Table 1: Summary statistics for the WTI price.
|
Mean
|
Std.dev.
|
Minimum
|
Maximum
|
Skewness
|
Kurtosis
|
price
|
70.5600
|
22.3256
|
26.19
|
145.31
|
0.4569
|
-0.5630
|
Table 2: Descriptive statistics of the IMF Constituents and the residual.
|
Mean
|
Correlation coefficient
|
Variance
|
Variance percentage (%)
|
IMF1
|
0.0034
|
0.0385 **
|
0.7824
|
0.1378
|
IMF2
|
-0.0089
|
0.0672 ***
|
1.0578
|
0.1863
|
IMF3
|
0.0089
|
0.0673 ***
|
2.0634
|
0.3635
|
IMF4
|
-0.0025
|
0.0874 ***
|
3.2350
|
0.5699
|
IMF5
|
0.0182
|
0.2835 ***
|
6.8539
|
1.2073
|
IMF6
|
0.2988
|
0.4000 ***
|
40.4483
|
7.1252
|
IMF7
|
2.9592
|
0.4376 ***
|
104.3398
|
18.3800
|
IMF8
|
-0.6237
|
0.4780 ***
|
130.1268
|
22.9225
|
IMF9
|
-1.2630
|
0.4749 ***
|
102.0168
|
17.9708
|
Resid
|
76.7175
|
0.3147 ***
|
176.7577
|
31.1367
|
Total
|
|
|
567.6819
|
100.0000
|
Note: *denote significance at the 10% level. **denote significance at the 5% level. ***denote significance at the 1% level.
Table 3: Test results for the impacts of significant events on the shock from extreme events.
Number
|
Actual time
|
Number
|
Actual time
|
Number
|
Actual time
|
1
|
2004/3/25
|
2
|
2004/9/7
|
3
|
2005/3/8
|
4
|
2005/4/7
|
5
|
2005/5/18
|
6
|
2005/7/15
|
7
|
2006/2/23
|
8
|
2006/4/20
|
9
|
2006/10/2
|
10
|
2007/3/26
|
11
|
2007/5/10
|
12
|
2007/6/27
|
13
|
2007/7/27
|
14
|
2007/8/31
|
15
|
2007/10/23
|
16
|
2008/2/13
|
17
|
2008/4/25
|
18
|
2008/8/29
|
19
|
2008/11/3
|
20
|
2009/5/27
|
21
|
2010/4/9
|
22
|
2010/11/16
|
23
|
2011/3/1
|
24
|
2011/7/12
|
25
|
2011/12/1
|
26
|
2012/4/18
|
27
|
2012/8/30
|
28
|
2013/4/9
|
29
|
2013/5/21
|
30
|
2013/6/27
|
31
|
2013/10/8
|
32
|
2014/4/10
|
33
|
2014/7/16
|
34
|
2014/8/20
|
|
|
|
|
Table 4: The comparison of SVM-type models and ARIMA-type models.
Model
|
MSE
|
MAE
|
MAPE
|
|
The ARIMA model
|
0.5923
|
0.6364
|
2.8590
|
51.59%
|
The cluster analysis model with VCE
|
0.5278
|
0.6135
|
2.5097
|
51.02%
|
The CEEMD-ARIMA model
|
0.4207
|
0.5434
|
2.3086
|
50.68%
|
The SVM model
|
0.3070
|
0.4235
|
3.6458
|
49.39%
|
The CEEMD-SVM model without structural breaks
|
0.3054
|
0.4224
|
3.6364
|
49.39%
|
The CEEMD-SVM model with structural breaks
|
0.2944
|
0.4107
|
3.5504
|
49.70%
|
TABLE 5: The comparison of CEEMD-ARIMA-SVM model.
Model
|
MSE
|
MAE
|
MAPE
|
|
The CEEMD-ARIMA- SVM model without structural breaks
|
0.1604
|
0.3098
|
2.2408
|
50.68%
|
The CEEMD-ARIMA -SVM model with structural breaks
|
0.1404
|
0.3490
|
1.6991
|
50.64%
|
TABLE 6: The loss function values of multi-situations without structural breaks.
|
The CEEMD-ARIMA-SVM model without structural breaks
|
Test set
|
MSE
|
MAE
|
MAPE
|
|
September 18, 2014 to May 23, 2018
|
0.2252
|
0.4029
|
3.1096
|
49.24%
|
September 18, 2014 to October 15, 2018
|
0.2046
|
0.3744
|
2.8279
|
49.80%
|
September 18, 2014 to March 14, 2019
|
0.1871
|
0.3486
|
2.5925
|
50.09%
|
September 18, 2014 to August 7, 2019
|
0.1729
|
0.3293
|
2.3997
|
51.15%
|
September 18, 2014 to December 31, 2019
|
0.1604
|
0.3098
|
2.2408
|
50.68%
|
TABLE 7: The loss function values of multi-situations with structural breaks.
|
The CEEMD-ARIMA-SVM model with structural breaks
|
Test set
|
MSE
|
MAE
|
MAPE
|
|
September 18, 2014 to May 23, 2018
|
0.1711
|
0.3878
|
2.1436
|
47.71%
|
September 18, 2014 to October 15, 2018
|
0.1614
|
0.3756
|
1.9897
|
48.43%
|
September 18, 2014 to March 14, 2019
|
0.1521
|
0.3632
|
1.8610
|
48.84%
|
September 18, 2014 to August 7, 2019
|
0.1457
|
0.3554
|
1.7564
|
50.00%
|
September 18, 2014 to December 31, 2019
|
0.1404
|
0.3490
|
1.6991
|
50.64%
|