I want to analyse data corresponding to events happening at arbitrary moments in time, and conveying quantitative information. My goal is to study the relationship between the sum of these quantities and the passage of time.
Some examples fitting this description would be: migration fluxes, network traffic, financial transactions. In an unit of time you can have two events with small quantities or one event with a bigger quantity, and they have a similar relevance because they are basically describing a flow. The problem is that there is not such a thing like an "unit of time". Time is continuous but my signal, in this case, is intrinsically discrete!
I do not even know whether is there a name for this kind of data, and i feel that before doing any kind of analysis, i need to convert it to time series. Is there a name for this conversion?
I find this important, because this conversion involves information loss, and it is not reversible. Since any time series has a sampling interval, multiple events falling within the same interval will need to be aggregated somehow, for example by calculating the sum of the value they convey. For example if i have a purchase for 100 at 18:30 on some day, and a purchase of 200 at 18:45 on the same day, i will need to aggregate this to a data point with a value of 300 for that day, or for the hour interval 18:00 - 19:00.
Now, this seems to me quite similar to resampling, and specifically downsampling, but i am not sure, because sampling is about a continuous signal recorded at a regular interval