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I am studying Johansen's Test using Tsay's book (Multivariate Time Series Analysis). The book has given some sample results of function ca.jo in r package urca, which is a typical way to do cointegration test in r:

m1 = VARorder(bnd) # summary table was suppressed.
selected order: aic =  11 
selected order: bic =  3 
selected order: hq =  3 


m2 = ca.jo(bnd, K = 2, ecdet = c("none"))

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

Test type: maximal eigenvalue statistic (lambda max) , with linear trend 

Eigenvalues (lambda):
[1] 0.054773196 0.004665298

Values of teststatistic and critical values of test:

          test 10pct  5pct  1pct
r <= 1 |  2.84  6.50  8.18 11.65
r = 0  | 34.19 12.91 14.90 19.19

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

           Aaa.l2    Baa.l2
Aaa.l2  1.0000000  1.000000
Baa.l2 -0.8856789 -2.723912

Weights W:
(This is the loading matrix)

           Aaa.l2      Baa.l2
Aaa.d -0.04696894 0.002477064
Baa.d  0.04046524 0.002139536

Tsay has mentioned that given the information criteria has picked order 3 as the optimal order, the example will be using $VAR(3)$ in the Johansen's Test; however as we can see in the command it was using order 2, i.e. $K=2$ in ca.jo function.

I don't think this is a typo. Does anyone know why it is of order 2 rather than order 3?

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The Johansen test does not select the lag order. Instead, it must be specified. If left unspecified, the default lag order chosen is $k=2$.

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  • $\begingroup$ thanks; but I have chosen a lag as K=2, right? Since I gave K a value in the function call. $\endgroup$ – stucash Mar 15 at 1:29
  • $\begingroup$ Yes, $k$ must be specified to use the function ca.jo. Are you sure Tsay wasn't referring to a different dataset when he stated the optimal lag length was 3? It could indeed be a typo. $\endgroup$ – dlnB Mar 15 at 1:34
  • $\begingroup$ I just double checked, I believe Tsay was talking about the same dataset throughout as the codes and text appeared in the same section. If you have the book, it is basically section 5.9.5 Illustration (p309-p312), the order was mentioned in the text and also done as part of the codes. I'll paste the codes here though. Anyway, thanks for your help! $\endgroup$ – stucash Mar 15 at 1:48

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