Table A.9: Johansen’s test results for the number (r) of cointegrating vectors: intercept and
time trend present, with cointegration restrictions on the trend parameters imposed
p |
r |
test |
crit. |
val. |
conclusions: |
test |
table(*) | |
10% |
5% | |||||||
6 |
0 |
18.2 |
16.9 |
19.2 |
reject |
accept |
lambda-max |
V |
1 |
6.7 |
10.6 |
23.5 |
accept |
accept |
’’ |
’’ | |
1 |
6.7 |
10.6 |
12.5 |
accept |
accept |
trace |
’’ | |
0 |
24.9 |
23.0 |
25.4 |
reject |
accept |
’’ |
’’ | |
1 |
0.00 |
2.71 |
3.84 |
accept |
accept |
trend restr |
. χ2(1) | |
r=1 |
r=0 | |||||||
8 |
0 |
27.2 |
16.9 |
19.2 |
reject |
reject |
lambda-max |
V |
1 |
7.9 |
10.6 |
23.5 |
accept |
accept |
’’ |
’’ | |
1 |
7.9 |
10.6 |
12.5 |
accept |
accept |
trace |
’’ | |
0 |
35.1 |
23.0 |
25.4 |
reject |
reject |
’’ |
’’ | |
1 |
2.06 |
2.71 |
3.84 |
accept |
accept |
trend restr |
. χ2(1) | |
r=1 |
r=1 |
(*) Cf. Johansen (1994). Table V applies if cointegration restrictions have been imposed on the trend
parameters. The χ2(1) test tests for cointegration restriction on the trend parameters, i.e., the hypothesis that there
is a linear trend in the cointegration relation rather than in the error correction model itself.
Table A.10: Johansen’s LR test of the hypothesis that
the space of cointegrating vectors is spanned by the
column of a 2× 1 matrix H (linear trend present)
HT: |
test |
conclusions |
5% | |
(1,-0.40) |
18.84 |
reject |
reject | |
(1,-0.50) |
16.32 |
reject |
reject | |
(1,-0.60) |
9.71 |
reject |
reject | |
(1,-0.65) |
3.86 |
reject |
reject | |
(1,-0.70) |
0.00 |
accept |
accept | |
(1,-0.75) |
3.78 |
reject |
accept | |
(1,-0.80) |
10.41 |
reject |
reject | |
(1,-0.90) |
17.65 |
reject |
reject | |
(1,-1.00) |
20.06 |
reject |
reject |
Additional references:
Newey,W.K. and K.D.West (1987), "A Simple Positive Definite Heteroskedasticity and
Autocorrelation Consistent Covariance Matrix", Econometrica 55, 703-708.
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