statsmodels.tsa.holtwinters.ExponentialSmoothing.fit¶

ExponentialSmoothing.fit(smoothing_level=None, smoothing_trend=None, smoothing_seasonal=None, damping_trend=None, *, optimized=True, remove_bias=False, start_params=None, method=None, minimize_kwargs=None, use_brute=True, use_boxcox=None, use_basinhopping=None, initial_level=None, initial_trend=None)[source]¶

Fit the model

Parameters:¶

smoothing_level : float, optional¶

The alpha value of the simple exponential smoothing, if the value is set then this value will be used as the value.

smoothing_trend : float, optional¶

The beta value of the Holt’s trend method, if the value is set then this value will be used as the value.

smoothing_seasonal : float, optional¶

The gamma value of the holt winters seasonal method, if the value is set then this value will be used as the value.

damping_trend : float, optional¶

The phi value of the damped method, if the value is set then this value will be used as the value.

optimized : bool, optional¶

Estimate model parameters by maximizing the log-likelihood.

remove_bias : bool, optional¶

Remove bias from forecast values and fitted values by enforcing that the average residual is equal to zero.

start_params : array_like, optional¶

Starting values to used when optimizing the fit. If not provided, starting values are determined using a combination of grid search and reasonable values based on the initial values of the data. See the notes for the structure of the model parameters.

method : str, default "L-BFGS-B"¶

The minimizer used. Valid options are “L-BFGS-B” , “TNC”, “SLSQP” (default), “Powell”, “trust-constr”, “basinhopping” (also “bh”) and “least_squares” (also “ls”). basinhopping tries multiple starting values in an attempt to find a global minimizer in non-convex problems, and so is slower than the others.

minimize_kwargs : dict[str, Any]¶

A dictionary of keyword arguments passed to SciPy’s minimize function if method is one of “L-BFGS-B”, “TNC”, “SLSQP”, “Powell”, or “trust-constr”, or SciPy’s basinhopping or least_squares functions. The valid keywords are optimizer specific. Consult SciPy’s documentation for the full set of options.

use_brute : bool, optional¶

Search for good starting values using a brute force (grid) optimizer. If False, a naive set of starting values is used.

use_boxcox : {True, False, 'log', float}, optional¶

Should the Box-Cox transform be applied to the data first? If ‘log’ then apply the log. If float then use the value as lambda.

Deprecated since version 0.12: Set use_boxcox when constructing the model

use_basinhopping : bool, optional¶

Deprecated. Using Basin Hopping optimizer to find optimal values. Use method instead.

Deprecated since version 0.12: Use method instead.

initial_level : float, optional¶

Value to use when initializing the fitted level.

Deprecated since version 0.12: Set initial_level when constructing the model

initial_trend : float, optional¶

Value to use when initializing the fitted trend.

Deprecated since version 0.12: Set initial_trend when constructing the model or set initialization_method.

Returns:¶

See statsmodels.tsa.holtwinters.HoltWintersResults.

Return type:¶

HoltWintersResults

Notes

This is a full implementation of the holt winters exponential smoothing as per [1]. This includes all the unstable methods as well as the stable methods. The implementation of the library covers the functionality of the R library as much as possible whilst still being Pythonic.

The parameters are ordered

[alpha, beta, gamma, initial_level, initial_trend, phi]

which are then followed by m seasonal values if the model contains a seasonal smoother. Any parameter not relevant for the model is omitted. For example, a model that has a level and a seasonal component, but no trend and is not damped, would have starting values

[alpha, gamma, initial_level, s0, s1, …, s<m-1>]

where sj is the initial value for seasonal component j.

References

[1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles

and practice. OTexts, 2014.