GARCH

garch.GARCH · inherits BaseForecaster

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

GARCH implements the BaseForecaster contract.

__init__(self, p: int = 1, q: int = 1, alias: str = 'GARCH', conformal_params: ConformalIntervals | None = None, allow_extended_iterations: bool = False, iteration_scaling: str = 'cubic')

Initialize 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'.

Attributes: * uses_exog: False

fit(self, y: jnp.ndarray, X: jnp.ndarray | None = None, n_iters: int | None = None, actual_len: int | None = None) -> GARCH

Fit GARCH model to data.

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: GARCH (the fitted model; sets self.model_).

predict(self, h: int, X: jnp.ndarray | None = None, level: list[int] | None = None, simulate: bool = False, n_sims: int = 1000, seed: int | None = None, return_paths: bool = True) -> dict

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

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: list[int] | None = None) -> dict

Return in-sample fitted values and conditional variance.

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: jnp.ndarray, h: int, X: jnp.ndarray | None = None, X_future: jnp.ndarray | None = None, level: list[int] | None = None, fitted: bool = False, n_iters: int | None = None, actual_len: int | None = None, simulate: bool = False, n_sims: int = 1000, seed: int | None = None, return_paths: bool = True) -> dict

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

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'.