Modeling Market Turbulence: GARCH, EGARCH & HAR for Volatility Forecasting
Volatility ≠ returns: heavy tails, clustering, mean reversion. Dedicated volatility models are essential for risk management, position sizing, and VaR.
1. Why Dedicated Volatility Models
You can forecast returns with a generic regressor, but volatility refuses to behave like one. Returns are close to unpredictable day to day; their magnitude is not. That asymmetry is why volatility gets its own family of models — they are built around the few properties that show up in almost every asset:
- Heavy tails: extreme moves happen far more often than a normal distribution predicts
- Clustering: calm follows calm and turbulence follows turbulence — high-vol days arrive in runs, not isolation
- Mean reversion: once a shock fades, volatility drifts back toward its long-run average
Get the vol forecast wrong and everything downstream inherits the error: risk limits, position sizing, and VaR all rest on it. That payoff is what justifies a dedicated model rather than a generic one.
Volatility Clustering Visual
2. GARCH Family
Intuition: today's volatility depends on yesterday's shock and yesterday's volatility.
r_t = σ_t ε_t, ε_t ~ N(0,1)σ_t² = ω + α r_{t-1}² + β σ_{t-1}²EGARCH / GJR-GARCH: allow for asymmetry (downside shocks impact vol more).
log(σ_t²) = ω + α(|ε_{t-1}| - E|ε_{t-1}|) + γε_{t-1} + β log(σ_{t-1}²)GARCH Response to Shock
Note how the large shock raises volatility and then gradually mean reverts. This demonstrates the clustering property of volatility: high vol periods follow high vol periods.
3. HAR-RV
Heterogeneous AutoRegressive model for realized volatility. Uses lags at multiple horizons: 1-day, 5-day, 22-day, etc.
Intuition: traders with different time horizons contribute to volatility dynamics.
4. How This Maps to volarixs
Volatility is one of the model classes you can select when you set up an experiment — alongside regression, tree & boosted, neural networks, and time-series models. So a volatility forecast in volarixs is built the same way as any other model: pick datasets and a feature set, choose a target horizon, and run it walk-forward over a time window, with results tracked per run.
A volatility forecast is rarely the end of the story, though — it is an input to other decisions. The pieces that consume it are what volarixs is built around:
- risk-adjusted signals, where a vol estimate scales raw direction and confidence
- macro and regime context, which records the inflation, policy, and liquidity state each run was made under
- the Factory, where production models are trained, monitored, and turned into predictions