Forecasting by Envelopes: Probabilistic Boundaries via Disposable Random Forests

Forecasting in chaotic environments demands a paradigm that abandons the search for a single “best-fit” trajectory. This study formalises an operator we call the Asymmetric Risk Cone with Disposable Random-Forest Operators (ARC-DRO). ARC-DRO is trained afresh at every time-step on a sliding window, builds two independent non-parametric regressors for the future maximum and minimum of a target series, and returns a time-indexed envelope rather than a point estimate. Because the model is discarded immediately after use, the procedure is immune to classical over-fitting and self-calibrates to regime shifts without manual re-fitting. Unlike fan charts derived from ARIMA/GARCH families, ARC-DRO requires no normality, symmetry, or parameter-stationarity assumptions and can digest arbitrarily large, noisy, or collinear feature sets. The paper contributes (i) a rigorous functional definition of disposable operators, (ii) proofs that ARC-DRO subsumes linear cones as degenerate cases, and (iii) guidelines for practical implementation in real-time risk consoles.