# [R] BDS test - results unclear to me

Tue Aug 14 13:15:45 CEST 2007

```Hi Nicolas

Most likely because the higher embedding dimension uses less data
points, even when applied to the lower dimension. Therefore, the actual
numbers should be similar, but do not exactly match. But it's a very
long time ago I last touched this code. So pls read bdstest.c from
tseries to be sure.

Best regards

> Subject:
> [R] BDS test - results unclear to me
> From:
> Nicolas Navet <Nicolas.Navet at loria.fr>
> Date:
> Mon, 13 Aug 2007 22:14:40 +0200
>
> To:
> r-help at stat.math.ethz.ch
>
>
> 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
>

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