, maxiter=1000, full_output=True, disp=True, callback=None, return_params=False, **kwargs)[source]

Fit an ETS model by maximizing log-likelihood.

Log-likelihood is a function of the model parameters \(\alpha, \beta, \gamma, \phi\) (depending on the chosen model), and, if initialization_method was set to ‘estimated’ in the constructor, also the initial states \(l_{-1}, b_{-1}, s_{-1}, \ldots, s_{-m}\).

The fit is performed using the L-BFGS algorithm.

start_paramsarray_like, optional

Initial values for parameters that will be optimized. If this is None, default values will be used. The length of this depends on the chosen model. This should contain the parameters in the following order, skipping parameters that do not exist in the chosen model.

  • smoothing_level (\(\alpha\))

  • smoothing_trend (\(\beta\))

  • smoothing_seasonal (\(\gamma\))

  • damping_trend (\(\phi\))

If initialization_method was set to 'estimated' (the default), additionally, the parameters

  • initial_level (\(l_{-1}\))

  • initial_trend (\(l_{-1}\))

  • initial_seasonal.0 (\(s_{-1}\))

  • initial_seasonal.<m-1> (\(s_{-m}\))

also have to be specified.

maxiterint, optional

The maximum number of iterations to perform.

full_outputbool, optional

Set to True to have all available output in the Results object’s mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information.

dispbool, optional

Set to True to print convergence messages.

callbackcallable callback(xk), optional

Called after each iteration, as callback(xk), where xk is the current parameter vector.

return_paramsbool, optional

Whether or not to return only the array of maximizing parameters. Default is False.


Additional keyword arguments to pass to the optimizer.