Nonparametric cointegration analysis



Table A.3 : Unit :

root and

trend stationarity tests for

the extended

Nelson-

Plosser data

Test :

Phillips

Bierens-Guo Cauchy

tests

(abs. values)

Bierens'

higher-order sample

-

Perron

autocorrelation t

ests (*

=detr.)

Variable

n

PPl

PP2

BGl

BG2

BG3

BG4

BG5

BG6

B(1,1)

B(2,2) B

* (1, D

B*(2,2)

concl.

LN[CPI]

129

2.29

-0.79

51.24

71.10

54.85

25.64

16.69

20.67

-16641

-6.15

-1.68

-8.49

UR?

LN[GNPDEFL]

100

1.43

-5.12

62.54

89.62

125.46

51.56

36.05

7.46

-10000

-3.85

-3.24

-9.71

UR?

LN[EMPLOY]

99

-0.27

-10.87

56.07

98.98

73.78

71.74

0.47

0.47

-0.86

-4.73

-43.20

-45.25

TST

LN[UNEMPLOY]

99

-21.35

-21.49

1.58

1.58

1.66

1.68

0.68

3.50

-2057

-2121

-2067

-2136

TST

LN[GNP]

80

0.56

-5.22

42.90

79.67

116.43

69.42

11.60

181.97

-0.04

-4.40

-2.87

-4.48

UR

LN[GNPPCAP]

80

0.16

-9.66

39.78

80.00

24.51

27.90

2.72

1.26

-0.91

-4.21

-90.71

-93.55

TST

LN[RealGNP]

80

0.17

-9.12

40.97

80.00

70.56

79.91

3.87

1.33

-0.27

-3.21 -

133.33

-137.51

TST

LN[WAGE]

89

0.47

-6.96

46.26

88.80

148.13

76.72

10.08

5.60

-0.01

-3.22

-5.89

-8.93

UR

LN[RealWAGE]

89

-0.73

-4.95

35.04

88.29

60.68

49.80

9.55

1.64

-0.63

-1.82

-10.79

-26.87

?

LN[INDPROD]

129

-0.48

-16.99

81.62

128.75

128.77

151.27

7.07

1.70

-0.67

-3.48

-16641

-16641

TST

LN[MONEY]

100

0.22

-9.21

60.68

99.99

421.71

158.28

6.00

2.14

-0.08

-3.58

-10.31

-14.18

?

INTEREST

89

-1.52

-4.39

112.42

86.44

5.12

5.03

24.49

4.64

-7921

-16.32

-1.80

-27.37

?

LN[STOCKPR]

118

1.42

-6.50

84.65

115.95

27.10

29.56

17.55

7.67

-13924

-5.51

-2.92

-5.66

UR?

LN[VELOCITY]

120

-4.19

-2.82

9.23

10.25

8.19

14.18

21.56

46.71

-3.20

-3.26

-2.08

-5.47

UR

LN[RealM]

100

-1.09

-7.66

54.73

97.32

188.25

195.08

8.44

5.17

-0.97

-3.81

-14.87

-19.14

TST?

RealINTEREST

89

-29.23

-29.30

4.03

4.03

4.05

4.05

0.39

0.81

-7921

-7921

-7921

-7921

ST

INFLATION

128

-46.30

-40.10

1.53

1.53

1.60

1.63

0.42

1.44

-13.63

-15.90

-17.91

-19.53

ST

5% R.R.

<-14.0

<-21.5

>12.71

>12.71

>12.71

>12.71

>12.71

>12.71

<-14.0

<-15.7

<-20.6

<-22.4

10% R.R.

<-ll .2

<-18.1

>6.31

>6.31

>6.31

>6.31

>6.31

>6.31

<-ll .2

<-13.1

<-17.1

<-18.9

H0:

UR

UR

ST

ST

ST

ST

TST

TST

UR

UR

UR

UR

H1:

ST

TST

UR

UR

UR

UR

UR

UR

ST

ST

TST

TST

Remarks : The

first two test are

the Phillips-

Perron t

ests Za

of the

null hypothesis

H0: y(t)

= y(t-

■1) + u (t) , E [u (t) ]

0, u(t) is alpha

-mixing,

against

the alternatives y(t

) = c +

u(t) and y(t)

= c + b.

t + u(t)

, respectively.

. The next s

tests are the

Bierens-Guc

'zs (1993) tests of the null

hypothe

sis H0:

y(t) =

c (+ d.t

) + u(t),

, E[u(t)]=0, u(

t) is alpha-

mixing, against the unit root (with drift) hypothesis. The Phillips-Perron tests and Bierens-GuozS test no. 4 employ a
Newey and West (1987) type variance estimator with truncation parameter m = [5n0,2] . The last four tests are Bierens
(1993) unit root tests on the basis of higher order sample autocorrelations. The first two test the unit root hypothesis
against stationarity, and the last two have as alternative linear trend stationarity. These four tests depend on
parameters μ > O,
a > O, and O < δ < 1, and the lag length is: m = 1+[αnδμz3μ+21 ] . The default values μ = 2, a = 5 and δ
= .5 are employed.

60



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