Optimized Moving Average Smoothing for Volatility Forecasting in Futures Markets

Common moving averages (MAs) used for volatility forecasting rely on fixed heuristic weights. We propose a Custom Moving Average (CMA) whose weights are learned to forecast the next-day True Range (TR). Using daily OHLC data for 55 futures contracts with a chronological 60/20/20 train/validation/test split, CMA weights are optimized for each look-back period p by projected subgradient descent against Mean Absolute Error (MAE), with validation-based early stopping. We benchmark CMA against nine standard MAs over 62 look-back periods, selecting the period on validation and reporting accuracy on the held-out test set. Learned weights concentrate on an effective horizon of 15–20 observations regardless of p: about 85% of the mass sits in lags 0–14 for both p=36 and p=120. EMA is the validation-best method at very short windows; CMA dominates from p≈16 onwards, winning on 53 of 55 instruments by p=120. Under a single-global-period rule, CMA at p*=36 attains the lowest test-set geometric-mean MAE, with EMA at p*=7 the closest competitor (0.87% higher); per-instrument validation selection does not overturn the ranking, with EMA again closest at 0.53%. Higher-order smoothers (T3, TEMA, DEMA) do not improve on CMA under either rule; CMA’s advantage is robust to the choice of selection granularity.