I am using the vecrank command in STATA to identify the number of cointegrating relationships for 2 dependent price series (a and b). The Johansen trace test uses a recursive method (i.e. first null hypothesis = no cointegrating relationship. If rejected, first null hypothesis = 1 cointegrating relationship, etc.). Because I have a total of two price series, there must be either 0 or 1 cointegrating relationships.
The results are showing me that both 0 and 1 cointegrated relationships are rejected. What could this mean? Should it lead me to believe that (because it cannot be more than 1) there exists 1 relationship? Additionally - I have tested for non-stationary and I accepted the null of a unit-root for both a and b.
Below is the code and output:
vecrank a b, lags(2) trend(constant) max ic
Johansen tests for cointegration
Trend: constant
Number of obs = 244
Sample: 4 - 247 Lags = 2
5%
maximum trace critical
rank parms LL eigenvalue statistic value
0 6 680.73707 . 25.0038 15.41
1 9 691.15394 0.08184 4.1700 3.76
2 10 693.23895 0.01695
5%
maximum max critical
rank parms LL eigenvalue statistic value
0 6 680.73707 . 20.8337 14.07
1 9 691.15394 0.08184 4.1700 3.76
2 10 693.23895 0.01695
maximum
rank parms LL eigenvalue SBIC HQIC AIC
0 6 680.73707 -5.444636 -5.495997 -5.530632
1 9 691.15394 0.08184 -5.462432* -5.539474* -5.591426
2 10 693.23895 0.01695 -5.456993 -5.542595 -5.600319