Simulation Parameters
Test Set Metrics
Visual Risk Horizon Canvas
Methodological Contrast & Insights
Vanilla Conformal Prediction
Vanilla conformal frameworks assume **exchangeability** of historical calibration samples and future observations. Because of this, the interval boundary is computed as a static threshold calibrated globally from the training split.
\([ \hat{\mu} - q, \hat{\mu} + q ]\)
Key Vulnerability: When data exhibits drift or structural variance modifications (nonstationarity), VCP's static window will fail, resulting in severe **undercoverage** during high-volatility regimes.
Nonstationary Z-Score Framework
Based on **Mare, Moreira, & Rossi (SSRN 2688367)**, \(Z_7^k\) fits linear trends over overlapping rolling windows, detrends each midpoint realization, and estimates a constant coefficient of variation from the resulting residuals.
\(PI_t=f(t)\mp t_{k-2}^{-1}((1+\alpha)/2) \cdot \sqrt{\hat{\sigma}_t^2+\epsilon_t^2}\) \(\epsilon_t=SE[f(t)]\) \(\hat{\sigma}_t=|\bar{\tau}f(t)|\)
Benefit: The forecast mean follows the latest local trend, while heteroskedasticity is represented by \(\bar{\tau}=(1+1/(4N))|s/m|\) and \(\hat{\sigma}_t=|\bar{\tau}f(t)|\).