smooth.AutoMSARIMA

class smooth.AutoMSARIMA(lags=None, ar_order=[3, 3], i_order=[2, 1], ma_order=[3, 3], orders=None, constant=False, initial='backcasting', initial_X=None, ic='AICc', loss='likelihood', h=None, holdout=False, bounds='usual', regressors='use', outliers='ignore', level=0.99, verbose=0, **kwargs)

Automatic Multiple Seasonal ARIMA with order selection.

Wraps AutoADAM with model="NNN" and distribution="dnorm" fixed, providing automatic ARIMA order selection for pure ARIMA (and SARIMA) models without ETS components.

Parameters:

lags (Optional[List[int]]) – Seasonal period(s). E.g. lags=[1, 12] for monthly data. If None, defaults to [1] (non-seasonal).
ar_order (Union[int, List[int], None]) – Maximum AR order(s) per lag level for selection (one entry per seasonal frequency in lags).
i_order (Union[int, List[int], None]) – Maximum integration order(s) per lag level.
ma_order (Union[int, List[int], None]) – Maximum MA order(s) per lag level for selection.
orders (Optional[Dict[str, Any]]) – Dict-style alternative to the scalar max-order arguments above. A dict with keys "ar", "i", "ma" (each an int or list). When provided, ar_order / i_order / ma_order are ignored.
constant (Union[bool, float]) – Whether to include a constant (drift) term.
initial (Union[str, Dict[str, Any], None]) – Initialisation method or dict of fixed initial values. String options: "backcasting", "optimal", "complete", "two-stage".
initial_X (Optional[NDArray]) – Initial values for regressor coefficients (equivalent to R’s initialX).
ic (Literal['AIC', 'AICc', 'BIC', 'BICc']) – Information criterion for model comparison during selection.
loss (Literal['likelihood', 'GPL', 'MSE', 'MAE', 'HAM', 'MSEh', 'MAEh', 'HAMh', 'MSCE', 'MACE', 'CHAM', 'TMSE', 'TMAE', 'THAM', 'GTMSE', 'GTAME', 'GTHAM', 'LASSO', 'RIDGE']) – Loss function for parameter estimation.
h (Optional[int]) – Forecast horizon. Can also be set in predict().
holdout (bool) – Whether to use a holdout sample.
bounds (Literal['usual', 'admissible', 'none']) – Parameter bounds type.
regressors (Literal['use', 'select', 'adapt']) – How to handle external regressors.
outliers (Literal['ignore', 'use', 'select']) – Outlier handling mode (see AutoADAM).
level (float) – Confidence level for outlier detection.
verbose (int) – Verbosity level. 0 = silent.
**kwargs – Additional arguments forwarded to AutoADAM.

See also

AutoADAM: Full automatic model selection.
MSARIMA: Fixed-order MSARIMA wrapper.

Examples

Automatic non-seasonal ARIMA:

>>> from smooth import AutoMSARIMA
>>> import numpy as np
>>> y = np.cumsum(np.random.randn(100)) + 100.0
>>> model = AutoMSARIMA(lags=[1])
>>> model.fit(y)
>>> print(model)

Automatic seasonal ARIMA for monthly data:

>>> model = AutoMSARIMA(lags=[1, 12])
>>> model.fit(y)
>>> fc = model.predict(h=24)

References

Svetunkov, I. (2023). Forecasting and Analytics with the Augmented Dynamic Adaptive Model. https://openforecast.org/adam/

Methods

`coefbootstrap`([nsim, size, replace, prob, ...])	Bootstrap the coefficient sampling distribution by refitting subsamples.
`confint`([parm, level, type, bootstrap, ...])	Confidence intervals for the estimated parameters.
`fit`(y[, X])	Fit the AutoADAM model.
`multicov`([type, h, nsim])	Covariance matrix of multi-step-ahead forecast errors.
`outlierdummy`([level, type])	Detect outliers and return a matrix of indicator dummy variables.
`plot`([which, level, legend, lowess])	Diagnostic plots for the fitted ADAM model (R: `plot.adam`).
`point_lik`([log])	Per-observation log-likelihood of the fitted model.
`predict`(h[, X, interval, level, side, ...])	Generate forecasts using the fitted ADAM model.
`predict_intervals`(h[, X, levels, side, nsim])	Generate prediction intervals using the fitted ADAM model.
`reapply`([nsim, type, bootstrap, heuristics, ...])	Re-run the model on the in-sample data for `nsim` parameter draws.
`reforecast`([h, X, occurrence, interval, ...])	Produce `h`-step-ahead forecasts via Monte-Carlo reforecasting.
`rmultistep`([h])	Return the (T-h) × h matrix of rolling in-sample multistep forecast errors.
`rstandard`()	Return standardised residuals.
`rstudent`()	Return studentised (leave-one-out) residuals.
`select_best_model`()	Select the best model based on information criteria and update model parameters.
`simulate`([nsim, seed, obs, randomizer])	Re-simulate `obs` observations from the fitted model.
`summary`([level, digits, type])	Generate a coefficient-table summary of the fitted model.
`vcov`([type, bootstrap, heuristics, step_size])	Variance-covariance matrix of the estimated parameters.

Attributes

`actuals`	Return original in-sample data.
`aic`	Return Akaike Information Criterion.
`aicc`	Return corrected Akaike Information Criterion.
`b_value`	$B).
`bic`	Return Bayesian Information Criterion.
`bicc`	Return corrected Bayesian Information Criterion.
`coef`	Return estimated coefficients (parameter vector B).
`coef_names`	Parameter names aligned with `coef` (the B vector).
`constant_value`	$constant).
`data`	$data).
`distribution_`	$distribution).
`error_type`	'A' (additive) or 'M' (multiplicative).
`fisher_information_`	Observed Fisher Information matrix at the estimated parameters.
`fitted`	Return in-sample fitted values.
`holdout_data`	$holdout).
`ic_weights`	$ICw).
`initial_type`	$initialType).
`initial_value`	$initial).
`is_combined`	Return True if model is a combination of multiple models.
`lags_used`	Return the vector of lags used in the model.
`loglik`	Return log-likelihood of the fitted model.
`loss_`	$loss).
`loss_value`	$lossValue).
`measurement`	$measurement).
`model_name`	modelName()).
`model_type`	Return ETS model type code (e.g., 'AAN', 'AAA', 'MAdM').
`models`	$models).
`n_param`	$nParam).
`nobs`	Return number of observations used for fitting.
`nparam`	Return number of estimated parameters.
`om_model`	Fitted occurrence model (OM / OMG / AutoOM), or None.
`orders`	Return ARIMA orders as dict with 'ar', 'i', 'ma' keys.
`persistence_vector`	$persistence).
`phi_`	$phi).
`profile`	$profile).
`residuals`	Return model residuals (errors from fitting).
`scale`	Internal optimisation scale of the error distribution (R: `adam_obj$scale`).
`sigma`	`sigma(adam_obj)`).
`states`	$states).
`time_elapsed`	Time taken to fit the model in seconds.
`transition`	$transition).