Temporal Concentration
Definition
Temporal Concentration (also Temporal Clustering) describes dynamic (time dependent) phenomena where the occurrence (rate, frequency or other measured quantity) of events exhibits non-uniform characteristics
Models
The archetype of a temporal process that does not exhibit concentration or clustering of events is the Poisson process. A variety of other proposed point processes can be used to model temporal concentration.
A special class of point process that exhibits enhanced clustering is the Hawkes process (also known as a self-exciting counting process). It is a simple point process but whose conditional intensity depends on the previous even count (hence the occurence of an event may precipitate more events).
Measurement using Concentation Indexes
For use cases where an index type measure is appropriate the following steps provide a standard treatment that is used in various domains:
- Binning of the temporal range of observation timestamps into intervals (e.g. hourly, daily, monthly etc)
- Aggregation of amounts or counts within each interval
- Application of standard Univariate Index
