Tail-risk forecasting for Actuarial Climate Indices

The Actuarial Climate Index (ACI) was developed by North American actuarial organizations as an objective tool to monitor observed changes in climate extremes. Regional adaptations exist for France, Iberia, Australia, Italy, and Turkey, all designed as retrospective monitoring tools. Because ACI components (temperature extremes, heavy precipitation, drought, wind power) are constructed from distributional tails, extreme value theory (EVT) provides a natural statistical framework for extending these indices from monitoring into forward-looking actuarial risk assessment.

We develop a tail-risk analysis and forecasting framework for the Colombian Actuarial Climate Index (ACI-CO) constructed from ERA5 reanalysis data (1961-2024) over five components and multiple regions. Colombia's interannual climate variability is dominated by the El Niño--Southern Oscillation (ENSO), making regime-conditioned tail analysis central to actuarial climate applications. First, we estimate nonstationary GEV and peaks-over-threshold (GPD) models for each ACI-CO component, allowing location and scale parameters to depend on time, season, region, and ENSO phase (ONI, Niño 3.4). This yields dynamic return levels and exceedance probabilities that vary with climate regime.

Second, we use the nonstationary EVT characterization to shift the forecasting target from the component level to the tail. Using SARIMAX/ARDL models as econometric baselines and gradient-boosted trees (XGBoost/LightGBM) as nonlinear alternatives, with lagged ENSO indices, seasonality, and regional effects as predictors, we produce forecasts of exceedance probabilities. Finally, we propose an ACI-CO Tail Risk Index (ACI-CO TRI) that aggregates excesses over component- and region-specific thresholds, capturing episodes of unusually excessive severity above regional thresholds. We compare the TRI against the standard composite in its ability to detect historically documented climate stress episodes.