4.1 Sequence stability test
For the time series, before the establishment of the model, the stationarity test is firstly carried out for each variable sequence. In this paper, the Augmented Dickey Fuller (ADF) test method is adopted to carry out the unit root test for each sequence.
The results are shown in the Table 1. It can be seen that when the first difference is made for all variables, all sequences reject the null hypothesis at the significant level of 5%. Therefore, it can be concluded that all the time series are single-order integral sequences, and the co-integration relation test can be conducted for variables.
Table 1: Results ADF unit root test
Variables
|
ADF Test Statistic
|
Prob
|
Results
|
Variables
|
ADF Test Statistic
|
Prob
|
Results
|
P
|
-0.135322
|
0.6335
|
unstable
|
DP
|
-7.904807
|
0.0000*
|
stable
|
CP
|
-6.073856
|
0.0000*
|
stable
|
DCP
|
-12.60852
|
0.0000*
|
stable
|
CC
|
-4.929950
|
0.0001*
|
stable
|
DCC
|
-10.44614
|
0.0000*
|
stable
|
CS
|
-1.007333
|
0.3172
|
unstable
|
DCS
|
-6.888365
|
0.0000*
|
stable
|
OP
|
-2.496652
|
0.3288
|
unstable
|
DOP
|
-2.566435
|
0.0110**
|
stable
|
GP
|
4.717350
|
1.0000
|
unstable
|
DGP
|
-8.228740
|
0.0000*
|
stable
|
CI
|
-5.480379
|
0.0000*
|
stable
|
DCI
|
-9.811221
|
0.0000*
|
stable
|
CE
|
-6.280936
|
0.0000*
|
stable
|
DCE
|
-7.602765
|
0.0000*
|
stable
|
OI
|
-9.524977
|
0.0000*
|
stable
|
DOI
|
-9.709297
|
0.0000*
|
stable
|
Notes: D presents the first difference of variables; *** indicates 10% significant level; ** indicates 5% significant level; * indicates 1% significant level.
4.2 Co-integration test analysis
If the time series is not stationary, constructing the model directly may lead to the phenomenon of false regression. Therefore, it is necessary to use the co-integration analysis method to verify whether the causal relationship described by the regression equation is false regression. To determine whether a group of linear combinations of non-stationary time series have a co-integration relationship, that is, whether there is a long-term equilibrium relationship between variables. The basic condition for the existence of a co-integration relationship is that time series must be unstable, and all of them are of the same order. The co-integration test mainly includes EG measurement step method and Johansen co-integration test method, and the Johansen co-integration test method is adopted here. The co-integration relationship is determined by the characteristic root-trace test statistics.
Table 2: Results of Johansen cointegration test (Trace)
Hypothesized
No.of CE(s)
|
Eigenvalue
|
Trace
Statistic
|
0.05
Critical Value
|
Prob**
|
None*
|
0.840005
|
396.7909
|
197.3709
|
0.0000
|
At most 1*
|
0.781052
|
272.1732
|
159.5279
|
0.0000
|
At most 2*
|
0.589590
|
168.8865
|
125.6154
|
0.0020
|
At most 3*
|
0.441805
|
108.3258
|
95.75366
|
0.0051
|
At most 4
|
0.351361
|
68.67860
|
69.81889
|
0.0614
|
At most 5
|
0.278376
|
39.24283
|
47.85613
|
0.2507
|
At most 6
|
0.130979
|
17.05774
|
29.79007
|
0.6358
|
At most 7
|
0.101666
|
7.511388
|
15.49471
|
0.5190
|
At most 8
|
1.003243
|
0.220867
|
3.841466
|
0.6384
|
Notes: The Prob** means MacKinnon-Haug-Michelis P values and * denotes that the null hypothesis of a unit root is rejected at the 5% significant level
The results are shown in Table2. According to the results of the Johansen co-integration test, it can be obtained that, under the significant level of 5%, there are 4 co-integration relationships between these variables, and VEC model can be established for further analysis.
4.3 VEC model results
The VEC model results are shown in Table 3 and Eq (3). In the long run, coal consumption, imports and exports will have no impact on coal prices. Raw coal production and crude oil imports will have a positive impact on coal prices, that is, as raw coal production and crude oil imports increase, coal will increase. The negative impact of coal social inventory, natural gas production and crude oil production on coal prices is that the coal price will decline with the increase of coal social inventory, natural gas production and crude oil production.
Table 3: The long run relationship of VEC model results
Cointegrating
|
P(-1)
|
CC(-1
|
CE(-1)
|
CI(-1)
|
CP(-1)
|
CS(-1)
|
GP(-1)
|
OI(-1)
|
OP(-1)
|
C
|
CointEq1
|
1.0000
|
0.0000
|
0.0000
|
0.0000
|
-0.0040
|
0.1003
|
10.4423
|
-0.1394
|
0.1823
|
-1927.726
|
(-0.4737)
|
5.0392
|
(5.7679)
|
(-2.7593)
|
(0.4754)
|
CointEq2
|
0.0000
|
1.0000
|
0.0000
|
0.0000
|
0.4314
|
-0.6814
|
85.1845
|
-1.1012
|
26.8773
|
-89673.57
|
(1.5618)
|
(-1.0427)
|
(1.4330)
|
(-0.6638)
|
(2.1354)
|
CointEq3
|
0.0000
|
0.0000
|
1.0000
|
0.0000
|
-0.0732
|
-0.0578
|
3.8080
|
-0.0620
|
1.0345
|
61.7661
|
(-4.6213)
|
(-1.5423)
|
(1.1166)
|
(-0.6510)
|
(1.4326)
|
CointEq4
|
0.0000
|
0.0000
|
0.0000
|
1.0000
|
-1.6568
|
-1.6786
|
-31.7376
|
2.6580
|
39.4663
|
-17447.69
|
(-6.2399)
|
(-2.6721)
|
(-0.5554)
|
(1.6668)
|
(3.2620)
|
In the short term, it is can be seen in the Eq (3), the error correction term coefficient is negative, indicating that the error correction mechanism is consistent with the error correction mechanism, and the error will return to the equilibrium state at a faster speed after it deviates from the long-term equilibrium in a short term. In the short term, coal consumption will have a significant impact on coal prices, but to a very small degree. Coal exports and crude oil imports do not have a significant impact on coal prices. The social stocks of coal will have a positive to negative impact on the price of coal. Natural gas production and crude oil production will have a positive impact on coal prices, and the impact will be large. Raw coal output and raw coal import will have negative and positive effects on coal price respectively, and the impact range will be relatively small.
4.4 Grange causality test
Grange causality test is essentially to test whether the lagged variables of one variable can be introduced into the equation of other variables. If a variable is later affected by other variables, it is said that there is a Grange causality between them.
Table 4: The VEC model Granger causality test
Dependent variable :D(P)
|
Excluded
|
Chi-qs
|
Df
|
Prob
|
D(CC)
|
17.79008
|
4
|
0.0014*
|
D(CE)
|
2.940136
|
4
|
0.5679
|
D(CI)
|
13.50939
|
4
|
0.0090*
|
D(CP)
|
10.68510
|
4
|
0.0303**
|
D(CS)
|
12.03389
|
4
|
0.0171**
|
D(GP)
|
9.008979
|
4
|
0.0609***
|
D(OI)
|
10.71410
|
4
|
0.0300**
|
D(OP)
|
10.92092
|
4
|
0.0275**
|
All
|
56.99555
|
32
|
0.0042*
|
Notes: * indicates significant at 1%; ** indicates significant at 5%; *** indicates significant at 10%.
According to the results of Grange test, D(CC) and D(CI) are the Granger causes of D(Y) at the significance level of 1%. At the significant level of 5%, D(CP), D(CS), D(OI) and D(OP) are the Granger causes of D(Y). At the significant level of 10%, D(GP) is the Granger cause of D(Y).
4.5 Variance decomposition
Variance decomposition is used to describe the relative importance of impacts of various variables in the VAR model to the dynamic change of system variables. The main idea is to decompose the prediction mean variance of the system into the contribution rate constituted by the impact of itself and other variables according to its causes, so as to understand the relative importance of impacts of various variables to the endogenous variables of the model. The contribution of each variable to the variance of coal price was investigated, and the lag period was set as 30.The result is shown in the figure.
From the results of variance decomposition, it can be seen that in the first phase, the explanatory power of coal prices was 100%. With the advance of time, the explanatory of coal prices to coal prices gradually declined, while the explanatory of other factors to coal prices gradually increased. In the eighth cycle, coal prices had fallen to 24 % of their explanatory, while other factors had contributed a total of nearly 76 %. Around the 20th period, the explanatory of each variable gradually stabilized and remained unchanged. Coal prices accounted for about 24%, coal stocks accounted for about 27%, natural gas production accounted for about 20%, oil production accounted for about 11%, and other factors accounted for a total of 18%.
Table 5: The variance decomposition of P
Period
|
P
|
CC
|
CE
|
CI
|
CP
|
CS
|
GP
|
OI
|
OP
|
1
|
100.0000
|
0.000000
|
0.000000
|
0.000000
|
0.000000
|
0.000000
|
0.000000
|
0.000000
|
0.000000
|
2
|
80.36801
|
5.805125
|
0.910672
|
1.876265
|
0.349756
|
2.712774
|
5.787761
|
0.072153
|
2.117489
|
3
|
62.75808
|
8.574931
|
2.203329
|
1.393288
|
0.413048
|
2.392311
|
14.65765
|
3.259115
|
4.348250
|
4
|
45.49970
|
8.012802
|
1.756743
|
4.094604
|
0.322913
|
13.23010
|
16.24581
|
4.962758
|
5.874570
|
5
|
35.43658
|
10.09418
|
1.159429
|
2.738451
|
1.041533
|
25.65979
|
14.32121
|
3.233524
|
6.315307
|
6
|
32.87869
|
13.55536
|
1.398162
|
1.918404
|
1.463870
|
23.29869
|
16.93726
|
2.233882
|
6.315680
|
7
|
27.75056
|
14.42978
|
1.593527
|
1.953936
|
1.589952
|
22.17856
|
22.89983
|
1.687695
|
5.916166
|
8
|
24.68631
|
14.28549
|
2.628148
|
1.516861
|
1.576359
|
24.47068
|
22.92160
|
2.016881
|
5.897672
|
9
|
24.65431
|
13.04923
|
3.301093
|
1.298451
|
1.391789
|
26.98393
|
19.97010
|
3.431878
|
5.919203
|
10
|
24.78043
|
11.64138
|
3.384098
|
1.216567
|
1.199970
|
28.49765
|
18.67566
|
4.230781
|
6.373465
|
11
|
25.05037
|
10.15543
|
3.331463
|
1.007145
|
1.103830
|
29.17649
|
18.24350
|
4.569873
|
7.361901
|
12
|
25.60609
|
8.696586
|
3.377327
|
0.890735
|
1.117025
|
29.07900
|
17.50257
|
4.809743
|
8.920932
|
13
|
25.46755
|
7.422059
|
3.333597
|
0.909102
|
1.571118
|
28.89457
|
16.96959
|
5.435859
|
9.996554
|
14
|
25.01667
|
6.640862
|
3.319861
|
0.800260
|
1.873241
|
28.63237
|
17.23023
|
5.928469
|
10.55804
|
15
|
24.70398
|
5.977663
|
3.179060
|
0.717390
|
1.889170
|
28.40313
|
17.91892
|
6.426419
|
10.78426
|
16
|
24.59823
|
5.436458
|
3.007720
|
0.646555
|
1.883961
|
28.17830
|
18.39465
|
6.789526
|
11.06460
|
17
|
24.69897
|
5.133289
|
2.851455
|
0.584943
|
1.951531
|
27.97506
|
18.64128
|
6.883552
|
11.27992
|
18
|
24.54874
|
5.042876
|
2.734160
|
0.537472
|
2.091740
|
27.45710
|
19.13788
|
7.078356
|
11.37168
|
19
|
24.32914
|
5.172474
|
2.625872
|
0.520574
|
2.204027
|
27.09364
|
19.68928
|
7.199000
|
11.16600
|
20
|
24.41072
|
5.479558
|
2.595919
|
0.521273
|
2.208682
|
26.75157
|
19.90653
|
7.185717
|
10.94003
|
21
|
24.62136
|
5.768433
|
2.613990
|
0.554655
|
2.199605
|
26.55444
|
19.76607
|
7.160616
|
10.76083
|
22
|
24.53602
|
6.038671
|
2.669565
|
0.576716
|
2.202640
|
26.51757
|
19.69694
|
7.038019
|
10.72386
|
23
|
24.39380
|
6.215047
|
2.736063
|
0.591897
|
2.202989
|
26.64966
|
19.56407
|
6.895071
|
10.75140
|
24
|
24.35269
|
6.249165
|
2.800814
|
0.610605
|
2.187337
|
26.82790
|
19.36065
|
6.765451
|
10.84538
|
25
|
24.38195
|
6.164497
|
2.837605
|
0.631286
|
2.190060
|
27.01671
|
19.19137
|
6.635291
|
10.95123
|