Volatility Regime Analysis AI Prompt

Analyze volatility regimes in this return series and build a regime classification model.

Asset / index: {{asset}}
Return series: {{returns}}

1. Realized volatility estimation methods:
   Compare these estimators and explain when each is appropriate:
   - Close-to-close: std(log returns) × sqrt(252). Simple but uses only end-of-day prices.
   - Parkinson: uses daily high-low range. More efficient than close-to-close.
   - Garman-Klass: uses OHLC prices. More efficient than Parkinson.
   - Yang-Zhang: handles overnight gaps. Best all-around estimator for daily OHLC.
   - Rolling window choice: 21-day (1 month), 63-day (1 quarter), 252-day (1 year) — each captures different features

2. GARCH volatility modeling:
   Fit a GARCH(1,1) model: σ²_t = ω + α ε²_{t-1} + β σ²_{t-1}
   - Report: ω, α, β, and their standard errors
   - Persistence: α + β. If > 0.99, volatility shocks are very long-lived.
   - Half-life of volatility shock: ln(0.5) / ln(α + β)
   - Likelihood ratio test: GARCH vs constant variance (ARCH test)
   - Plot conditional volatility over time

3. Regime detection:
   Method A — Hidden Markov Model (HMM):
   - Fit a 2-state Gaussian HMM to the returns
   - State 1 typically: low volatility, higher mean (bull)
   - State 2 typically: high volatility, lower/negative mean (bear)
   - Report: state means, state variances, transition probability matrix
   - Plot: smoothed state probabilities over time

   Method B — Threshold-based regime classification:
   - Low vol: rolling 21-day vol < 33rd percentile of historical vol
   - Medium vol: 33rd–67th percentile
   - High vol: > 67th percentile
   - Simpler, more transparent, but not probabilistic

4. Regime statistics:
   For each regime, report:
   - Mean return (annualized)
   - Volatility (annualized)
   - Sharpe ratio
   - Average duration (how long do regimes last?)
   - Transition frequency

5. Practical implications:
   - Does the current period appear to be in a high-vol regime?
   - How should portfolio risk management differ across regimes?

Return: volatility estimator comparison, GARCH results, HMM regime probabilities, regime statistics table, and current regime assessment.