Forecasting✓ Mathematical
◆ The PatternEstimate and forecast return variance with GARCH, EWMA, and realized measures
Volatility clusters — large moves beget large moves. GARCH(1,1) captures this:
σ²t = ω + α · r²t−1 + β · σ²t−1
EWMA is a special case with ω = 0 and α + β = 1 (RiskMetrics uses λ = 0.94). Realized volatility sums intraday squared returns for a model-free estimate.
// Interactive — EWMA decay parameter and conditional variance
EWMA λ
| Model | Parameters | Use Case |
|---|---|---|
| EWMA | λ | Quick daily VaR |
| GARCH(1,1) | ω, α, β | Conditional forecasting |
| Realized Vol | Sampling freq | High-frequency data |
Pattern bridge: Variance estimation underpins The Toolkit — Variance.