modeling interval data, a.k.a. irregular timeseries
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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