Volatility forecasts are essential for financial risk management because both their overall level and day‑to‑day movements influence downstream decisions. Most studies compare forecasting models while keeping the training loss fixed, yet different losses emphasize distinct error types and may target different properties of future volatility. Consequently, raw comparisons mix persistent forecast‑level differences with daily movement differences, leaving unclear whether loss choice matters mainly because of the forecast level it targets or because of residual differences after level adjustment.
We address this gap by comparing seven loss functions and five models across major cryptocurrencies. A validation‑based alignment first adjusts the forecast level, after which both raw and aligned forecasts are evaluated using statistical scores and one‑day Value‑at‑Risk (VaR). Before alignment, score variation across losses is larger; after alignment, model choice becomes the dominant source of variation in the full five‑model comparison, while cross‑loss differences in VaR breach rates narrow substantially.
Our contribution is a comprehensive evaluation of loss and model choice that explains why losses can appear highly influential in raw comparisons and how this interpretation changes when forecast level and downstream risk are explicitly considered.
Review