[R] BDS test - results unclear to me

[Nicolas Navet]

Hello,

I would like to use the BDS test from the tseries package, but there is 
something I don't understand in the results of the test. Let's say, I 
want the BDS values for an embedding dimension equal to 2 :

 > bds.test(c, m = 2, eps = seq(0.5 * sd(c), 2 * sd(c), length = 
4),trace=FALSE);
Here are the outputs:
data:  c
Embedding dimension =  2
Epsilon for close points =  0.0097 0.0194 0.0291 0.0388
Standard Normal =
      [ 0.0097 ] [ 0.0194 ] [ 0.0291 ] [ 0.0388 ]
[ 2 ]    14.6006    13.9003    12.5745    11.4012


Now for dimension 3 (m=3), we obtain:

Standard Normal =
      [ 0.0097 ] [ 0.0194 ] [ 0.0291 ] [ 0.0388 ]
[ 2 ]    14.5544    13.8758    12.5540    11.3897
[ 3 ]    20.9149    18.7640    16.1562    14.2518

what I don't understand is why the values for embedding dimension 2 are 
not equal when BDS is computed with parameter m=2 and m=3, could someone 
please explain that to me ? In the documentation, it is said that "m is 
an integer indicating that the BDS test statistic is computed for 
embedding dimensions 2, ..., m.", so why don't we get the same result in 
both cases?

Thank you for your help,
Best regards,

Nicolas