[R] correlating irregular time series

[paul sorenson]

I don't have the texts you mention but I get the general idea.  The 
diagram I posted shows only a small fraction of the events I have.

Thank you

Christophe Pouzat wrote:
> Hi Paul,
> 
> Here is how an amateur statistician deals with this problem when 
> analyzing spike trains from simultaneously recorded neurons.
> 
> Start by estimating the "hazard function" h(t) of your several point 
> processes (if you have a copy of MASS, check out the chapter 13, If you 
> have a copy of Jim Lindsey, "The Statistical Analysis of Stochastic 
> Processes in Time", check out chap 3 & 4; the hazard function is also 
> called the "conditional intensity" or the "stochastic intensity").
> 
> In practice if you have a renewal process, meaning that the successive 
> intervals between your events times are independent, you can first 
> estimate the "Inter Event Interval" pdf, f(t), and its cumulative 
> distribution function F(t). h(t) is then given by:
> 
> h(t) = f(t) / (1-F(t)),
> 
> where the quantity S(t) = 1-F(t) is often called the survivor function.
> 
> Fine, now if your processes are well approximated by renewal processes, 
> you can look for the distribution of "time to next event" (TTN) and 
> "time to former event" (TTF). By that I mean that for each of the black 
> events of your figure, you must get the interval separating it from the 
> last red event preceding it (the time to former) and the next red event 
> following it (the time to next). Under the null hypothesis of no 
> correlation these to random variables have the same pdf given by:
> 
> TTN(i) = S(i) / <IEI>,
> 
> where S(i) in that case is the survivor function of the red (test) 
> process and <IEI> is its inter event interval expected value.
> Using this approach I typically estimate the TTN and TTF pdfs with 
> histograms and compare these histograms to their expected values under 
> the null hypothesis. A warning though, I have most of the time much more 
> events than you seem to have on your figure.
> 
> Let me know if any of this makes sense.
> 
> Christophe.
> 
> paul sorenson wrote:
> 
>> I have some time stamped events that are supposed to be unrelated.
>>
>> I have plotted them and that assumption does not appear to be valid. 
>> http://metrak.com/tmp/sevents.png is a plot showing three sets of 
>> events over time.  For the purpose of this exercise, the Y value is 
>> irrelevant.  The series are not sampled at the same time and are not 
>> equispaced (just events in a log file).
>>
>> The plot is already pretty convincing but requires a human-in-the-loop 
>> to zoom in on "hot" areas and then visually interpret the result.  I 
>> want to calculate some index of the events' temporal relationship.
>>
>> I think the question I am trying to ask is something like: "If event B 
>> occurs, how likely is it that an event A occurred at almost the same 
>> time?".
>>
>> Can anyone suggest an established approach that could provide some 
>> further insight into this relationship?  I can think of a fairly basic 
>> approach where I start out with the ecdf of the time differences but I 
>> am guessing I would be reinventing some wheel.
>>
>> Any tips would be most appreciated.
>>
>> cheers
>>
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> 
>