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)

Fit the model

Parameters:

smoothing_levelfloat, optional

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

smoothing_trendfloat, 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_seasonalfloat, 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_trendfloat, optional

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

optimizedbool, optional

Estimate model parameters by maximizing the log-likelihood.

remove_biasbool, optional

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

start_paramsarray_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.

methodstr, 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_kwargsdict[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_brutebool, 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_basinhoppingbool, optional

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

Deprecated since version 0.12: Use method instead.

initial_levelfloat, optional

Value to use when initializing the fitted level.

Deprecated since version 0.12: Set initial_level when constructing the model

initial_trendfloat, 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:

HoltWintersResults

See statsmodels.tsa.holtwinters.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.