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Periodic Time Series Models$

Philip Hans Franses and Richard Paap

Print publication date: 2004

Print ISBN-13: 9780199242023

Published to Oxford Scholarship Online: August 2004

DOI: 10.1093/019924202X.001.0001

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(p.126) Appendix B Critical values of the Johansen trace statistics

(p.126) Appendix B Critical values of the Johansen trace statistics

Source:
Periodic Time Series Models
Publisher:
Oxford University Press

Table B.1 Quantiles of the Johansen trace statistics in the case of no deterministic elements

q

80%

90%

95%

99%

1

1.89

2.98

4.14

7.02

2

8.41

10.35

12.21

16.16

3

18.83

21.58

24.08

29.19

4

33.10

36.58

39.71

46.00

5

51.25

55.54

59.24

66.17

6

73.27

78.30

82.61

91.12

7

99.12

104.93

109.93

119.58

8

128.61

135.16

140.74

151.70

Source: Johansen (1995, Table 15.1).

(p.127)

Table B.2 Quantiles of the Johansen trace statistics for restricted intercept parameters under H 0

q

80%

90%

95%

99%

1

5.85

7.50

9.13

12.73

2

15.31

17.79

19.99

24.74

3

28.65

31.88

34.80

40.84

4

45.86

49.92

53.42

60.42

5

66.92

71.66

75.74

83.93

6

91.75

97.17

101.84

111.38

7

120.52

126.71

132.00

142.34

8

152.75

159.74

165.73

177.42

Source: Johansen (1995, Table 15.2).

Table B.3 Quantiles of the Johansen trace statistics for unrestricted intercept parameters under H 0

q

80%

90%

95%

99%

1

1.64

2.71

3.84

6.64

2

11.06

13.31

15.34

19.69

3

23.72

26.70

29.38

34.87

4

40.08

43.83

47.21

53.91

5

60.23

64.74

68.68

76.37

6

84.10

89.37

93.92

102.95

7

111.79

117.73

123.04

133.04

8

143.19

149.99

155.75

166.95

Source: Johansen (1995, Table 15.3).

(p.128)

Table B.4 Quantiles of the Johansen trace statistics for restricted trend parameters under H 0

q

80%

90%

95%

99%

1

8.59

10.56

12.39

16.39

2

20.22

22.95

25.47

30.65

3

35.58

39.08

42.20

48.59

4

54.73

58.96

62.61

70.22

5

77.65

82.68

86.96

95.38

6

104.29

110.00

114.96

124.61

7

134.77

141.31

146.75

157.53

8

168.85

176.13

182.45

194.12

Source: Johansen (1995, Table 15.4).

Table B.5 Quantiles of the Johansen trace statistics for unrestricted trend parameters under H 0

q

80%

90%

95%

99%

1

1.64

2.71

3.84

6.64

2

13.53

15.94

18.15

22.78

3

28.28

31.57

34.56

40.61

4

46.41

50.67

54.11

61.28

5

68.76

73.62

77.79

86.11

6

94.43

99.97

104.76

114.23

7

123.95

130.39

135.66

146.05

8

157.25

164.24

170.15

181.62

Source: Johansen (1995, Table 15.5).