[R-SIG-Finance] Interpretation of results from ca.jo in urca package

[William Ferreira]

Hello

I am using the ca.jo function in urca 1.0-9 running inside R-2.4.1. I have 
been performing cointegration analysis on log stock-price time series; I am 
looking for co-integration between pairs of stocks. I am not testing the 
log-price of the stock explicitly for I(1), as I am taking it as a given. 
Nonetheless I sometimes get results of the form:

######################
# Johansen-Procedure #
######################

Test type: trace statistic , without linear trend and constant in 
cointegration

Eigenvalues (lambda):
[1] 1.662315e-02 6.273138e-03 2.383972e-18

Values of teststatistic and critical values of test:

          test 10pct  5pct  1pct
r <= 1 |  7.05  2.82  3.96  6.94
r = 0  | 25.82 13.34 15.20 19.31


which lead me to reject the hypothesis of at most one cointegrating vector, 
and therefore that all the variables must be I(0), which is not the case. 
Any idea what might be going wrong?

Secondly, when I get a result which means I cannot reject (at the 5% level) 
the likelihood of more than 1 co-integrating vectors (ie. the original 
series were I(1)), then which matrix should I use to generate a series of 
residuals; is it PI?, for example:

######################
# Johansen-Procedure #
######################

Test type: trace statistic , without linear trend and constant in 
cointegration

Eigenvalues (lambda):
[1] 2.198524e-02 3.078562e-03 9.978092e-18

Values of teststatistic and critical values of test:

          test 10pct  5pct  1pct
r <= 1 |  3.45  2.82  3.96  6.94
r = 0  | 28.35 13.34 15.20 19.31

Eigenvectors, normalised to first column:
(These are the cointegration relations)

           datai.l1  dataj.l1   constant
datai.l1  1.0000000  1.000000  1.0000000
dataj.l1 -0.4417583 -0.565435  0.7770033
constant -0.8937223 -0.431884 -9.0212883

Weights W:
(This is the loading matrix)

            datai.l1      dataj.l1      constant
datai.d -0.035998263 -0.0009870617 -3.549719e-17
dataj.d  0.004612461 -0.0021116569 -2.171292e-17

(my print-out)

[1] "PI"
            datai.l1      dataj.l1     constant
datai.d -0.036985325  0.0164606502  0.032598747
dataj.d  0.002500804 -0.0008435882 -0.003210269

because sometimes I get very different looking residual series depending on 
whether I use the first or second row of PI to construct the series. 
Sometimes the residual series looks like a straight line which never crosses 
zero when I use row one, and for row two looks like a classic AR(m) series 
mean-reverting around zero (which is what I would expect), or vice-versa. 
Can anyone explain what is going on ?

Caveat: this is my first time using R (or any other s/w) to apply 
theoretical results to real data.

Kind regards

Bill