Signal Persistence in Long-Horizon Risk Projection: Boundary Conditions for the Hybrid GPR-HS Framework

Abstract Long-horizon forecasting requires models to retain meaningful predictive differentiation across extended horizons. This study introduces the Signal Persistence Horizon (SPH), a model-agnostic diagnostic measuring how long forecasts retain material differentiation over a specified evaluation horizon, and applies it to nine-quarter volatility projection using Gaussian Process Regression (GPR) and GARCH. Across eight commodity and emerging-market FX series, baseline GPR forecasts rapidly lose differentiation, motivating an investigation of the underlying persistence structure. The Matérn kernel length-scale consistently converges to the imposed optimization boundary across alternative search ranges and specifications, indicating that persistence is not reliably identified by maximum marginal likelihood from daily returns alone. Further experiments separate persistence from signal amplitude and identify distinct failure modes associated with premature forecast convergence and asset-invariant long-horizon variance. A revised specification combining free kernel amplitude with a horizon-aligned, sensitivity-tested length-scale is tested to address these persistence and amplitude failure modes and restores stable, asset-differentiated nine-quarter forecasts. The results suggest that forecast persistence should be treated as an explicit modelling assumption and sensitivity dimension when data do not identify a unique long-horizon persistence structure.