smooth.SMA

class smooth.SMA(order=None, ic='AICc', h=10, holdout=False, fast=True, verbose=0, **kwargs)

Simple Moving Average in Single Source of Error state space form.

SMA(m) is an AR(m) state-space model where every AR coefficient is fixed at 1/m. It is implemented as a thin wrapper over ADAM with model="NNN" and the AR vector hard-coded, so it inherits the full ADAM fit / predict / diagnostics surface (multi-step forecasts, prediction intervals, residual diagnostics). If order is left unspecified, the order is selected automatically by information criterion.

Parameters:

• order (Optional[int]) – Order of the moving average. If None, selected automatically using the information criterion (ternary search when fast=True, sequential scan when fast=False).

• ic (Literal['AIC', 'AICc', 'BIC', 'BICc']) – Information criterion used for automatic order selection.

• h (int) – Forecast horizon (used with holdout=True to reserve a test set).

• holdout (bool) – Whether to hold out the last h observations for validation.

• fast (bool) – If True, use ternary search for order selection (fast, finds a local minimum). If False, evaluate all orders 1 … min(200, T) sequentially. When a pandas Series with a DatetimeIndex is passed, the inferred seasonal period is always evaluated as a candidate regardless of this flag.

• verbose (int) – Verbosity level. 0 = silent.

• **kwargs – Additional arguments passed to ADAM (e.g. n_iterations).

model

Model name, e.g. "SMA(3)".

Type:

str

ICs_

IC values for each evaluated order (only present after auto-selection). Keys are order integers, values are IC floats.

Type:

dict

See also

ADAM

Parent class; all ADAM attributes are available after fit().

MSARIMA

General multiple-seasonal ARIMA wrapper.

Examples

Fixed order:

>>> import numpy as np
>>> from smooth import SMA
>>> y = np.cumsum(np.random.randn(60)) + 100
>>> model = SMA(order=4, h=5)
>>> model.fit(y)
>>> fc = model.predict(h=5)
>>> fc.mean

Auto-selected order:

>>> model = SMA(h=5)
>>> model.fit(y)
>>> print(model.model)   # e.g. "SMA(3)"
>>> print(model.ICs_)

References

• Svetunkov, I., & Petropoulos, F. (2017). Old dog, new tricks: a modelling view of simple moving averages. International Journal of Production Research. https://doi.org/10.1080/00207543.2017.1380326

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 SMA model to time series data.
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).