GARCH

chronax.models.GARCH · inherits BaseForecaster

Models time-varying volatility where conditional variance depends on past squared errors and past conditional variances.

Instance Attributes:

Attribute	Type	Description
p	int	ARCH order (lagged squared shocks).
q	int	GARCH order (lagged variances).
alias	str	Display name for the model (e.g., GARCH(1,1)).
conformal_params	ConformalIntervals \| None	Configuration for conformal prediction intervals.
allow_extended_iterations	bool	If True, allows up to 120 iterations for complex data.
iteration_scaling	str	'cubic' or 'quadratic' complexity-to-iteration mapping.
uses_exog	bool	False (Model does not use exogenous variables).
model_	dict	Fitted model state, including omega, alpha, beta, sigma2 (conditional variance series), fitted, y_mean, and state variables for forecasting (y_centered_last, sigma2_last, init_var).

__init__(self, p=1, q=1, alias='GARCH', conformal_params=None, allow_extended_iterations=False, iteration_scaling='cubic')

Initialize GARCH model with ARCH/GARCH orders and optimization settings.

Parameter	Type	Default	Description
p	int	1	ARCH order (lagged squared shocks), must be >= 1.
q	int	1	GARCH order (lagged variances), must be >= 0.
alias	str	"GARCH"	Display name for the model.
conformal_params	ConformalIntervals \| None	None	Configuration for conformal prediction intervals.
allow_extended_iterations	bool	False	If True, allows up to 120 iterations for complex data.
iteration_scaling	str	"cubic"	Complexity-to-iteration mapping: 'cubic' or 'quadratic'.

fit(self, y, X=None, n_iters=None, actual_len=None) -> Self

Fit GARCH model to data.

Parameters:

Parameter	Type	Default	Description
y	jnp.ndarray	-	Input time series (may be padded).
X	jnp.ndarray \| None	None	Exogenous variables (unused).
n_iters	int \| None	None	Fixed iteration count. None estimates from data.
actual_len	int \| None	None	Actual data length for padded inputs.

Returns: Self (the fitted forecaster; sets self.model_).

predict(self, h, X=None, level=None, simulate=False, n_sims=1000, seed=None, return_paths=True) -> dict

Generate h-step forecasts (deterministic or Monte Carlo).

Parameters:

Parameter	Type	Default	Description
h	int	-	Forecast horizon.
X	jnp.ndarray \| None	None	Exogenous variables (unused).
level	list[int] \| None	None	Confidence levels for prediction intervals. When simulate=False, intervals are analytical (normal quantiles). When simulate=True, intervals are percentile-based from simulation paths.
simulate	bool	False	Use Monte Carlo simulation instead of analytical forecasting.
n_sims	int	1000	Number of simulation paths (only used when simulate=True).
seed	int \| None	None	PRNG seed for reproducibility (only used when simulate=True).
return_paths	bool	True	Include full simulation paths in output (only used when simulate=True).

Returns: dict When simulate=False: Keys: 'mean', 'sigma2', and optionally 'lo-{lv}', 'hi-{lv}'. When simulate=True: Keys: 'mean', 'median', 'sigma2_mean', 'sigma2_median', and optionally 'paths', 'sigma2_paths', 'lo-{lv}', 'hi-{lv}'.

predict_in_sample(self, level=None) -> dict

Return in-sample fitted values and conditional variance.

Parameters:

Parameter	Type	Default	Description
level	list[int] \| None	None	Confidence levels for fitted prediction intervals.

Returns: dict Keys: 'fitted', 'sigma2', and optionally 'fitted-lo-{lv}', 'fitted-hi-{lv}'.

forecast(self, y, h, X=None, X_future=None, level=None, fitted=False, n_iters=None, actual_len=None, simulate=False, n_sims=1000, seed=None, return_paths=True) -> dict

Stateless fit-and-predict (deterministic or Monte Carlo).

Parameters:

Parameter	Type	Default	Description
y	jnp.ndarray	-	Input time series (may be padded).
h	int	-	Forecast horizon.
X	jnp.ndarray \| None	None	Exogenous variables (unused).
X_future	jnp.ndarray \| None	None	Future exogenous variables (unused).
level	list[int] \| None	None	Confidence levels for prediction intervals. When simulate=True, forecast intervals are percentile-based from paths, while fitted intervals remain analytical.
fitted	bool	False	Whether to return in-sample fitted values.
n_iters	int \| None	None	Fixed iteration count. None estimates from data.
actual_len	int \| None	None	Actual data length for padded inputs.
simulate	bool	False	Use Monte Carlo simulation instead of analytical forecasting.
n_sims	int	1000	Number of simulation paths (only used when simulate=True).
seed	int \| None	None	PRNG seed for reproducibility (only used when simulate=True).
return_paths	bool	True	Include full simulation paths in output (only used when simulate=True).

Returns: dict Keys: 'mean', 'sigma2', and optionally intervals and fitted values. When simulate=True, also includes 'median', 'sigma2_mean', 'sigma2_median', and optionally 'paths', 'sigma2_paths'.