advanced-math-trading/time-series-regimes

Regime detection identifies structural breaks and shifts in market behavior by applying statistical tests and algorithms to historical price data. This Skill implements regime-detection workflows that segment time series into distinct regimes, enabling you to build trading models that adapt to changing market conditions.

ARIMA models temporal dependencies and trends in stationary series, while GARCH captures volatility clustering and regime-dependent volatility. This Skill combines both to fit regime-aware ARIMA-GARCH models that reflect how market volatility changes across detected regimes.

Stationarity testing applies statistical tests like unit-root tests to check whether a series has constant mean and variance over time. This Skill includes stationarity testing procedures required to validate whether your price data is suitable for ARIMA-GARCH estimation and regime modeling.

Yes. Stochastic differential equations model continuous price evolution with optional jump components, and regime-aware SDE discretization applies different parameters per regime. This Skill provides SDE discretization schemes that integrate regime detection to generate regime-conditioned Monte Carlo simulations.

You need historical price data—typically closing prices or returns—across multiple time horizons and assets. This Skill requires access to historical price series and applies stationarity tests, ARIMA-GARCH estimation, and regime-detection algorithms to transform raw price data into regime-aware trading signals.

Integration links regime identification with model diagnostics and backtesting by embedding detection algorithms into a multi-step pipeline. This Skill supports diagnostic workflows that test stationarity, fit regime-specific ARIMA-GARCH models, and validate regime transitions across multiple assets and time horizons.