Description

Dynamic Tail Event Curves (DYTEC)

1. Tail Event Curves (TECs) quantify extreme behaviour across functional data (e.g., storms, demand, climate).

2. Expectile regression provides smooth tail-sensitive curves for any τ-level, generalizing quantiles via asymmetric loss.

3. Time-varying TECs require dimensionality reduction; functional PCA or expectile-based PECs build the spatial basis.

4. Dependence and non-stationarity are handled by a Dynamic Functional Factor Model (DFFM).

5. DFFM decomposes curves into time-basis functions and space-basis functions with τ-specific factor loadings.

6. Estimation uses penalized asymmetric loss with group-lasso structure and the GMD optimization algorithm.

7. The iterative DYTEC algorithm alternates between estimating factors and updating asymmetric weights.

8. Simulations show robustness across error distributions, τ-levels, and sample sizes; skewed errors increase MSE.

9. Empirical studies (Chinese temperatures, hurricanes) reveal trend breaks, periodic patterns, and strong tail dynamics.

10. DYTEC provides a unified framework for modeling, forecasting, and interpreting dynamic extremes in functional data.