StateSpaceModel

chronax.auto_arima.StateSpaceModel · inherits NamedTuple

Immutable container describing the ARIMA state-space representation used by Kalman filtering and forecasting kernels.

Attribute	Type	Description
T	Array	Transition dynamics.
Z	Array	Observation mapping.
V	Array	Process covariance.
a0	Array	Initial state location.
P0	Array	Initial uncertainty.

ARIMAResult

chronax.auto_arima.ARIMAResult · inherits NamedTuple

Immutable selection summary for a candidate ARIMA specification.

Attribute	Type	Description
loglik	float	Exact log-likelihood for the model.
sigma2	float	Innovation variance estimate.
aic	float	Akaike Information Criterion.
bic	float	Bayesian Information Criterion.
aicc	float	Small-sample corrected AIC.
ic	float	Selected information criterion value.
success	bool	Indicates finite and valid fit result.

AutoARIMA

chronax.auto_arima.AutoARIMA · inherits BaseForecaster

Performs automatic ARIMA model selection and fitting over configured search spaces, then exposes forecasting and interval prediction APIs.

Attributes: * uses_exog: True * model_: dict[str, Any] | None * standardize: bool * _cached_order: tuple[int, int, int] | None * _cached_seasonal_order: tuple[int, int, int] | None * _cached_delta: Array | None

__init__(self, d=None, D=None, max_p=5, max_q=5, max_P=2, max_Q=2, max_order=5, max_d=2, max_D=1, start_p=2, start_q=2, start_P=1, start_Q=1, stationary=False, seasonal=True, ic='aicc', stepwise=True, nmodels=94, method='CSS-ML', allowdrift=True, allowmean=True, period=None)

Set up AutoARIMA search bounds, options, and internal caches.

Parameter	Type	Default	Description
d	Optional[int]	None	Optional non-seasonal differencing override; None to infer.
D	Optional[int]	None	Optional seasonal differencing override; None to infer.
max_p	int	5	Maximum non-seasonal AR order.
max_q	int	5	Maximum non-seasonal MA order.
max_P	int	2	Maximum seasonal AR order.
max_Q	int	2	Maximum seasonal MA order.
max_order	int	5	Maximum total ARMA order budget.
max_d	int	2	Upper bound for inferred non-seasonal differencing.
max_D	int	1	Upper bound for inferred seasonal differencing.
start_p	int	2	Stepwise starting AR order.
start_q	int	2	Stepwise starting MA order.
start_P	int	1	Stepwise starting seasonal AR order.
start_Q	int	1	Stepwise starting seasonal MA order.
stationary	bool	False	Force stationary differencing (d=D=0) when true.
seasonal	bool	True	Enable seasonal search behavior.
ic	str	'aicc'	Information criterion for selection.
stepwise	bool	True	Stepwise vs full grid search.
nmodels	int	94	Max stepwise iterations.
method	str	'CSS-ML'	CSS, ML, or CSS-ML.
allowdrift	bool	True	Drift and mean inclusion.
allowmean	bool	True	Drift and mean inclusion.
period	Optional[int]	None	Seasonal period or None for auto-detect.

fit(self, y, X=None) -> AutoARIMA

Fit automatic ARIMA model selection on a series.

Optionally standardizes the series, infers/uses seasonal period, executes automatic order search, and caches the winning order for subsequent fast forecast calls.

Parameters:

Parameter	Type	Default	Description
y	jnp.ndarray	-	Training target series.
X	Optional[jnp.ndarray]	None	Optional exogenous regressors.

Returns: AutoARIMA (The fitted estimator instance; sets self.model_).

forecast(self, h, y, X=None, X_future=None, level=None, fitted=False) -> Dict[str, jnp.ndarray]

Produce fast forecasts from history with cached-order optimization.

On first invocation, this method runs full automatic selection via fit. On later calls, it reuses cached orders and only runs the optimization/forecast kernels needed for fresh predictions.

Parameters:

Parameter	Type	Default	Description
h	int	-	Forecast horizon.
y	jnp.ndarray	-	Input history series.
X	Optional[jnp.ndarray]	None	Optional exogenous matrix.
X_future	Optional[jnp.ndarray]	None	Future exogenous regressors (unused; included for BaseForecaster compliance).
level	Optional[list]	None	Confidence levels (unused; included for BaseForecaster compliance).
fitted	bool	False	Whether to return fitted values (unused; included for BaseForecaster compliance).

Returns: dict[str, jnp.ndarray] (Forecast dictionary containing mean). Return Keys: * mean: jnp.ndarray

predict(self, h, X=None, level=None) -> Dict[str, jnp.ndarray]

Forecast from the fitted automatic ARIMA model.

Uses stored fitted model state to generate mean forecasts and, when confidence levels are provided, symmetric interval bounds.

Parameters:

Parameter	Type	Default	Description
h	int	-	Forecast horizon.
X	Optional[jnp.ndarray]	None	Optional future exogenous matrix.
level	Optional[Union[int, Tuple[int, ...]]]	None	Confidence levels.

Returns: dict[str, jnp.ndarray] (Mean forecast and optional interval bounds). Return Keys: * mean: jnp.ndarray * lo-{level}: jnp.ndarray (If level is provided) * hi-{level}: jnp.ndarray (If level is provided)

summary(self) -> str

Return a compact textual summary of the fitted model.

Builds an ARIMA order summary string with AICc when fitted, or a not-fitted status message otherwise.

Parameters:

Parameter	Type	Default	Description
self	-	-	(undocumented)

Returns: str (Human-readable model summary).

ARIMA

chronax.auto_arima.ARIMA · inherits BaseForecaster

Fixed-order ARIMA forecaster backed by shared JAX optimization kernels.

Attributes: * uses_exog: True * model_: dict[str, Any] | None * _delta: Array * _arma: tuple[int, ...]

__init__(self, order=(0, 0, 0), seasonal_order=(0, 0, 0), period=1, include_mean=True, method='CSS', alias='ARIMA', standardize=True)

Set up fixed-order ARIMA and precompute differencing and ARMA metadata.

Stores order, seasonal_order, period, include_mean, method, and alias. Precomputes and caches the differencing polynomial (delta), ARMA structure tuple (_arma), and parameter counts (_narma, _ncxreg, _n_exog) so that fit() and forecast() do not recompute them. Initializes model to None and optional standardization stats (_y_mean, _y_std). No fitting is performed.

Parameters:

Parameter	Type	Default	Description
order	Tuple[int, int, int]	(0, 0, 0)	(p, d, q).
seasonal_order	Tuple[int, int, int]	(0, 0, 0)	(P, D, Q).
period	int	1	Seasonal period.
include_mean	bool	True	Include intercept/drift.
method	str	'CSS'	CSS, ML, or CSS-ML.
alias	str	'ARIMA'	Display name.
standardize	bool	True	Whether to standardize series in fit/forecast.

fit(self, y, X=None) -> ARIMA

Estimate ARIMA parameters and store the fitted model and training state.

Optionally standardizes y (and caches y_mean, _y_std), then calls arima_fit with the instance's order, seasonal_order, period, include_mean, and method. Stores the returned dict in model and ensures model_["arma"] has the correct tuple. Saves y_fit as y_train_ for use in predict (e.g. for _reconstruct_forecast). Returns self for method chaining.

Parameters:

Parameter	Type	Default	Description
y	jnp.ndarray	-	Training target series.
X	Optional[jnp.ndarray]	None	Optional exogenous regressors (same length as y).

Returns: ARIMA (self, with model_ and y_train_ set; sets self.model_).

forecast(self, h, y, X=None, X_future=None, level=None, fitted=False) -> Dict[str, jnp.ndarray]

Fit the fixed-order model on the given series and return h-step forecasts in one shot.

Standardizes y if standardize is True, then runs BFGS (CSS and/or ML) using the cached _delta and _arma without building the full arima_fit result (no AIC/BIC/residuals). Uses _forecast_from_params for a single XLA dispatch from params to forecasts, then _reconstruct_forecast to integrate differencing and _aa_denormalize to map back to original scale. Exogenous X is not used in this fast path. Returns a dict with key "mean" containing the forecast array. Useful when only point forecasts are needed and fitting state is not retained.

Parameters:

Parameter	Type	Default	Description
h	int	-	Forecast horizon.
y	jnp.ndarray	-	Training series (used only for this call).
X	Optional[jnp.ndarray]	None	Exogenous regressors; not used in current fast path.
X_future	Optional[jnp.ndarray]	None	Future exogenous regressors (unused; included for BaseForecaster compliance).
level	Optional[list]	None	Confidence levels (unused; included for BaseForecaster compliance).
fitted	bool	False	Whether to return fitted values (unused; included for BaseForecaster compliance).

Returns: Dict[str, jnp.ndarray] ({"mean": array of shape (h,)}). Return Keys: * mean: jnp.ndarray

predict(self, h, X=None, level=None) -> Dict[str, jnp.ndarray]

Produce h-step forecasts (and optional interval bands) from the fitted model.

Requires a prior fit (model_ is not None). Calls predict_arima with model_, n_ahead=h, newxreg=X, and se_fit=(level is not None). Reconstructs forecasts from differenced space via _reconstruct_forecast and denormalizes if standardize was used. When level is provided, scales standard errors for integrated models (d+D>0) by cumulative sum of squared SEs and builds symmetric intervals using _quantiles. Returns a dict with "mean" and optionally "lo" / "hi" keys for each level.

Parameters:

Parameter	Type	Default	Description
h	int	-	Forecast horizon.
X	Optional[jnp.ndarray]	None	Future exogenous regressors; shape (h, n_exog).
level	int \| tuple[int, ...] \| None	None	Confidence level(s), e.g. 90 or (80, 95).

Returns: Dict[str, jnp.ndarray] (At least "mean"; if level given, "lo" and "hi" per level). Return Keys: * mean: jnp.ndarray * lo-{level}: jnp.ndarray (If level is provided) * hi-{level}: jnp.ndarray (If level is provided)