I'd like to know if this table structure has a particular name. How can I determine the tendency for 2017-09?

Churn (by months of tenure)

Cumulative churn


It has a number of possible names; such structure occurs in numerous contexts.

From the labels, you might refer to it as age-period-cohort data though such data aren't always (or perhaps even usually) given in that particular arrangement. (In your triangle, the periods are the diagonals running in this direction $.\cdot ^{{\:\cdot}}$ (cohorts are labelled and the ages are marked M1,M2,...)

In general insurance (property & casualty insurance) incremental claims (loss) triangles take just the form you have (though they're often cumulated by practitioners, it's really the incremental payments that are observed).

The same data structure is seen in the aids reporting data (e.g. see Davison & Hinkley's book on bootstrapping where it's presented in just this way)

Similar data can be found in other contexts.

While trends can occur in all three directions, because period = age + cohort, the three directions can't be modelled independently -- some constraints must be imposed.

You'll need to formulate a suitable model for your data; this should be informed by subject matter expertise (which we can't supply) as well as an understanding of the impact of the APC structure -- that linear trends in any of the three directions impact the others because of that connection between them..


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