AutoARIMA

auto_arima.AutoARIMA · inherits BaseForecaster

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

Attributes:

Name	Type	Description
uses_exog	bool	Whether exogenous features are supported.
model_	dict[str, Any] \| None	Fitted model payload after fit.
standardize	bool	Whether to normalize series before optimization.

__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.
D	Optional[int]	None	Optional seasonal differencing override.
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	Initial stepwise AR order.
start_q	int	2	Initial stepwise MA order.
start_P	int	1	Initial stepwise seasonal AR order.
start_Q	int	1	Initial stepwise 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 model selection.
stepwise	bool	True	Enable stepwise search over full grid search.
nmodels	int	94	Max number of candidate fits during stepwise search.
method	str	'CSS-ML'	Fitting objective path (CSS, ML, or hybrid).
allowdrift	bool	True	Allow drift models when integration order is one.
allowmean	bool	True	Allow mean term for stationary candidates.
period	Optional[int]	None	Seasonal period, or auto-detect when None.

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

Fit automatic ARIMA model selection on a series.

Parameters:

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

Returns: Self (The fitted estimator instance.)

forecast(self, h, y, X=None, X_future=None, level=None, fitted=False) -> dict

Produce fast forecasts from history with cached-order optimization.

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

Key	Type	Description
"mean"	jnp.ndarray	Point forecasts.

predict(self, h, X=None, level=None) -> dict

Forecast from the fitted automatic ARIMA model.

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

Key	Type	Description
"mean"	jnp.ndarray	Mean forecast.
"lo-{level}"	jnp.ndarray	Lower bound of the confidence interval (if level is provided).
"hi-{level}"	jnp.ndarray	Upper bound of the confidence interval (if level is provided).

summary(self) -> str

Return a compact textual summary of the fitted model.

Parameters:

Parameter	Type	Default	Description
self	-	-	This method takes no explicit parameters beyond self.

Returns: str (Human-readable model summary.)

ARIMA

auto_arima.ARIMA · inherits BaseForecaster

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

Attributes:

Name	Type	Description
uses_exog	bool	Indicates exogenous support.
model_	dict[str, Any] \| None	Fitted model payload.
alias	str	Friendly model label.
standardize	bool	Whether to normalize series during fitting.

__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.

Parameter	Type	Default	Description
order	Tuple[int, int, int]	(0, 0, 0)	Non-seasonal order (p, d, q).
seasonal_order	Tuple[int, int, int]	(0, 0, 0)	Seasonal order (P, D, Q).
period	int	1	Seasonal period.
include_mean	bool	True	Include deterministic mean/drift term.
method	str	'CSS'	Optimization method selector.
alias	str	'ARIMA'	Friendly model label.
standardize	bool	True	Normalize series during fitting.

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

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

Parameters:

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

Returns: Self (self, with model_ and y_train_ set.)

forecast(self, h, y, X=None, X_future=None, level=None, fitted=False) -> dict

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

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

Key	Type	Description
"mean"	jnp.ndarray	Point forecasts.

predict(self, h, X=None, level=None) -> dict

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

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

Key	Type	Description
"mean"	jnp.ndarray	Mean forecast.
"lo-{level}"	jnp.ndarray	Lower bound of the confidence interval (if level is provided).
"hi-{level}"	jnp.ndarray	Upper bound of the confidence interval (if level is provided).

detect_period

auto_arima.detect_period

Detect the dominant seasonal period from a time series using ACF peaks.

Parameter	Type	Default	Description
y	np.ndarray	-	Univariate time series; will be cast to float64.
max_period	Optional[int]	None	Maximum period to consider. If None, set to min(n // 4, 200). If < 2, returns 1.

Returns: int (Detected seasonal period (>= 1). 1 means no seasonality detected.)

arima_fit

auto_arima.arima_fit

Fit an ARIMA model to a univariate series and return coefficients, metrics, and diagnostics.

Parameter	Type	Default	Description
x	jnp.ndarray	-	Training series; converted to float64.
order	Tuple[int, int, int]	(0, 0, 0)	Non-seasonal (p, d, q).
seasonal	Optional[Dict[str, Any]]	None	"order" (P, D, Q) and "period" (m); default (0,0,0), period 1.
xreg	Optional[jnp.ndarray]	None	Exogenous regressors; optional.
include_mean	bool	True	Whether to include intercept/drift.
method	str	'CSS-ML'	"CSS", "ML", or "CSS-ML" for optimization path.
optim_control	Optional[Dict[str, Any]]	None	Optional "steps" (maxiter) for optimizer.

Returns: Dict[str, Any] (Fitted model dict with coef, model, residuals, innovations, sigma2, loglik, aic, aicc, bic, arma, delta, nobs, use_drift, drift_coef, success.)

predict_arima

auto_arima.predict_arima

Produce n_ahead-step forecasts (and optionally standard errors) from a fitted ARIMA model.

Parameter	Type	Default	Description
model	Dict[str, Any]	-	Fitted model dict from arima_fit (coef, model, arma, sigma2, use_drift, drift_coef, innovations, etc.).
n_ahead	int	-	Forecast horizon.
newxreg	Optional[jnp.ndarray]	None	Future exogenous values; if None and n_exog > 0, a constant/intercept column is used.
se_fit	bool	True	If True, return (pred, se); otherwise pred only.

Returns: Union[jnp.ndarray, Tuple[jnp.ndarray, jnp.ndarray]] (Forecasts array, or (forecasts, se) when se_fit is True. Single model: shapes (n_ahead,) and (n_ahead,); batch: (batch_size, n_ahead) and (batch_size, n_ahead).)

ndiffs

auto_arima.ndiffs

Determine the number of non-seasonal differences needed for stationarity.

Parameter	Type	Default	Description
x	jnp.ndarray	-	Univariate time series.
alpha	float	0.05	Significance level for KPSS; default 0.05. Stationary if pval >= alpha.
max_d	int	2	Maximum number of differences to consider; static, usually 2.

Returns: int (Number of non-seasonal differences (0, 1, or max_d).)

nsdiffs

auto_arima.nsdiffs

Determine number of seasonal differences (Optimized).

Parameter	Type	Default	Description
x	jnp.ndarray	-	Input time series
period	int	-	Seasonal period (e.g., 12 for monthly data)
max_D	int	1	Maximum seasonal differences allowed
alpha	float	0.64	Threshold for seasonal strength (default 0.64 matches statsforecast)

Returns: int (Number of seasonal differences needed (0 to max_D))