Backtest a loss / premium / loss-ratio projection on existing data

Hold out the latest holdout calendar diagonals from the input Triangle, refit a target-specific projection on the earlier portion, project the held-out cells, and compare the projection to the actual values that were withheld.

The target is selected with target:

target = "ratio" – score the loss-ratio projection from fit_ratio().
target = "loss" – score the loss projection from fit_loss().
target = "premium" – score the premium projection from fit_premium().

The A/E Error (ae_err) follows the standard actuarial A/E convention and is computed cell-wise as $$ae\_err = \frac{value_{actual}}{value_{proj}} - 1$$ so that positive values flag under-projection (the model under-estimated; actual exceeded expected) and negative values flag over-projection. Aggregated by development period (col_summary) and by calendar diagonal (diag_summary).

Usage

backtest(
  x,
  holdout = 6L,
  target = c("ratio", "loss", "premium"),
  loss_method = c("ed", "cl", "sa", "bf", "cc"),
  premium_method = c("ed", "cl"),
  loss_alpha = 1,
  premium_alpha = 1,
  sigma_method = c("locf", "min_last2", "loglinear", "mack", "none"),
  recent = NULL,
  loss_regime = NULL,
  premium_regime = NULL,
  maturity = "auto",
  se_method = c("fixed", "delta"),
  rho = 0.95,
  conf_level = 0.95,
  bootstrap = NULL,
  B = 999L,
  seed = NULL,
  ...
)

# S3 method for class 'Backtest'
print(x, ...)

# S3 method for class 'Backtest'
summary(object, ...)

# S3 method for class 'summary.Backtest'
print(x, ...)

Arguments

x

A "Triangle" object (or a "Backtest" object for the S3 print() method).

holdout

Integer. Number of latest calendar diagonals to mask before refitting. Default 6L.

target

Character scalar. Which projection to backtest. One of "ratio" (default), "loss", "premium". Determines which fitter is called on the masked triangle and which column on x is treated as the held-out actual.

loss_method

Method for the loss-side projection. Passed to fit_ratio() / fit_loss() as their method argument. One of "ed" (default), "cl", "sa", "bf", or "cc". "bf" / "cc" need their prior arguments supplied through .... Unused for target = "premium".

premium_method

Method for the premium-side projection. Passed to fit_ratio() / fit_loss() / fit_premium(). One of "ed" (default) or "cl".

loss_alpha, premium_alpha

Mack alpha for loss-side / premium-side chain-ladder estimation.

sigma_method

Method used to extrapolate sigma for links where it cannot be estimated. One of "locf" (default), "min_last2", "loglinear", "mack", or "none". "mack" applies the Mack (1993, Appendix B) tail estimator to the last unestimated link only, falling back to LOCF for any earlier ones with a warning. "none" performs no extrapolation; sigma stays NA and downstream variance terms drop those links via finite-value guards. Passed to .extrapolate_sigma_ata().

recent

Calendar-diagonal recency filter forwarded to the fitter.

loss_regime, premium_regime

Regime spec for the loss / premium side. Each accepts one of four input types, dispatched by .resolve_regime():

NULL (default) – no regime filter.
A Regime object (e.g. from detect_regime()) – used as-is.
The string "auto" – runs detect_regime() on the masked triangle (leakage-safe; uses only data available at the simulated backtest cutoff).
A function function(tri) -> Regime – called on the masked triangle for the same leakage-safe reason.

premium_regime is resolved independently from loss_regime.

maturity

Maturity input. Used only for target = "ratio" and target = "loss" (stage-adaptive). Accepts one of four input types, dispatched by .resolve_maturity():

NULL – skip maturity filtering.
A Maturity object (e.g. from detect_maturity() or maturity_at()) – used as-is. Caller takes responsibility for any leakage in their pre-computation.
The string "auto" (default) – runs detect_maturity() on the masked triangle (last holdout calendar diagonals removed), avoiding look-ahead leakage.
A function function(tri) -> Maturity (e.g. from maturity_spec()) – called on the masked triangle for the same leakage-safe reason.

se_method

Standard-error composition for fit_ratio(). Unused for target = "loss" / target = "premium".

rho

Loss-premium correlation used by fit_ratio() delta method. Unused for target = "loss" / target = "premium".

conf_level

Confidence level for fit_ratio() / fit_loss() intervals. Unused for target = "premium".

bootstrap, B, seed

Bootstrap controls forwarded to the target-specific fitter (fit_ratio() / fit_loss() / fit_premium()). bootstrap = NULL (default) defers to the fitter's method-dependent resolution: bootstrap for SA/ED methods, analytical for pure CL. The fitter accepts the full 4-type dispatch (NULL / logical / "auto" / BootstrapTriangle / function). For a leakage-safe backtest with a custom bootstrap configuration, prefer a function function(tri) -> BootstrapTriangle (it is invoked on the masked triangle, not the original) over a pre-built BootstrapTriangle object (which may have been built on the unmasked data and would leak hold-out cells into the residual pool).

...

Additional arguments passed to the underlying fitter.

object

A "Backtest" object. Used by the S3 summary() method.

Value

An object of class "Backtest" with components:

call: Matched call.
data: Original Triangle.
masked: Triangle used for fitting (with held-out cells removed).
fit: The fit object returned by the target-specific fitter.
ae_err: data.table of held-out cells with columns (group, cohort, dev, actual, expected, aeg, ae_err, incr_actual, incr_expected, incr_aeg, incr_ae_err, cal_idx). aeg = actual - expected (signed error in target units); ae_err = actual / expected - 1 (relative error). incr_ siblings are the same metrics on the incremental view.
col_summary: Per-dev aggregate A/E Error and AEG (mean / median / weighted) with incr_ variants and n.
diag_summary: Per-calendar-diagonal aggregate A/E Error and AEG (same columns as col_summary, keyed by cal_idx).
target, holdout, dispatcher: Call metadata.
groups, cohort, dev: Variable name relays from x.

Examples

if (FALSE) { # \dontrun{
data(experience)
tri <- as_triangle(
  experience,
  groups   = "coverage",
  cohort   = "uy_m",
  calendar = "cy_m",
  loss     = "incr_loss",
  premium = "incr_premium"
)

bt_ratio    <- backtest(tri, holdout = 6L, target = "ratio")
bt_loss     <- backtest(tri, holdout = 6L, target = "loss")
bt_premium <- backtest(tri, holdout = 6L, target = "premium")

print(bt_ratio)
summary(bt_ratio)
plot(bt_ratio)
} # }

Backtest a loss / premium / loss-ratio projection on existing data

Usage

Arguments

Value

See also

Examples