Financial Risk Horizons

An Interactive Contrast: Vanilla Conformal vs. Nonstationary SSRN 2688367

Simulation Engine Active

Simulation Parameters

Timeline Steps (\(T\)) 200
Forecast Horizon Start 120
Base Volatility (\(\sigma_0\)) 0.010
Volatility Drift (Nonstationarity) 0.0003
High drift breaks Exchangeability
Coverage Level (\(1 - \alpha\)) 95%
Rolling Window (\(W\)) 20

Test Set Metrics

Vanilla Conformal Static Interval
Observed Coverage: --
Mean Bound Width: --
Nonstationary Model Adaptive Interval
Observed Coverage: --
Mean Bound Width: --

Visual Risk Horizon Canvas

Shaded areas depict the predicted uncertainty boundary (\(1 - \alpha\))

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.

Interval Width is Static:
\([ \hat{\mu} - q, \hat{\mu} + q ]\)

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 **Marè, Moreira, & Rossi (SSRN 2688367)**, this approach models nonstationarity explicitly. Instead of assuming identical distributions, it computes local statistical moments over localized rolling memory frames to scale boundaries parameter-by-parameter.

Interval Width is Dynamic:
\([ \mu_t - t_{crit} \cdot s_t \sqrt{1 + 1/W}, \mu_t + t_{crit} \cdot s_t \sqrt{1 + 1/W} ]\)

Benefit: Dynamically adapts to local parameter drifts. By integrating Student's \(t\) degrees-of-freedom scaling and rolling finite estimation adjustments, it preserves target coverage rates across volatile timelines.