In a time series, I am trying to illustrate a situation where I have two types of events:
- some occurring at a shorter interval from each other, that corresponds to events happening at time $t$
- some occuring at a longer interval from each other, that corresponds to rarer events happening at time $T$
both types of events' recurrence have no relations to each other (e.g. unlike seconds accumulate to minutes).
My solution is the following if I want to sum between two longer intervals:
$$d_{T+1} = \sum_{t = t >^1 T}^{ t <^1 T+1} ...$$
$d_{T+1}$ being anything that has to be estimated.
I want to express the next $t$ right after $T$ and the last $t$ just before $T+1$ in a compact form. This is what my little 1 tries to indicate. I feel like it is a similar idea to floor and ceiling ($⌈x⌉$ and $⌊x⌋$), except that they refer to integers.
Is there a better way to do this?