The effect of international energy market shocks on coal price of China based on the fuzzy integrated vector auto regressive and error correction model

Abstract

From the perspective of external market shocks, this paper proposed fuzzy integrated vector auto regression (FVAR) model that determines the long-term basis and short-term basis interactions of China’s coal price with international energy prices. The proposed FVAR preform coal price fluctuation based on long-term and short term span in six stages including unit root testing, Johansen cointegration test, vector auto regression (VAR) model construction, fuzzification of VAR model, vector error correction (VEC) model and an impulse response function(IRF). It is observed that there is a steady long-term stability and equilibrium bond between the China’s domestic coal price, international coal price and the international crude (unrefined) oil price. The international coal and international crude oil price have an opposite effect on China’s domestic coal price. In addition, the former has a stronger fuzzy price discovery function on China’s domestic coal market than the latter. In the short term, China’s domestic coal price is more complex to instability reactions and is affected by market expectations. The international energy market is more effective than domestic coal market, and there is a relatively stable price adjustment mechanism between the two, with the international coal price playing a leading role in the fuzzy guidance of China’s coal price. Therefore, in reference to international energy pricing models, the paper proposes a fuzzy pricing model for a coal futures index based on the coal futures trading price and supplemented by the premium and discount agreed to by both trading parties.

Keywords

China’s coal price international energy market fuzzy price discovery shocks fuzzy linear regression vector auto regressive (VAR) model vector error correction (VEC) model impulse response function(IRF)

1 Introduction

President Trump’s America First Energy Plan, aimed at making the U.S. energy independent, encourages the use of remain of plants and animals waste termed as fossil fuels that include pure coal, oil and shale gas which shocks China’s energy market to a certain extent. Conferring to statistics of China National Bureau survey, in the year 2019 raw coal rests as the primary energy consumption choice in China, accounting for about 69.3 percent of the total energy production domestically (as shown in Fig. 1). Coal is mostly used for power generation in China and the coal-to-electricity strategy devises great effecton economic development of China and energy security [1 , 23]. China’s rapid economic development in current year stake great move to equilibrium of international energy market domicile and made China’s domestic coal arcade gradually increases that integrate into the international economy. Therefore, its coal price fluctuation is greatly influenced by the international coal market. As a biggest producer and buyer of coal in the world, China overtook Japan as the largest coal importer in 2012. The scope of the coal trade is essential to domestic coal supply and demand balance and plays a significant role in protecting strategic energy security of China. As the resilient association among coal rate and oil rate is a comparatively new portent, coal prices instability creates great impact on oil prices, which leads to impact great effect on global international energy market [2]. International oil market shocks often cause fluctuations in China’s coal price through imports and exports, which impacts the smooth operation of China’s macro-economy. In fact, since the implementation of China’s dual-track coal price system, the domestic coal market has experienced considerable volatility. In particular, around 2008 both domestic and international coal prices exhibited dramatic “roller coaster” type changes, which seriously shocked China’s energy market and economic output [3, 26]. Since 2011, due to the fatigue in international energy market and the impact of domestic coal imports, China’s coal price has experienced a persistent continuous decline. On this basis, it is necessary to study the long-term and short-term interactions of China’s coal price with international energy prices as well as the latter’s fuzzy price discovery function in order to avoid market risks and ensure the orderly operation of China’s coal market.

Fig. 1

China’s composition of total energy production in 2019.

Due to the increasing demand for coal in China and the rapid changes in international energy markets, the substitution effect with regard to energy resources and energy trade can lead to large changes in the influence energy prices have on each other. However, many current studies analyse coal price changes from the perspective of market supply and demand and economic development. There is no sufficient research on the interaction between China’s coal price and international energy prices. The marginal contribution of this paper is to analyse the relationship between China’s coal price and international energy prices, and to uncover the fuzzy mechanisms that trigger and stabilize fluctuations in coal price of China from the perception of external shocks, which is helpful to reveal the fuzzy price discovery function of international energy markets with regard to coal market of China. This research work aims to answer the subsequent interrogations: Is there a long-standing equilibrium association among the domestic or local coal, international or global coal and international crude (unpolished) oil prices? If this long-standing equilibrium association exists, what are the interactions and effects of the factors? Do international energy prices have a fuzzy price discovery function with regard to the domestic coal price?

The remainder of this research paper is arranged as follows: relevant research carried in this direction is brief in section 2; Section 3 demonstrate and explain the framework architecture and data description of proposed model; the empirical outcomes with discussion are provided in Section 4; The whole work with result analysis and future enhancement is concluded in in Section 5.

2 Related work

The fluctuation of coal price of China has long been a key issue in the field of energy economy research. Nowadays more attentions are paid to China’s stable coal-electricity price linkage and supply chain [10 , 25]. Numerous factors influence the price of coal, and many scholars at home and abroad have conducted extensive research from different perspectives. In [18], Kanamura et al. studied the volatility of energy prices from the perspective of equilibrium state in supply and demand model established the outline of the energy source curve determines the features of price fluctuations of energy. In [20], Guo et al. concluded that financial deterioration, extreme manufacture, low demand, alternatives, and port shares have been demonstrated qualitatively and quantitatively as the leading issues in the coal pricesdrop. Factors such as the low price elasticity of coal supply and demand, the economic cycle, market expectations, price fluctuations of alternative products and production costs lead to sharp fluctuations in the coal price. In addition, other scholars conducted extensive research on factors such as coal industry productivity, market structure, production delay, scarcity rent and government regulatory policy, claiming that these factors are related to coal price fluctuation [13 , 24].

Coal price is widely understood to be affected not only by price constituents such as production costs, resource taxes and transport but also mutually by energy substitutions and their different prices [4 , 19]. Adopting the multiple time series method, Mjelde et al. in [12] performed an empirical analysis of the wholesale spot price of US electricity and weekly prices of major power-generation fuels including natural gas, crude oil, and coal. In [14], Joëts et al. used the nonlinear panel cointegration method to study the relationship between coal, oil, natural gas and electricity prices. In fact, due to the interchangeability of energy products, the interactions between energy price systems vary due to differences in time and space. Adopting a wavelet analysis approach, Polanco et al. in [11] studied WTI advertisement price of crude oil dynamics against long-standing forth coming prices. In [17], Westgaard et al. noted that there is no long-standing balance association among the International Exchange (ICE) crude oil stocks price cost and the promotion price, as price deviations between the two may take several years or longer to return to equilibrium. In [6] Mohammadi et al. observed the long-standing equilibrium association and short-term price fluctuation dynamics among the price rate of the major three energy sources including crude oil, natural gas and coal. He believed that price of crude oil plays a leading role on a global scale, natural gas prices play a dominant role on a regional scale, and coal price is determined by long-term contract prices. Chan and Woo (2016) [7] used the threshold cointegration method to analyse the dynamic association among the Daqing crude oil price in China and WTI, Brent and Dubai crude oil prices. They observed that a with the existence of long-term equilibrium association between the domestic and international oil price, China has a definite control over domestic oil market.

3 Framework and data

To analyse the impact of international energy market shocks on domestic coal price fluctuations, this paper conducts empirical research as described below from the perspectives of long-term and short-term influence as well as fuzzy price discovery function. First, this study analyses the data stationarity of the prices of domestic coal, international coal and international crude oil using an augmented dickey-fuller (ADF) unit root test. Second, it constructs a vector auto regression (VAR) model and uses the Johansen cointegration test to study the long-term equilibrium relationship between the domestic coal price and international energy prices, and to analyse the degree and direction of the impact of the international energy market on the domestic coal price in order to as certain that in which direction the international energy market would lead the domestic coal price. Third, to enhance the accuracy of forecasting, we use fuzzy forecasting method through fuzzy linear regression. Fourth, applying a vector error correction (VEC) model to study the short-run effect of domestic coal price fluctuations, it analyses how fluctuations in the domestic coal price and international energy market can be amended through short-term adjustment under the condition of deviation from long-term equilibrium, and determines various factors’ scale of guidance capability and speed of adjustment with regard to domestic coal price fluctuation. Finally, it uses an impulse response function to analyse the dynamic interaction effect among the domestic coal price, international coal price and international crude oil price, and evaluate the price discovery function on. Figure 2 represent framework architecture of proposed fuzzy integrated vector regression (FVAR) model.

Fig. 2

Framework architecture of proposed Fuzzy Integrated Vector Regression (FVAR) Model.

3.1 Data Description

This paper selects indices representing the domestic coal price, international coal price and international crude oil price. The research sample includes 108 monthly data points from January 2005 to December 2013. The index selection and data processing occur as follows.

Domestic coal-price (cp) . The domestic coal price system is intricate. Because of the effect of coal source, excellence and conveyance links, it is difficult to obtain an average market price. The price of Qinhuangdao (China) coal is typically regarded as the barometer of domestic coal price fluctuations. Therefore, this paper takes the average FOB Qinhuangdao 5500 kcal/kg coal price to represent the domestic coal price. The data are sourced from the China Coal Resources Network.

International coal price (icp). The current international coal price catalog includes three groups: the BJ catalog, which replicates the drift of thermal coal- price in the market of Asia-Pacific;the rate catalog announced in global COAL trading platform; and the Platts coal price index. Based on the impact of China’s coal import sources, this paper selects FOB Newcastle, Australia, published in global COAL trading platform, as the index representing the international coal price.

International crude oil price (iop). The WTI futures price and Brent crude oil futures price are important pricing benchmarks in the global oil market.

For the sake of comparison, international coal price and international crude oil price are converted according to the monthly average exchange rate of the RMB against the US dollar. In this study, to remove the impact of heteroscedasticity and dimension, the above seasonally adjusted data are taken the natural logarithm and denoted as lncp, lnicp, lniop, respectively.

3.2 Unit root testing

In this step, analysis of time series is performed to scrutinize the integration order for all input variables utilized in the study. To analyze time series Augmented Dickey Fuller (ADF) and Phillips and Perron (PP) tests were performed to extract the stationary properties of domestic coal price(cp), international coal price and international crude oil price variables. Following equation is used to conduct unit root statistics test for cp, icp, andiop variables.

$Δ X_{t} = a + bt + {cx}_{t - 1} + \sum_{m = 1}^{l} δ Δ x_{t - m} + α_{t}$ (1) $t = 1, 2, \dots T$

Where,

x_t represent input variablestime series, a represent constant factor, b represent time trend coefficient, α_t represent error factor term and l represent number of lag computed during auto-regressive procedure. While c represent time series stationary deterministic coefficient that conduct two hypothesis (H₁, H₂)

$\begin{matrix} H_{1} : c = 0, x has unit test root \\ H_{2} : c = 0, time series x has stationary characterstics \end{matrix}$

3.3 Co-Integration testing

In this step estimation of long-run stability, of time series method is performed using Johansen Co-integration testing estimation represented by following equation $Δ x_{t} = {PC}_{0} + \prod x_{t - 1} + \sum_{m = 1}^{l - 1} Γ_{m} Δ x_{t - m} + α_{t}$ (2)

Where, x_t = [x_1t, x_2t, …, x_qt] represent (Q × 1) vector of time series data of input varaible, l represent number of lags, α_t represent error factor term, PC₀ represent (Q × 1) of constant values, ∏ represent (v × r) where v represent number of input variable and r represent number of co-integrating vector and is computed using foloowing equation: $\prod = \sum_{m = 1}^{l} {PC}_{m} - I$ (3)

Γ_m repressent coeffeceint matrix related to short-run dynamic paraphernalia and is computed using following equation: $Γ_{m} = - \sum_{n = m + 1}^{l} {PC}_{n}$ (4)

3.4 VAR model

The VAR model based on the unstructured method can effectively reflect the dynamic relationship between variables and therefore is widely used in dynamic analysis of economic systems. This paper builds the following VAR model for coal price fluctuations:

$x_{t} = {PC}_{0} + \sum_{m = 1}^{l - 1} {PC}_{m} x_{t - m} + {Ez}_{t} + α_{t}$ (3)

Where, x_t = [x_1t, x_2t, …, x_qt] represent (Q × 1) vector of time series data of input varaible, PC₀ represent (Q × 1) of constant values, l represent number of lags, PC_m represent (Q × Q) parametric coeffecient matrix, α_t represent error factor term, z_t = [z_1t, z_2t, …, z_ft] represent (F × 1) vector matrix of exogenous parametric variable and E represent (Q × F) parametric variable coefficient matrix. If x_t is not exaggerated by z_t = [z_1t, z_2t, …, z_ft] timeseriesof (F × 1) vector matrix of exogenous parametric variable then eq (3) can be re-written as: $x_{t} = {PC}_{0} + \sum_{m = 1}^{l - 1} {PC}_{m} x_{t - m} + α_{t}$ (4)

Lag period in VAR model is selected using Akaike Information criterion (AIC) (A) and Swartz Criteria (SC) (S) and is computed using following equation: $A = - \frac{2 u}{L} + \frac{2 v}{L}$ (5) $S = = - \frac{2 u}{L} + \frac{v ln L}{L}$ (6)

Where, v represent total number of parametric variable, L represent time-series sample length and u is computed using following equation: $u = - \frac{Lq}{2} (1 + ln 2 π) - \frac{L}{2} ln | \overset{⌢}{Σ} |$ (7)

Practically, the unit root ADF and PP test is used to determine the stationary time series, while the integration Johansen test is conducted to detect correlation and long-term stability. If the VAR model is steady and stable, then our study can carry on to forecast the coal price using Fuzzy regression model and error test using Vector error correction model.

3.5 Fuzzification VAR Model

After determining stationary and stable time series, in this step we determine parameter uncertainty with more accurate forecasting using fuzzy linear regression model and therefore time series x_t can be represented using fuzzy linear regression model equation:

$\tilde{X} = {\tilde{ω}}_{0} + {\tilde{ω}}_{1} y_{1} + {\tilde{ω}}_{2} y_{2} + \dots {\tilde{ω}}_{v} y_{v} = \sum_{m = 0}^{v} {\tilde{ω}}_{m} y_{m} = y^{'} \tilde{ω}$ (8)

Where, y represent vector of independent input variable, v represent number of input variable and ${\tilde{ω}}_{m}$ represent the fuzzy set of m^th parameter of model and is represent with probability distribution of L-type fuzzy number using following equation: $μ_{{\tilde{ω}}_{m}} (ω_{m}) = L {(∁_{m} - ω_{m} / γ)}$ (9)

The eq . (9) can be represented in triangular fuzzy number (TFN) using following equation:

$μ_{{\tilde{ω}}_{m}} (ω_{m}) = {\begin{matrix} 1 - \frac{| ∁_{m} - ω_{m} |}{γ_{m}}, ∁_{m} - γ_{m} ⩽ ω_{m} ⩽ ∁_{m} + γ_{m} \\ 0, otherwise \end{matrix}$ (10)

Where, $μ_{{\tilde{ω}}_{m}} (ω_{m})$ represent fuzzy membership function of parameter ω_m, _∁m represent center of fuzzy number, γ_m represent spread or width around fuzzy number center. Now we represent time series $x_{t} = y_{t}^{'} \tilde{ω}$ in the form fuzzy membership function using following equation: $μ_{\tilde{x}} (x_{t}) = {\begin{matrix} 1 - \frac{| x_{t} - y_{t} ∁ |}{γ^{'} | y_{t} |}, & if y_{t} \neq 0 \\ 1, & if y_{t} = 0 and x_{t} = 0 \\ 0, & if y_{t} = 0 and x_{t} \neq 0 \end{matrix}$ (11)

Where, ∁ and γ are center and spread of all model variable and t = 1, 2, … T represent number of observation for time series up to sample length L. $μ_{\tilde{x}} (x_{t}) = {Low (L), Medium (M), High (H)}$ represent linguistic fuzzy variable for input variable time series based on that coal price fluctuation is forecasted.

3.6 Vector error correction model

The co-integration equation (2) describes the long-term stability relationship between the time series, and it is essential to construct a VEC model to study the short-term effects of coal price fluctuation on commodity prices. Based on the co-integration theory, if there is a co-integration relationship between nonstationary variables, then these variables can be derived from the VAR lag model to form the VEC model to reflect the influence on short-term changes when the relationship between variables deviates from the long-term equilibrium state. According to the co-integration test and VAR model construction if there is a integration relationship between the I (1) sequences in x_t, and equation (2) can be rewritten as follows: $Δ x_{t} = {PC}_{0} + α_{1} α_{2}^{'} x_{t - 1} + \sum_{m = 1}^{l - 1} Γ_{m} Δ x_{t - m} + α_{t}$ (12)

Where, α₁, α₂ represent (v × r) matrix in which α₁ is coefficient adjustment factor and α₂ consist of co-integrating vectors, represent error correction factor which returns long-term steadiness associations between input variables, and equation (10) can be re-written as follows: $Δ x_{t} = {PC}_{0} + α_{1} + {ecf}_{t - 1} \sum_{m = 1}^{l - 1} Γ_{m} Δ x_{t - m} + α_{t}$ (13)

The eq (11) represent vector error correction model in which each equation represent error correction.

3.7 Impulse response function

The VAR, fuzzification and VEC determines the dynamics of the inter-relationships between the input variables and forecast coal price fluctuation.

Based on these forecasting of coal price fluctuation, impulse response function (IRF) determines impact of fluctuation on international energy market shocks.

4 Empirical results and discussion

In this section, we perform evaluation proposed FVAR model, first we computed unit roots for each variable using ADF and PP testing and determines the stationary and non-stationary level of each. In the formula, y_t = (lncp, lnicp, lniop) ^T, namely, y_t is a column vector that includes endogenous variables such as domestic and international coal price, and international crude oil price. According to data sample from January 2005 to December 2013, the paper establishes a VAR (2) model with two lagged periods. According to the testing results, the three equations in the VAR system have suitable goodness of fit. The fit coefficients of the lncp, lnicp and lniop equations are 0.966, 0.954 and 0.894, respectively. For the VAR system, the AIC and the SC value are small, and the reciprocal of the modulus of all characteristic roots is within the unit circle, which show that the system structure is stable. To avoid the problem of “false regression” in the traditional OLS estimation method, the paper performs an ADF unit root test on the stationarity of the original data In the ADF testing form of each index, the constants and time trend items are determined by the characteristics of each index data, and the lagging order is determined according to AIC and SC order-deciding criteria and LR statistics. An important problem in VAR model estimation is the determination of lag period: not enough lag period cannot fully reflect the dynamic relationship between variables, while too much lag period leads to a decrease of freedom, which affects the validity of model parameter estimation. The testing results of optimal autoregressive order p of the VAR model with a lag of 1 to 8 orders are shown in Table 1. At the 95% confidence level, the optimal lag time to meet FPE, AIC and HQ criteria is 2. Based on AIC criteria, this paper determines the optimal lag time of the model to be 2.The results of unit root testing are shown in Table 2.

Table 1
VAR model lag evaluation statistics

Lag LogL LR FPE AIC SC HQ

0 55.1811 NA 5.79e-05 –1.2424 –1.1556 –1.2075

1 339.1126 540.8219 8.32e-08 –7.7884 –7.4411* –7.6488

2 357.7390 34.1484 6.62e-08* –8.0176* –7.4099 –7.7733*

3 362.7172 8.7712 7.31e-08 –7.9218 –7.0537 –7.5729

4 368.9018 10.4549 7.84e-08 –7.8548 –6.7262 –7.4011

5 373.8974 8.0881 8.69e-08 –7.7595 –6.3704 –7.2011

6 386.1497 18.9619* 8.12e-08 –7.8369 –6.1874 –7.1738

7 394.3052 12.0391 8.40e-08 –7.8168 –5.9069 –7.0490

8 404.2566 13.9793 8.36e-08 –7.8394 –5.6691 –6.9670

Lag	LogL	LR	FPE	AIC	SC	HQ
0	55.1811	NA	5.79e-05	–1.2424	–1.1556	–1.2075
1	339.1126	540.8219	8.32e-08	–7.7884	–7.4411*	–7.6488
2	357.7390	34.1484	6.62e-08*	–8.0176*	–7.4099	–7.7733*
3	362.7172	8.7712	7.31e-08	–7.9218	–7.0537	–7.5729
4	368.9018	10.4549	7.84e-08	–7.8548	–6.7262	–7.4011
5	373.8974	8.0881	8.69e-08	–7.7595	–6.3704	–7.2011
6	386.1497	18.9619*	8.12e-08	–7.8369	–6.1874	–7.1738
7	394.3052	12.0391	8.40e-08	–7.8168	–5.9069	–7.0490
8	404.2566	13.9793	8.36e-08	–7.8394	–5.6691	–6.9670

Table 2

Unit root test outcome based ADF

Variable sequence	Test type (c,t,d)	ADF statistic	Critical value			Stationarity judgement
			a = 1%	a = 5%	a = 10%	Concomitant probability	Stationarity
lncp	(c,t,1)	–3.010970	–4.068290	–3.462912	–3.157836	0.1353	Nonstationary
d(lncp)	(c,t,0)	–7.213829	–4.068290	–3.462912	–3.157836	0.0000	Stationary
lnicp	(c,t,2)	–2.472758	–4.069631	–3.463547	–3.158207	0.3407	Nonstationary
d(lnicp)	(c,t,1)	–4.197868	–4.069631	–3.463547	–3.158207	0.0069	Stationary
lniop	(c,t,1)	–2.559917	–4.068290	–3.462912	–3.157836	0.2995	Nonstationary
d(lniop)	(c,t,0)	–6.431248	–4.068290	–3.462912	–3.157836	0.0000	Stationary

Note: The critical values of unit root test in this paper are all those in MacKinnon cointegration test.

Table 2 represent unit root testing out coming that shows that at the confidence levels: a = 1%, a = 5% and a = 10%, the sequences of lnCP, lnICP and lnIOP are nonstationary sequences, whereas sequences with a one-order difference are stationary ones, that is, they are integrations of order one I (1), indicating that there is a cointegration relationship between them.

4.1 Long-term effects of energy price correlation

The cointegration test is typically used to explain the long-run equilibrium relationship between variables. In the cointegration test of multivariate equation, the Johansen test method is typically believed to be more effective than the E-G two-step method (Johansen, 1991) [16]. From the ADF stationarity test, we can see that the variables lncp, lnicp and lniop are all sequences of integration of order one, satisfying the conditions of the cointegration test. Additionally, from the VAR lag order, we know that the lag time in the Johansen cointegration test is appropriately set at 2. Based on AIC and SC information criteria, we can verify that the sequences demonstrate a deterministic linear trend, and the cointegration equation has the intercept termand the trend term. The test results are shown in Table 3.

Table 3
Determination of the number of Johansen co-integration relationships

Null hypothesis Trace statistic Max-Eigenstatistic

Eigenvalue Statistic 5% Critical value P value Statistic 5% Critical value P value

None* 0.2639 43.4451 42.9153 0.0442 27.2663 25.8232 0.0321

At most 1 0.1246 16.1788 25.8721 0.4783 11.8481 19.3870 0.4294

At most 2 0.0475 4.3307 12.5180 0.6939 4.3307 12.5180 0.6939

Null hypothesis	Trace statistic	Max-Eigenstatistic
None*	0.2639	43.4451	42.9153	0.0442	27.2663	25.8232	0.0321
At most 1	0.1246	16.1788	25.8721	0.4783	11.8481	19.3870	0.4294
At most 2	0.0475	4.3307	12.5180	0.6939	4.3307	12.5180	0.6939

Note: *denotes rejection of the hypothesis at 5% significance level.

The test results show that only one cointegration relationship between the domestic coal price, international coal price and international crude oil price exists at the critical value of 5%. Based on the maximum trace statistics and the maximum eigenvalue statistics, the paper determines the corresponding cointegration equation as:

$\begin{matrix} lncp = 0.2873 \cdot lnicp - 0.1634 \cdot lniop + 0.00 71 \cdot \\ @ trend (05 m 01) + 5.1424 \end{matrix}$ (14)

According to the test results, there is a long-standing steady balance association among the domestic and international coal price as well as international crude oil price, and there is an obvious time trend. co-integration test proposed by Johansen shows that long-lasting effect in the international coal price have a large same-direction impact on the domestic coal price, while the international crude oil price shows a small reverse effect on domestic coal price fluctuation [29]. there will not be large changes in the long run in terms of coal serving as the basic source of energy [29].

4.2 Short-term effects of energy price correlation

At this stage, we use Eviews6.0 to obtain the following test results of the cointegration equation and the VEC model (see Equation (15)and Equation (16)) The testing reveals that both the AIC and SC of the model are very small, indicating that the overall effect of the model is significant. Meanwhile, according to the statistical coefficient of the error correction term, it fits the meaning of correction.

$\begin{matrix} {ecm}_{t} = {lncp}_{t} - 0.329 \cdot {lnicp}_{t} + 0.0 66 \cdot {lniop}_{t} \\ - 0.00 6 \cdot @ trend (05 m 01) - 4.309 \end{matrix}$ (15)

$\begin{matrix} [\begin{matrix} Δ ln {cp}_{t} \\ Δ ln {icp}_{t} \\ Δ ln {iop}_{t} \end{matrix}] = [\begin{matrix} - 0.2588 \\ - 0.3390 \\ - 0.5136 \end{matrix}] {ecm}_{t - 1} \\ + [\begin{matrix} 0.3770 \\ 0.5018 \\ 0.1713 \end{matrix} \begin{matrix} 0.1313 \\ - 0.1830 \\ - 0.00 10 \end{matrix} \begin{matrix} 0.0 554 \\ 0.2311 \\ 0.0 750 \end{matrix}] [\begin{matrix} Δ ln {cp}_{t - 1} \\ Δ ln {icp}_{t - 1} \\ Δ ln {iop}_{t - 1} \end{matrix}] \\ + [\begin{matrix} 0.0021 \\ 0.0004 \\ 0.0043 \end{matrix}] \end{matrix}$ (16)

The results show that the short-term fluctuation of the domestic coal price is affected not only by the long-term trend of change but also by the previous period’s domestic coal, international coal and international crude oil prices. Among the impacts, the previous period coal cost price variations have a higher effect on the present period coal price with an elasticity of 0.3770. Analysis reveals that the root causes of this are development inertia and market expectations with regard to domestic coal price fluctuation. When other conditions remain unchanged, the current period domestic coal price increases by 0.1313% on average for every 1% increase in the previous period international coal price, and the current period domestic coal price increases by 0.0554% for every 1% increase in the previous period global price of crude oil.

Based on ecf statistical results, when the domestic coal price in short-run differs from its long-run balance state, the mechanism of error correction will effect ln cp of one lagged period with the speed of –0.2588; after short-term error correction, it will ultimately achieve long-term equilibrium. In addition, comparison of the error correction effect of each equation in the VEC model shows that the error correction factor ecf coefficients in equations for input variable time series ln cp_t, ln icp_t and ln iop_t are–0.2588, –0.3390 and –0.5136, respectively, all of which have good correction effect. Among them, the error correction effect of ln cp_t is relatively small, indicating that the domestic coal market is less sensitive to a non-equilibrium response and has a slower adjustment speed than the international coal and crude oil markets [8].

According to the VEC model study and from test result, it is seen the domestic coal price is sensitive to unbalanced reaction and can influence domestic coal price fluctuation of lagged periods with a correction rate of –0.2588 before ultimately achieving long-term equilibrium [30]. In addition, due to the inertia of the domestic coal price and the impact of market expectations, previous period rate variations have a large effecton price rate fluctuation in the existing period, that is, former price levels play an amplified fuzzy price discovery and guidance role in current price fluctuation.

4.3 Guidance capability of energy price fluctuation

The impulse response function can directly reflect the dynamic interaction between the variables in the VAR system and their fuzzy guidance capability. To eliminate the synchronization-related problems of random error terms in different equations in the VAR model, this paper adopts the Cholesky decomposition method to provide the hypothetical impact of a standard deviation on lncp, lnicp and lniop, and obtain the impulse response function of the domestic coal price. The following figure is the impulse response function curve based on VAR and the analytic simulation, in which the solid line is the impulse function response value, representing the degree of change based on relevant influencing factors, the dotted line is the confidence interval of plus or minus two standard deviations, and the horizontal axis is the tracking period (unit: month). According to Fig. 2, there is a clear convergence effect in the impulse response function, which indicates its effectiveness.

Figure 3 - (1) -(2) represent shock impulse response curve that shows the effect of international coal and crude oil price shocks on the local level domestic coal price. According to the curve in Fig. 3 - (1) -(2), when the international coal price in current period is affected by the positive impact of one unit, the domestic coal price continues to increase in the first eight months, peaks in the eighth period (0.047) and then gradually decreases and tends to the value of 0. The international coal price can be considered to have a same-direction impact on the domestic coal price, namely, a deterioration in the global coal cost price directly leads to a lower domestic coal price. In contrast, the global crude oil cost price has a comparatively lesser effect on the fluctuation of the local coal price. When the international coal price in current period has a positive impact of one unit, the domestic coal price continues to grow in the first five months, peaks in thefifth period (0.027), and then slowly decreases and converges to a lower level.

Fig. 3

Impulse response curve of correlated variables.

Figure 3 - (3)-(4) represent shock impulse response curve that shows the effect of domestic (local) coal-price cost and international (global) crude oil price shocks on the international (global) coal-price. When the domestic coal price in current period has an impact of one unit, the international coal price fluctuates in the same direction as the domestic coal price in the first 12 months, peaks in the second month (0.038), and then decreases gradually and converges to a lower price. A reasonable explanation is that China is one of the world’s major coal importers and mainly plays a buyer’s role in the international coal market. Therefore, China should endeavour to expand its influence as much as possible in international energy markets. Next we present comparative analysis of impulse response curve of Fig. 3(4) with impulse response curve of Fig. 3(1) and impulse response curve of Fig. 3(2), Form comparison result it was deducing that effect of the international crude oil price over both domestic and the international coal price is same in term of degree and effectiveness. When the global crude oil price in existing period has encouraging effect of one unit, the international coal price continues to increase in the first five months, peaks in the fifth period (0.036), and then slowly decreases and converges to a lower level.

Figure 3-(5) ∼ (6) represent shock impulse response curve that shows the effect over international crude oil price instigated by the effect of domestic and international coal price shocks. From the Fig. 3-(5) ∼ (6), the global crude oil price impulse response instigated by a domestic(local) coal price shock appears to be relatively small, and the impact effectiveness is relatively short [27]. When the domestic coal price in current period has an impact of one unit, the international crude oil price peaks in the second period (0.030) and then slowly decreases and converges to the value of 0.On the contrary, the effect of the global coal price over the global crude oil and the domestic coal price is same demonstrating in both cases the feature of a two-stage change [28]. When the international coal price in current period has an impact of one unit, the international crude oil price peaks in the second period (0.056) and then slowly decreases and changes to a negative value in the 13th period.

With regard to domestic coal price fluctuation, due to the gradual liberalization of the international coal trade and the domestic coal market, the external shocks of international energy prices generate different degrees of same-direction influence on the domestic coal price through international trade, that is, the shocks of international energy prices are the reason why China’s coal price is continuously declining. Therefore, based on this conclusion, and in the light of domestic coal supply and demand and international energy price trends, the government should consider regulating the domestic coal market to promote its orderly operation.

The impulse response analysis shows that both the international coal and crude oil price have a same-direction effect on the domestic coal price, and their impact effectiveness is relatively long. In terms of the impulse response effect, the impact effect of international coal market changes on China’s coal price is larger than that of the international crude oil market. This result is consistent with the VEC test result, indicating that the international coal market plays a fuzzy guidance role in domestic coal price fluctuation than the international crude oil market and can generate stable guidance for the domestic coal price over a long period of time. We can safely assume that with the gradual advancement of the international coal trade and the reform of the domestic coal market, the external shocks of international energy prices will have different degrees of same-direction influence on the domestic coal price through international trade.

5 Concluding remarks

This paper implements methods including unit root testing, co-integration test, stability checking model (VAR), Fuzzification for more accuracy and error correction model and impulse response function to analyse the long-term and short-term correlation effects between the domestic coal price and international energy prices. From the perspective of fuzzy price discovery, it reveals the mechanism of coal price fluctuation in China, studies the dynamic interaction between the domestic coal price and international energy prices and quantitatively depicts the fuzzy discovery role of international energy markets with regard to domestic coal price fluctuation. The research conclusions are as follows:

To sum up, this paper suggests that domestic coal pricing should not only consider domestic supply and demand but also pay attention to the impact of international energy imports and exports. Most of the current domestic coal pricing models adopt a sampling statistic method to determine a spot index pricing model, which has the following disadvantages. First, because of the representation of the sample selection, its credibility is often questioned by both buyers and sellers. Second, these pricing models are lagged in time, making it difficult to reflect trends in market prices and are prone to periods of distortion. Third, the pricing cycle is cluttered, and contract price is often inconsistent with actual price. It is difficult for buyers and sellers to predict the spot price, thereby increasing the risks for upstream and downstream coal business operations. Considering the above-mentioned shortcomings of spot index pricing, this paper suggests referring to the mature experience of international energy futures pricing methods and establishing a fuzzy domestic coal pricing model based on futures index pricing as one option, that is, using the coal futures trade price as the fuzzy pricing basis and supplementing with the premium and discount agreed to by both the supply and demand sides to determine the fuzzy coal pricing mechanism (spot price = futures price + premium and discount). Not only can this fuzzy coal price stabilization mechanism compensate for the shortcomings of the current spot index pricing models, it also possesses the capability to guide forward prices. In the future, it may rely on national and regional coal trading centres to build an e-commerce platform to promote its application.

Funding

This work was supported by National Social Science Fund Late-funded Project (No.19FGLB057), National Natural Science Foundation of China (No.71974191), The Key Project of Social Science in Universities of Jiangsu (No.2017ZDIXM162), The Fundamental Research Funds for the Central Universities (No. 2020ZDPYSK05; No. 2020QN18), Jiangsu Postdoctoral Research Support Program, and China Postdoctoral Science Foundation (230081).

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