# [Gretl-users] Johansen

Allin Cottrell cottrell at wfu.edu
Wed Jan 3 16:24:05 EST 2007

```On Wed, 3 Jan 2007, enrico wrote:

> Johansen's  test give me [re-formatted for legibility]

Rango  Autovalore    Test traccia    Test L-max
0      0,88       181,7 [0%]       66,0 [0%]
1      0,76       115,7 [0%]       43,7 [2%]
2      0,58        71,9 [3%]       26,7 [29%]
3      0,50        45,3 [8%]       21,3 [27%]
4      0,34        24,0 [21%]      12,8 [49%]
5      0,30        11,2 [20%]      11,1 [15%]
6      0,00        0,17 [68%]      0,17 [68%]

> This is no cointegration H0: r=0
> or only 1 equation cointegrated H0: r=1 ????

The tests seem to indicate the presence of 2 cointegrating
relations (denoted 'c' below).

> Why p value is zero for both cases?

If you're talking about the first two tests in the Trace column,
the p-values are zero (to four decimal places) because both H0: c
= 0 and H0: c = 1 are strongly rejected in favour of the
alternative c = 7.

You should read the Help on this test: Cri Riagmonti has done a
nice translation to Italian.  Here's what happening:

Trace test:

H0: c = 0; H1: c = 7: reject H0
H0: c = 1; H1: c = 7: reject H0
H0: c = 2; H1: c = 7: reject H0
H0: c = 3; H1: c = 7: fail to reject H0

Lmax test:

H0: c = 0; H1: c = 1: reject H0
H0: c = 1; H1: c = 2: reject H0
H0: c = 2; H1: c = 3: fail to reject H0

Allin Cottrell

```