigma}_{9}^{2}$

${\sigma}_{10}^{2}$

${\sigma}_{11}^{2}$

${\sigma}_{12}^{2}$

${\sigma}_{t}^{2}\left(1\right)$

0.912 (0.000) 
0.928 (0.000) 
0.877 (0.000) 
0.937 (0.000) 
0.933 (0.000) 
0.954 (0.000) 
0.902 (0.000) 
0.965 (0.000) 
0.927 (0.000) 
0.542 (0.000) 
0.915 (0.000) 
0.900 (0.000) 
${\epsilon}_{1}^{2}\left(1\right)$

0.085 (0.000) 
0.001 (0.000) 










${\epsilon}_{2}^{2}\left(1\right)$

−1.96E−05 (0.441) 
0.066 (0.000) 










${\epsilon}_{3}^{2}\left(1\right)$



0.126 (0.000) 
−0.0002 (0.000) 








${\epsilon}_{4}^{2}\left(1\right)$



0.0004 (0.000) 
0.058 (0.123) 








${\epsilon}_{5}^{2}\left(1\right)$





0.067 (0.000) 
0.0001 (0.000) 






${\epsilon}_{6}^{2}\left(1\right)$





2.48E−05 (0.083) 
0.044 (0.005) 






${\epsilon}_{7}^{2}\left(1\right)$







0.096 (0.000) 
6.75E−05 (0.222) 




${\epsilon}_{8}^{2}\left(1\right)$







0.0005 (0.000) 
0.033 (0.000) 




${\epsilon}_{9}^{2}\left(1\right)$









0.059 (0.000) 
0.013 (0.000) 


${\epsilon}_{10}^{2}\left(1\right)$









3.04E−05 (0.233) 
0.289 (0.000) 


${\epsilon}_{11}^{2}\left(1\right)$











0.084 (0.000) 
0.065 (0.000) 
${\epsilon}_{12}^{2}\left(1\right)$











6.04E−05 (0.332) 
0.009 (0.000) 
Rsquared 
0.999 
0.999 
0.999 
0.999 
0.999 
0.999 
0.999 
0.999 
0.999 
0.997 
0.999 
0.917 
Adjusted
Rsquared 
0.999 
0.999 
0.999 
0.999 
0.999 
0.999 
0.999 
0.999 
0.999 
0.997 
0.999 
0.917 
S.E. of regression 
1.74E−06 
2.57E−06 
8.75E−07 
1.86E−06 
6.69E−07 
1.19E−06 
1.13E−06 
1.05E−06 
6.53E−06 
9.72E−05 
2.02E−06 
8.32E−05 
Sum squared resid 
1.46E−08 
3.21E−08 
3.52E−09 
1.60E−08 
1.75E−09 
5.58E−09 
3.95E−09 
3.42E−09 
9.19E−08 
2.04E−05 
8.77E−09 
1.50E−05 
Log likelihood 
57558.55 
55650.25 
57650.70 
54173.47 
50069.66 
47800.04 
38170.51 
38392.65 
22737.19 
16892.72 
25287.26 
17243.54 
DurbinWatson stat 
0.012 
0.034 
0.073 
0.025 
0.011 
0.013 
0.086 
0.023 
0.023 
0.078 
0.016 
1.974 
Mean dependent var 
0.0002 
0.0003 
0.0001 
0.0002 
0.0002 
0.0003 
0.0001 
0.0002 
0.0004 
0.0006 
0.0003 
0.0003 
S.D. dependent var 
0.0002 
0.0004 
0.0001 
0.0001 
0.0001 
0.0003 
0.0001 
9.22E−05 
0.0004 
0.002 
0.0003 
0.0003 
Akaike info criterion 
−23.690 
−22.905 
−25.059 
−23.547 
−25.596 
−24.436 
−24.553 
−24.696 
−21.040 
−15.639 
−23.390 
−15.949 
Schwarz criterion 
−23.686 
−22.901 
−25.055 
−23.543 
−25.591 
−24.431 
−24.547 
−24.690 
−21.032 
−15.631 
−23.382 
−15.941 
Hannan
Quinn criter. 
−23.689 
−22.903 
−25.057 
−23.546 
−25.595 
−24.434 
−24.551 
−24.694 
−21.038 
−15.631 
−23.387 
−15.946 
Note: ${\sigma}_{1}^{2}$
, ${\sigma}_{2}^{2}$
, ${\sigma}_{3}^{2}$
, ${\sigma}_{4}^{2}$
, ${\sigma}_{5}^{2}$
, ${\sigma}_{6}^{2}$
, ${\sigma}_{7}^{2}$
, ${\sigma}_{8}^{2}$
, ${\sigma}_{9}^{2}$
, ${\sigma}_{10}^{2}$
, ${\sigma}_{11}^{2}$
, ${\sigma}_{12}^{2}$
is the conditional variance of the price yield of Shanghai copper, London copper, Shanghai aluminum, London aluminum, Shanghai zinc, London zinc, Shanghai lead, London lead, Shanghai nickel, London nickel, Shanghai tin, and London tin futures, ${\sigma}_{t}^{2},t=1,2,3,4,5,6,7,8,9,10,11,12$
They are Shanghai copper, London copper, Shanghai aluminum, London aluminum, Shanghai zinc, London zinc, Shanghai lead, London lead, Shanghai nickel, London nickel, Shanghai tin, London tin and London tin futures price yield disturbances, the positive data in parentheses are the standard deviation, and the negative values are the lag order.
the fluctuation of the current yield of London aluminum futures price. The absolute disturbance of the early stage of the price yield of London zinc and Shanghai zinc futures has a positive impact on the current yield fluctuation of Shanghai zinc and London zinc futures prices, respectively, and the impact of Shanghai zinc on the London zinc market is more significant. The absolute disturbance of the early stage of the price yield of London lead and Shanghai lead futures has a positive impact on the fluctuation of the current yield of Shanghai lead and Shanghai lead futures, respectively, and the impact of London lead on the Shanghai lead market is more significant. The absolute disturbance of the early stage of the price yield of London nickel and Shanghai nickel futures has a positive impact on the fluctuation of the current yield of Shanghai nickel and London nickel futures respectively, and the impact of Shanghai nickel on the London nickel market is more significant. The absolute disturbance of the yield of London and Shanghai tin futures prices in the early stage has a positive impact on the fluctuation of the current yield of Shanghai tin and London tin futures prices, respectively, and the impact of Shanghai tin on the London tin market is more significant.
This shows that there are spillover effects between domestic and foreign nonferrous metals (copper, aluminum, zinc, lead, nickel and tin) futures markets, and the spillover effects of domestic copper, zinc, nickel and tin futures markets on foreign copper, zinc, nickel and tin futures markets are stronger than those of foreign copper, zinc, nickel and tin futures markets on domestic copper, zinc, nickel and tin futures markets. The spillover effect of foreign aluminum and lead futures markets on the domestic aluminum and lead futures markets is stronger than that of the domestic aluminum and lead futures markets on foreign aluminum and lead futures markets. The asymmetry of the spillover effect between the domestic and foreign nonferrous metal futures markets shows that there is a mutual influence on the volatility transmission of the domestic and foreign nonferrous metal futures markets. The above shows that after years of development, China’s nonferrous metal futures market has a strong demonstration role in the global market in terms of yield level and volatility, especially the international pricing power and influence of copper, zinc, nickel and tin have been significantly improved.
5. Conclusion
In this paper, we use the cointegration correlation theory and GARCH model method to conduct an empirical study on the price discovery function and influence of nonferrous metals copper, aluminum, zinc, lead, nickel and tin futures listed on the Shanghai Futures Exchange, as well as the international pricing power and volatility risk transmission.
It is found that the domestic nonferrous metal copper, aluminum, zinc, lead, nickel and tin futures prices have a strong price discovery function, and the domestic nonferrous metal futures have a strong international pricing influence of copper, aluminum and zinc, while the international pricing influence of lead, nickel and tin is weak. There is a significant longterm codirectional movement relationship between domestic nonferrous metal futures and LME nonferrous metal futures market, and the lead futures in China and LME market have the strongest codirectional change relationship. There is an interaction between domestic nonferrous metal futures and LME metal futures price yields and shortterm fluctuations, and although there are different shortterm fluctuation patterns between futures price yields, there is also a longterm cointegration trend. In addition to the Shanghai nickel futures market, the risk premium of the Shanghai nickel futures market is higher than that of the LME nickel futures market, and the risk premium of the other copper, aluminum, zinc, lead and tin futures markets is higher than that of the domestic futures market, and there are theoretical arbitrage opportunities in the domestic and foreign metal futures markets. In addition to aluminum, from the copper, zinc, lead, nickel, tin domestic and foreign futures market comparison, the risk of the foreign market is greater than the risk of the domestic market, due to the degree of influence of the bullish news at home and abroad, the normal price relationship is often distorted, therefore, through the copper, zinc, lead, nickel, tin futures market crossmarket arbitrage there is a greater risk. The risks of domestic and foreign nonferrous metal futures markets have strong mutual influences, and the risk transmission of copper, nickel and tin futures prices at home and abroad has obvious asymmetry. There is asymmetry in the spillover effect between domestic and foreign nonferrous metal futures markets, and there is mutual influence on the volatility transmission of domestic and foreign nonferrous metal futures markets. After years of development, China’s nonferrous metal futures market has a strong demonstration role in the global market in terms of yield level and volatility, especially the international pricing power and influence of copper, zinc, nickel and tin have been significantly improved.
In short, China’s nonferrous metal futures have a strong price discovery function, have a certain international influence, international pricing power, at that time the domestic nonferrous metal futures market and the foreign LME market still have a certain gap, therefore, the following suggestions are put forward for the development of the domestic nonferrous metal futures market:
First, further promote the international development of the domestic nonferrous metal futures market. Promote the internationalization of existing nonferrous futures varieties as soon as possible. Docking with the international futures market and improving the trading rules of the international futures market. Strengthening cooperation with international futures exchanges. Continuously enhance the price guiding role of domestic nonferrous metal futures on foreign nonferrous metal futures. On the basis of allowing QFIIs and RQFIIs to participate in the trading of specific domestic products, we will widely introduce international industrial and institutional customers, enrich the trader structure of the nonferrous metal futures market, and further enhance the level of internationalization.
Second, further enrich the varieties of domestic nonferrous metal futures and options to meet the needs of different traders. On the basis of the existing nonferrous metal futures and options, more subdivided varieties of nonferrous metal futures will be launched according to different market needs, and the research and development of nonferrous metal intermediate products will be actively carried out, especially the development of some minor metal futures varieties, so as to meet the diversified needs of international investors. In addition, on the basis of the existing futures varieties, we can consider the optimization of contracts and launch mini contracts to meet the needs of some investment customers. Enhance the international competitiveness of domestic nonferrous metal futures through variety development and contract optimization.
Third, further establish and improve the basic construction of the domestic nonferrous metal futures market. Explore the construction of overseas nonferrous metal futures delivery warehouses to meet the delivery needs of international institutional investors. Promote the improvement of the development of the nonferrous metal OTC commodity trading market, and optimize the logistics and warehousing service system. Regulate the business of futures companies, promote the rapid development of futures business, create a good futures business environment, and promote the international development of the nonferrous metal futures market.
Fourth, within the framework of the Futures Law, strengthen the risk supervision of the nonferrous metal futures market. In the face of the complex international political and economic environment, the continuous outbreak of political and economic risks, the international market of nonferrous metals soars and plummets from time to time, and the transaction risks of domestic and foreign markets continue to gather. Therefore, both market trading entities and regulatory authorities should do a good job in risk prevention and control. In response to abnormal trading behaviors in the market, the regulatory authorities should supervise them in a timely manner to prevent further expansion of risks and maintain the normal operation of the market.