# Terminology: what is the name for sets of aggregated values over periods of time?

In statistics/analytics, let's say we have a time series of data points, i.e., pairs of timestamps and values:

t: 0
y: 42

t: 1
y: 32

t: 2
y: 29

t: 7
y: 0


As for terminology, I would probably refer to these items as samples (or, well, data points).

But when referring to aggregated data, such as this:

t_start: 0
t_end: 2
avg: 42

t_start: 2
t_end: 5
avg: 39

t_start: 7
t_end: 12
avg: 29


What is a commonly used term for each such aggregated item, consisting of a time interval and an aggregated value (such as an average, a sum, a max etc) over that time? Can each such item be referred to as a sample, or does sample implicitly mean "a single measured value at one point in time"? Is there a better term?

• It would be unusual to perform this operation unless the times are equally spaced. With equal spacing and equal duration of each aggregate, some communities call it a "focal mean."
– whuber
Commented Dec 5, 2023 at 20:47

In time series analysis, I don't think "sample" is used often. I like "observation", or "value", if the interval nature is obvious enough - "observation" is probably better if it is a sum of timestamped observations; if the value comes from an averaging, then "value" sounds better.

Related terms are "aggregation" or "aggregation dimension" (sometimes you want to aggregate across multiple dimensions, not only time), or "bucketizing". If you want to distinguish the original timestamped observations from the aggregates, then something like "bucketized value" or "bucketized observation" would work. Though you probably don't want to use that particular term throughout a document or a presentation...

• Thanks for your suggestions. The context of the question is the API for a program which needs to handle lists of these {startTime, endTime, average} objects. I'm already using the term samples to refer to lists of {timestamp, value} objects, but for the aggregated data I'm now leaning towards aggregation or aggregateItems.
– JHH
Commented Dec 5, 2023 at 12:38
• aggregatedItems sounds best to me (note the d). aggregation suggests an action, not the result of the aggregation. Commented Dec 5, 2023 at 20:30

I would call these measurements over rolling windows. This is the terminology used in Pandas. The start and end times define the window, and the aggregated value would then be called the rolling average or moving average.

• I believe that's not quite it: rolling and moving average terminologies always apply to windows that are fixed in length in one of two senses: constant duration or constant number of data.
– whuber
Commented Dec 5, 2023 at 20:48
• Thanks for the suggestions. A term somewhat related to window is frame, which seems to be used in some similar contexts, where events are measured over moving time intervals.
– JHH
Commented Dec 6, 2023 at 13:26