Is a ts of length one a ts? (PR#245)

[Martyn Plummer]

On 11-Aug-99 Prof Brian D Ripley wrote:
> On Wed, 11 Aug 1999, Martyn Plummer wrote:
> 
>> On 10-Aug-99 ripley@stats.ox.ac.uk wrote:
>> > Is there any good reason why a time series of length one is not
>> > allowed by [.ts (you can certainly create one with ts)?
>> 
>> It certainly has a start and an end value, but what's the
>> frequency?  If you want the tsp attribute of a time series
>> to be well defined, then maybe you should disallow series
>> of length 1.
> 
> I think the frequency is perfectly well defined, as that of the series you
> subsetted.

Is it?

R 0.64.2:

R> x <- ts(1:10)
R> frequency(x)
[1] 1
R> y <- x[c(2,4,6,8,10)]
R> frequency(y)
[1] 0.5

This agrees with the S-PLUS treatment of "regular" time series:

S> x <- rts(1:10)
S> frequency(x)
 frequency 
         1
S> y <- x[c(2,4,6,8,10)]
S> frequency(y)
 frequency 
       0.5

By this logic, the frequency of a single element selected from
a time series is undefined. S-PLUS can get round this problem
because it has the richer time series class "its":

S> z <- x[1]
S> class(z)
[1] "its"

So although z still has a time dimension, it has no frequency.

S-PLUS does allow you to create an "rts" object of length one.  There is
a certain logic to this. The time series parameters must satisfy the
equation

frequency * (end - start) = length - 1

For a series of length 1:

frequency * 0 = 0

which is satisfied by any user-specified value of the frequency.

Martyn
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