Modeling and Prediction of the Volatility of the Freight Rate in the Roadway Freight Market of China
Table 1
Statistical description of the volatility.
R_CTG
R_CTK
R_CTQ
R_GTC
R_GTK
R_GTQ
R_KTC
R_KTG
R_KTQ
R_QTC
R_QTG
R_QTK
Sample size
21254
20019
21094
26098
22213
21689
28087
27067
21683
27094
23090
21924
Mean
1.585
1.299
1.271
1.313
1.401
1.621
2.071
1.519
2.237
1.774
2.797
2.015
Median
0.972
1.016
0.936
1.047
0.88
1.071
0.96
0.915
0.925
1.215
0.987
0.941
Maximum
11.647
5.25
4.056
4.329
6.614
12.837
15.925
8.075
14.683
10.387
33.24
28.715
Minimum
0.123
0.134
0.178
0.196
0.127
0.098
0.048
0.086
0.089
0.049
0.056
0.123
SD
1.87
0.936
0.925
0.935
1.39
2.156
3.128
1.642
3.16
2.158
6.091
4.205
Skewness
3.434
1.873
1.334
1.65
2.274
3.495
3.045
2.434
2.539
2.516
3.956
5.373
Kurtosis
18.023
7.738
4.188
5.531
8.356
16.793
12.591
9.01
9.407
9.174
18.563
34.03
J–B
568.468 (0.000)
75.995 (0.000)
17.759 (0.000)
36.046 (0.000)
102.868 (0.000)
498.182 (0.000)
268.934 (0.000)
124.626 (0.000)
139.225 (0.000)
132.187 (0.000)
634.989 (0.000)
2246.588 (0.000)
ADF (lags)
−8.111[0]
−9.925[0]
−4.005[0]
−5.997[0]
−9.125[0]
−8.010[0]
−5.197[0]
−5.550[0]
−8.748[0]
−8.949[0]
−3.498[0]
−7.751[0]
Q (5)
6.929 (0.226)
8.335 (0.139)
8.265 (0.142)
11.594 (0.053)
7.066 (0.216)
2.673 (0.750)
3.456 (0.630)
5.741 (0.332)
4.720 (0.451)
7.272 (0.201)
2.106 (0.834)
1.780 (0.879)
Q (10)
9.004 (0.532)
11.721 (0.304)
16.683 (0.182)
15.829 (0.105)
8.545 (0.576)
14.346 (0.158)
4.847 (0.901)
7.505 (0.677)
11.622 (0.311)
8.596 (0.571)
3.907 (0.951)
3.037 (0.981)
LM (lag = 1)
2.236 (0.036)
4.745 (0.000)
4.152 (0.001)
4.367 (0.000)
3.165 (0.005)
2.78 (0.011)
2.115 (0.027)
2.881 (0.009)
2.957 (0.010)
3.392 (0.041)
2.153 (0.041)
2.229 (0.037)
-values are reported in parentheses. SD represents the standard deviation. J–B represents the Jarque–Bera test in which a goodness-of-fit test is performed for examining whether the time series follows a normal distribution [30]. Q (5) and Q (10) are the statistics of the Ljung–Box test [31] in which there is a serial autocorrelation for the series up to fifth and tenth orders. ADF represents the Augmented Dickey–Fuller (ADF) test with a null hypothesis of existence of autocorrelation in the sample series [32].
