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I'm trying to find the correct terminology for a dataset I'm working with: the data consists of events that have a time of occurrence (irregular, i.e. not from a fixed sample rate) and a scalar value. The aggregated values (their sum) represent the system's state. The events are largely independent w.r.t. both timing and value. An example would be transactions on a bank account.

So far I'm referring to the stream of events as a time series, which is (according to Wikipedia) "a series of data points indexed [...] in time order". However, most of the materials on time series that I've found seem to assume that each data point is a sample from the same underlying and time-dependent "value" (a stock price, temperature, ...). In my case that's true for the system state (the "account balance") but not for the individual events.

What is the appropriate terminology for such a dataset?

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The term intermittent comes to mind reflecting a measure of an activity that takes place but not at fixed intervals such as the quantity of gas purchases for your auto.

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  • $\begingroup$ This is a good description but it does not appear to be generally used in any technical way and therefore does not seem to qualify as "terminology." If I'm wrong about that, could you supply a reference? $\endgroup$ – whuber Feb 25 '17 at 23:18
  • $\begingroup$ This article discusses "intermittent demand" lancaster.ac.uk/lums/news/… and may shed some light on the issue. $\endgroup$ – IrishStat Feb 27 '17 at 22:49
  • $\begingroup$ Thank you. That article appears to use "intermittent" in a subtly but importantly different sense than the one described in the question here. It refers to a regularly spaced time series of non-negative amounts in which values may frequently be zero. Here, "intermittent" means events having irregular times of occurrence. $\endgroup$ – whuber Feb 27 '17 at 23:08
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Unevenly spaced time series is a term that is used. While most statistics theory is about evenly spaced time series. In the comments there is also proposed point process, but that seems to be a special case where only the times itself are observed and of interest.

So if the observations are occurrence times of earthquakes in California, that would be a point process, also since there is no value associated with other (non-nonoccurence) times. But when there is a continuous, underlying value, for example the luminosity of a variable star, but it is only observed at irregular times, due to weather conditions and observer availability, it is an unevenly spaced time series.

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