Series

S/No

Statistic

Mean

Median

True Value

Estimated Value

Min

Max

Skewness

Kurtosis

JB

value

Q*

Estimate of Test Statistic

Decision

at

5% level

σ 2

S 2

γ 1

γ 2

( n 1 ) S X t 2 2 2 σ ^ 0 4

( n 1 ) S X t 3 2 15 σ ^ 0 6

1

X t

0.0000

−0.0011

1.0000

1.0000

−2.05

2.39

0.11

−0.60

1.70

1.05

-

-

Do not Reject

X t 2

0.9900

0.5866

2.0000

1.3546

0.00

5.71

1.82

3.60

109.21

6.33

67.05

-

X t 3

0.1079

0.0000

15.0000

7.8106

−8.60

13.66

1.63

8.73

361.84

2.55

-

51.55

2

X t

0.0000

0.0131

1.0000

1.0000

−2.09

2.43

0.08

−0.69

2.09

0.43

-

-

Do not Reject

X t 2

0.9900

0.4951

2.0000

1.2681

0.00

5.90

1.72

3.39

97.19

5.04

62.77

-

X t 3

0.0753

0.0000

15.0000

7.1472

−9.12

14.32

1.05

9.38

384.98

0.21

-

47.17

3

X t

0.0000

0.2008

1.0000

1.0000

−2.29

2.07

−0.16

−0.61

1.98

3.25

-

-

Do not Reject

X t 2

0.9900

0.5060

2.0000

1.3493

0.00

5.25

1.79

2.74

84.68

4.84

66.79

-

X t 3

−0.1592

0.0096

15.0000

7.7045

−12.03

8.93

−0.74

6.30

174.50

5.80

-

50.85

4

X t

0.0000

−0.0543

1.0000

1.0000

−3.07

−2.88

−0.06

0.41

0.76

0.45

-

-

Do not Reject

X t 2

0.9900

0.4760

2.0000

2.3030

0.00

9.44

3.27

13.81

972.87

2.56

114.00

-

X t 3

−0.0627

−0.0002

15.0000

19.0055

−28.99

23.90

−1.32

28.04

3305.05

0.60

-

125.43

5

X t

0.0000

0.0399

1.0000

1.0000

−2.75

3.13

−0.03

0.46

0.90

1.64

-

-

Reject

X t 2

0.9900

0.4353

2.0000

2.3529

0.00

9.77

3.30

13.82

977.30

2.80

116.47

-

X t 3

−0.0284

0.0001

15.0000

19.6277

−20.83

30.54

1.88

27.99

3323.24

2.59

-

129.54

6

X t

0.0000

0.1302

1.0000

1.0000

−2.74

3.07

−0.15

0.52

1.50

3.00

-

-

Reject

X t 2

0.9900

0.4605

2.0000

2.4129

0.00

9.42

3.12

11.80

742.41

2.56

119.44

-

X t 3

−0.1487

0.0023

15.0000

19.5947

−20.47

28.92

1.40

23.91

2414.70

0.23

-

129.33