[R] Turning points in a series

[(Ted Harding)]

On 17-Sep-09 08:10:47, ogbos okike wrote:
> Good morning once more. My problem of yesterday has been addressed.
> Having learned a few tricks from that, I wish to ask another question
> in connection with that. My data is a cosmic ray data consisting of
> dates and counts.
> When I plot a graph of counts versus dates, the resultant signal
> shows a number of maximum and minimum points. These minimum points
> (turning points) are of interest to me. Reading these dates and counts
> off from the plot is difficult as I am dealing with a large data.
> I have been looking at turnpoints function in pastecs library but have
> not been able to figure out the appropriate commands that one can use
> to find the minima/maxima (turning points) or pits/peaks in a series.
> My data is of the form shown below where y stands for year, m month,
> d day and finally count. Is there a way I could find these minima
> together with the dates they occurred?
> I would be indebted to those of you who will show me the way out of
> these problem.
> Thank you.
> Best regards
> Ogbos
> 
> 
> y  m   d  count
> 93 02 07 3974.6
> 93 02 08 3976.7
> 93 02 09 3955.2
> 93 02 10 3955.0
> 93 02 11 3971.8
> 93 02 12 3972.8
> 93 02 13 3961.0
> 93 02 14 3972.8
> 93 02 15 4008.0
> 93 02 16 4004.2
> 93 02 17 3981.2
> 93 02 18 3996.8
> 93 02 19 4028.2
> 93 02 20 4029.5
> 93 02 21 3953.4
> 93 02 22 3857.3
> 93 02 23 3848.3
> 93 02 24 3869.8
> 93 02 25 3898.1
> 93 02 26 3920.5
> 93 02 27 3936.7
> 93 02 28 3931.9

The following simple function TP() (for "Turning Point") locates
the positions i where x[i] is greater than both of its immediate
neighbours (local maximum) or less than both of its neighbours
(local minimum).

  TP <- function(x){
    L <- length(x)
    which( ((x[1:(L-2)]<x[2:(N-1)])&(x[2:(L-1)]>x[3:L]))
          |((x[1:(L-2)]>x[2:(N-1)])&(x[2:(L-1)]<x[3:L])) ) + 1
  }

Applied to your series "count" above:

  TP(count)
  # [1]  2  4  6  7  9 11 14 17 21

If you assign these values to an index:

  ix <- TP(count)
  rbind(d[ix],count[ix])

  # [1,]    8.0   10   12.0   13   15   17.0   20.0   23.0   27.0
  # [2,] 3976.7 3955 3972.8 3961 4008 3981.2 4029.5 3848.3 3936.7

Of course, this is only a very simplistic view of "turning point",
and will pick out everything which is a local minimum or maximum.

The above function can be extended (in a fairly obvious way) to
identify each position i where x[i] is greater than its neighbours
out to 2 on either side, or less than these neighbours; or more
generally out to k on either side.

A lot depends on how you want to interpret "turning point". With
your "count" series, it might be that you were only interested
in identifying the relatively extreme turning points, such as
i=4 (maybe), i=9 (maybe), i=14, i=17, i=21(maybe).

Hoping this helps,
Ted.

--------------------------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk>
Fax-to-email: +44 (0)870 094 0861
Date: 17-Sep-09                                       Time: 09:47:53
------------------------------ XFMail ------------------------------