smooth.ES.sm

ES.sm(**kwargs)

Fit a scale model for this fit (R: sm.adam).

A scale model is a second ADAM fitted to a transform of this model’s residuals, so the error’s scale varies over time instead of being a single number. It is scored by this model’s log-likelihood, with the scale model’s fitted values supplying the distribution’s scale at each observation – the state-space counterpart of a GARCH or GAMLSS scale equation.

The fitted scale model is returned, not attached. Assign it to scale_model to put it to work: that is R’s implant(), which Python does not need as a separate function.

Parameters:

model (str, optional) – Scale model specification, "YYY" by default (select among multiplicative ETS), exactly as in R.
lags – Passed to ADAM. lags defaults to this model’s and constant to False.
orders – Passed to ADAM. lags defaults to this model’s and constant to False.
constant – Passed to ADAM. lags defaults to this model’s and constant to False.
regressors – Passed to ADAM. lags defaults to this model’s and constant to False.
X – Passed to ADAM. lags defaults to this model’s and constant to False.
**kwargs – Any other ADAM argument (initial, ic, bounds).

Returns:

The fitted scale model, with is_scale_ set.

Return type:

ADAM

Raises:

ValueError – If this model was not estimated with loss="likelihood", or if its distribution is one sm() cannot score.

Notes

Only arguments passed explicitly are forwarded, mirroring R, where the matched call means sm()’s own defaults never reach adam() and adam()’s apply instead – so the scale model uses initial="backcasting" unless told otherwise.

Examples

>>> model = ADAM(model="MNN", lags=[1, 12], distribution="dnorm")
>>> model.fit(y)
>>> scale_model = model.sm()
>>> model.scale_model = scale_model      # R's implant()
>>> forecast = model.predict(h=12, interval="prediction")