[R] embed?

[Ravi Varadhan]

Kevin,

The documentation is quite clear.

What "embedding" does is that it takes a scalar time series, x[t], and
"embeds" it in a higher-dimensional space of dimension, "dimension".  The
entries in the matrix you see are the indices of the time-series.  

So, for example, if dimension = 2, you embed your time-series on a 2-Dim
space: (x, y), where the points are:  (x[2], x[1]), (x[3], x[2]), ...,
(x[N], x[N-1]).

> embed(x, dimension=2)
      [,1] [,2]
 [1,]    2    1
 [2,]    3    2
 [3,]    4    3
 [4,]    5    4
 [5,]    6    5
 [6,]    7    6
 [7,]    8    7
 [8,]    9    8
 [9,]   10    9
>

This is allso known as Ruelle-Takens embedding in non-linear dynamical
systems, where this device is helpful in detecting the existence of a
low-dimensional attractor of the time-series.
 
Ravi.

----------------------------------------------------------------------------
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Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology 

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu

Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html

 

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-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of rkevinburton at charter.net
Sent: Friday, April 03, 2009 11:05 AM
To: r-help at r-project.org
Subject: [R] embed?

I have a question on the function 'embed'. I ran the example

x <- 1:10
embed(x, dimension=3)

This gives the output:

     [,1] [,2] [,3]
[1,]    3    2    1
[2,]    4    3    2
[3,]    5    4    3
[4,]    6    5    4
[5,]    7    6    5
[6,]    8    7    6
[7,]    9    8    7
[8,]   10    9    8

I don't quite understand the output and why it is useful. First, there are
only 8 rows down from 10 and the first element starts with 3. Of course I
can think of explanations as to what is occuring but I cannot see how this
is useful. I am sure it has application as i see this command used in much
of the source but I just cannot see it now.

The documentation states:

Each row of the resulting matrix consists of sequences x[t], x[t-1], ...,
x[t-dimension+1], where t is the original index of x. If x is a matrix,
i.e., x contains more than one variable, then x[t] consists of the tth
observation on each variable. 

This explanation doesn't seem to account for the dimension argument.

Thank you for your comments.

Kevin

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