Table 1 Summary statistics

Mean

0.332

0.275

0.411

0.244

0.168

0.297

0.31

0.229

Variance

0.042

0.018

0.027

0.016

0.007

0.025

0.028

0.014

Skewness

4.847***

2.487***

1.616***

2.784***

2.352***

2.975***

2.340***

2.661***

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

Kurtosis

42.721***

12.187***

5.171***

11.613***

8.638***

15.606***

10.486***

12.124***

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

JB

268663.762***

24255.651***

5205.988***

23221.302***

13542.539***

39051.474***

18460.757***

24544.847***

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

ERS

−6.694***

−5.529***

−4.429***

−7.011***

−5.191***

−9.587***

−11.443***

−6.323***

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

Q(20)

21489.650***

21963.781***

13290.228***

19714.223***

15742.101***

12794.413***

6777.043***

13134.576***

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

\(Q^2(20)\)

11714.631***

14952.371***

7831.009***

16963.601***

12407.747***

6003.273***

4022.247***

10190.779***

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

Pearson correlation coefficients

Crude oil

1.00

0.79

0.31

0.36

0.27

0.27

0.28

0.36

Heating oil

0.79

1.00

0.33

0.38

0.28

0.27

0.27

0.34

Natural gas

0.31

0.33

1.00

0.23

0.25

0.26

0.19

0.22

Copper

0.36

0.38

0.23

1.00

0.42

0.41

0.32

0.31

Gold

0.27

0.28

0.25

0.42

1.00

0.68

0.31

0.37

Silver

0.27

0.27

0.26

0.41

0.68

1.00

0.33

0.39

Palladium

0.28

0.27

0.19

0.32

0.31

0.33

1.00

0.45

Platinum

0.36

0.34

0.22

0.31

0.37

0.39

0.45

1.00