Martial Systems LLC
Quantitative research · equity volatility

Short-horizon realized volatility forecasts for SPY

This page summarizes a walk-forward study of models that forecast next-five-trading-day annualized realized volatility for the S&P 500 ETF (SPY). Training uses data through 2018; out-of-sample evaluation runs from 2019 to the latest available session. Models are compared against naive persistence and GARCH(1,1) under a common protocol. Results are research aggregates only and are not trading recommendations.

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Selected model MAE
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Naive persistence
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trailing 5-day RV
GARCH(1,1)
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multi-step baseline
Monthly LGBM reference
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expanding window

Error by calendar year (selected model)

Out-of-sample MAE by year. Elevated points coincide with major volatility-regime breaks (2020, 2022).

Method summary

  • Target: annualized realized volatility over the five trading sessions after each close.
  • Features: information available at or before that close only (trailing RV, GARCH-family volatility, returns, volume, technicals; optional VIX and calendar fields in secondary tests).
  • Validation: chronological walk-forward; no shuffled cross-validation.
  • Baselines: trailing five-day realized vol (persistence) and causal GARCH(1,1).
  • Selection: lowest aggregate MAE among completed runs, with documented stress-period and calendar diagnostics.

Technical note (PDF)

Specification comparison (MAE ascending)

Each row is a completed walk-forward specification. Lower mean absolute error (MAE) and root-mean-square error (RMSE) are better. Primary ranking uses MAE on the raw volatility scale.

# Specification MAE RMSE Retrain Window Model Retrains

Limitations and diagnostics

Stress periods — selected model vs monthly reference

Month-level MAE for the selected weekly specification versus the monthly-retrain LightGBM reference, with naive persistence on the same dates. Multi-day gaps and crisis regimes are of particular interest.

Period Selected MAE Monthly ref. Naive vs monthly vs naive