The Finalized Trinity of Models for Gold/Silver Bullion Portfolio (Part 1)

 Model No. 1 of 3: GOLD & SILVER 20-DAY AND 60-DAY QUANTILE FORECASTS

Introduction: These three consecutive posts (after a long absence) is the culmination of many months of hard work resulting in a suite of 3 models for the monitoring, forecasting and risk/reward calculation of my Gold and Silver bullion portfolio. Why do we need three models? Because Gold and Silver are monetary metals that carry no yield (interest-earning capacity) but are also hedges against inflation, currency debasement and geopolitical uncertainty. Additionally, Silver is an industrial metal that is required for nearly all products of the modern economy- from EV batteries, semiconductors, solar panels, smart weapons, and indeed anything that requires electrical conductivity. Thus, we need to monitor not only the USD which is the currency that Gold and Silver are quoted in, but also bond yields, inflation and majore currencies such as USD/EUR and USD/JPY. 

 It's my last hurrah , and my legacy (turning 80 next year) to do something I have always wanted to do but could not-until recent develpments in AI and computing power but all this possible. 

Example Report generated from 04/0726 Run.

1. Executive Summary

This report presents probabilistic 20-day and 60-day price forecasts for COMEX Gold (GC=F) and Silver (SI=F) futures as of 04 July 2026. The model architecture is a two-stage ensemble: Stage 1 uses LightGBM with pinball (quantile) loss to forecast Q10, Q25, Q50, Q75, Q90 log returns; Stage 2 runs GARCH(1,1) bootstrap Monte Carlo with drift biased by the Stage 1 median. Final output quantiles are a 50/50 blend of both stages. Gold/Silver Ratio (GSR): 66.7. Gold spot: $4,187.30.  Silver spot: $62.81.

Model Methodology

Stage 1 — GBDT (Gradient-Boosted Decision Trees);  Quantile Forecasting:

LightGBM models are trained with pinball (quantile) loss for quantiles Q10, Q25, Q50, Q75, Q90 at both 20-day and 60-day horizons, yielding 20 models in total. Training data spans 2022–2024; test set is 2025 to the current date. Quantile crossing is corrected via isotonic sorting. Features: RSI (14), MACD line (12/26), MACD signal (9), Bollinger Band position, ADX (14), +DI, -DI, GARCH(1,1) annualised conditional volatility, and lagged log returns at 1-day, 5-day, and 10-day horizons.

Stage 2 — GARCH(1,1) Bootstrap Monte Carlo:

A GARCH(1,1) model is fitted to the full log return history. Standardised residuals are bootstrapped (with replacement) as the shock distribution. 10,000 paths are simulated at each horizon, with per-step drift biased by the Stage 1 Q50 median log return. Terminal price distributions yield MC quantiles.

Blending:

Final quantiles are a 50/50 weighted average of Stage 1 (GBDT log-return quantiles converted to prices) and Stage 2 (Monte Carlo terminal prices). Q95 is sourced from Monte Carlo only (GBDT is trained to Q90). Random seed 42 throughout.

Model Diagnostics: Pinball Loss Calibration

Pinball loss measures quantile forecast accuracy. Lower values indicate better-calibrated quantile predictions. Results below are computed on the out-of-sample test set (2025–present).

Feature Importance

LightGBM split gain importances averaged across all 20 quantile models. Higher gain indicates greater contribution to forecast accuracy

Example 20-Day Fancharts