This repository implements a lightweight framework for generating yearly uncertainty estimates from monthly forecasts, combining:

• Monte Carlo simulation
• Stationary bootstrap for residual resampling
• Anchoring to monthly prediction intervals using Adaptive Conformal Inference (ACI)

The goal is to produce coherent, distribution‑aware yearly prediction intervals that respect both monthly uncertainty and temporal dependence.

Most demand forecasting pipelines provide monthly point forecasts and monthly prediction intervals, but business planning often requires yearly uncertainty. This project bridges that gap by:

• Sampling monthly forecast distributions via Monte Carlo
• Modeling temporal dependence using stationary bootstrap
• Aggregating simulated monthly paths into yearly totals
• Ensuring consistency with monthly ACI‑derived intervals

The result is a robust, simulation‑based uncertainty quantification (UQ) workflow suitable for hierarchical or business‑critical forecasting.

• Monthly point forecasts
• Monthly prediction intervals (e.g., 5th–95th) from ACI
• Historical residuals for bootstrap resampling

Residuals are resampled using stationary bootstrap, preserving autocorrelation and seasonal structure.

For each iteration:

• Sample residual paths
• Apply them to monthly forecasts
• Generate a full 12‑month trajectory
• Aggregate to yearly totals

Typical configuration: 20,000+ iterations for stable tail estimates.

From the simulated yearly totals:

• Compute quantiles
• Construct prediction intervals
• Optionally compare against monthly‑level uncertainty for coherence and anchor back for monthly corresponding interval