[R] modeling interval data, a.k.a. irregular timeseries

[Rolf Turner]

It seems to me you that have a sequence (``series'') of random times,  
rather than
a sequence of values of a random variable observed at a irregularly  
spaced times.
Hence I would say that point process modelling, rather than time  
series modelling,
would be more appropriate.

You could consider yourself to have two related point processes ---  
the process of
starting times and the process of stopping times.  Or you could  
consider the process,
of starting times only, as a marked point process, with the marks  
being the interval
lengths (i.e. tj_2 - tj_1).

How you would go about analyzing such data, I don't know.  In the  
point process context
``regularity'' would amount to having a homogeneous Poisson process  
(with the marks,
i.e. the interval lengths, being independent of the [starting]  
points).  There may be
tests for this sort of null hypothesis, against an unspecified  
alternative, out there.
I would start by having a look at the book (2 volumes) by Daley and  
Vere-Jones (second ed.).

One way to proceed might be to fit some sort of conditional intensity  
function (conditional
on the past, including the past marks) and test this model against  
the null model by
a likelihood ratio test.  The problem, it seems to me, is to specify  
an appropriate
and sufficiently alternative general conditional intensity function.   
The fitting could then be
done using the Berman-Turner device (see ``Approximating point  
process likelihoods using GLIM'',
M. Berman and T. R. Turner, Applied Statistics vol. 41, 1992, pp. 31  
-- 38.  See also
the paper by Ogata cited therein.)

HTH.

	cheers,

		Rolf Turner

On 4/09/2008, at 4:44 PM, Alexy Khrabrov wrote:

> Greetings -- I've got some sensor data of the form
>
> t1_1, t1_2
> t2_1, t2_2
> ...
> tN_1,tN_2
>
> -- time intervals measuring starts and stops of sensor activity.   
> I'd like to see whether there's any regularity in it.  Seems  
> natural to consider these data timeseries -- except most of the  
> timeseries packages and models assume regular ones, with a fixed  
> frequency. 
> I wonder what's a good way to apply existing regular timeseries  
> packages to these data, and perhaps try some others?  I like David  
> Stoffer's book a lot, yet he uses R's own ts methods (with some  
> extras).  I also like the zoo package, which allows for irregular  
> timeseries, yet I'm not sure how to apply the "usual" models to zoo  
> objects -- even though zoo strives to be compatible with ts...  Is  
> zoo directly usable for ts-like time domain and spectral analysis  
> as per Stoffer?
>
> Another way I was pondering is to map the above to a an artificial  
> index 1:n and consider it multivariate timeseries.  Is it something  
> done in irregular timeseries analysis?
>
> Cheers,
> Alexy
>
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