Find ata maturity by group — detect

Identify the first mature age-to-age (ata) link from a Triangle. Internally builds a single-variable Link table, computes the per-link diagnostic via summary.Link() with model = "ata", and then locates the first link whose statistics satisfy all maturity criteria.

Maturity is determined using a combination of:

cv < max_cv
rse < max_rse
valid_ratio >= min_valid_ratio
n_valid >= min_n_valid
optional consecutive maturity over min_run ata links

Both cv and rse must be satisfied simultaneously. cv captures the raw variability of observed ata factors across cohorts, while rse reflects the precision of the WLS-estimated factor. Using both criteria together provides a more robust maturity assessment than either alone.

Default loss = "loss" (cumulative loss). Maturity in chain ladder is methodologically a property of loss development: the ATA factors of cumulative loss stabilize when chain ladder becomes reliable, which in turn makes downstream LR projection reliable. ATA factors of ratio itself (a ratio of two cumulative quantities) carry additional noise and tend to give less precise maturity decisions. Override loss only when you specifically want maturity of premium development or another cumulative metric.

Usage

detect_maturity(
  x,
  loss = "loss",
  groups = NULL,
  weight = NULL,
  alpha = 1,
  max_cv = 0.15,
  max_rse = 0.05,
  min_valid_ratio = 0.5,
  min_n_valid = 3L,
  min_run = 2L
)

Arguments

x: A Triangle object.
loss: Cumulative metric for the link factor. Default "loss" (chain-ladder convention; see Description). Forwarded to as_link().
groups: Optional character subset of attr(x, "groups") selecting which columns define the maturity partition. Maturity is typically a structural property of the development curve driven by coverage rather than by demographic mix (age, channel, ...), so a Triangle aggregated by c("coverage", "age_band", "channel") may still want a per-coverage maturity. NULL (default) keeps the current Triangle grouping (fully backward compatible). character(0) pools across all groups and returns a single global maturity row. Any non-NULL, non-empty value must be a subset of attr(x, "groups"); column order is irrelevant. When the requested groups is coarser than the Triangle grouping, the underlying loss / premium / ratio columns are re-aggregated to the coarser partition before computing ata links.
weight: Optional WLS weight variable. Forwarded to as_link().
alpha: Numeric scalar controlling the variance structure in the underlying WLS fit. Default 1. Forwarded to summary.Link().
max_cv: Maximum allowed coefficient of variation. Default is 0.15.
max_rse: Maximum allowed relative standard error. Default is 0.05.
min_valid_ratio: Minimum proportion of finite ata values required. Default is 0.5.
min_n_valid: Minimum number of finite ata factors required. Default is 3L.
min_run: Minimum number of consecutive ata links satisfying the maturity criteria. Default is 2L.

Value

A data.table with class "Maturity" containing one row per group. Columns include ata_from, change (the maturity point, i.e. the to-index of the first mature ata link), ata_link, and the diagnostic statistics (mean, median, wt, cv, f, f_se, rse, sigma, n_cohorts, n_valid, n_inf, n_nan, valid_ratio). If no mature link is found, all values for that group are NA.