One Step Ahead Predictions with ExponentialSmoothing

[dtoniolo]

The problem

I have a time series divided in two consecutive train and test partitions. I need the model to perform well in one step ahead predictions. However, there seems to be no way to do this without refitting the model.

Code

I test the model in this toy example:

from statsmodels.tsa.holtwinters import Holt

data = load_data_from_somewhere()
n = data.size
train = data[:0.8*n]
test = data[0.8*n:]
mod = Holt(train)
fitted_mod = mod.fit(smoothing_level=.5, smoothing_slope=.05)

at this point, if fitted_mod where a state space model, i could do the following (related to what's explained here, but without the cross validation):

complete_mod = Holt(data)
fitted_complete_mod = complete_mod.filter(fitted_mod.params)
pred = fitted_complete_mod.predict(start=0.8*n)
# then compute metrics like MSE between pred and train

however, this is not possibile with Holt: the filter method fails. I can find no other way to do this. I'd like to make it clear that I do not want to refit the parameters, instead I wish to keep the same ones from the train fit.

Additional problem

As explained in the user guide, Exponential Smoothing are not compatible, in general, with the state space formulation. For this reason, three different implementations are provided.

The Hold instance provided here should be of class statsmodels.tsa.holtwinters.Holt, but is of type statsmodels.tsa.statespace.structural.UnobservedComponents instead. I do not now how this behaviour is possible and generates inconsistency, because fitted_complete_mod is of type statsmodels.tsa.holtwinters.results.HoltWintersResultsWrapper, instead of the statsmodels.tsa.statespace.structural.UnobservedComponentsResultsWrapper one would expect as output of the fit method of an UnobservedComponents.

Solution

There should be a clearer distinction between the classes of incompatible objects. Moreover, there should be a clear way to create an exponential smoothing model with some predefined parameters.

Note

If what I have described above is intended behaviour, then I apologise for opening the issue. If this is the case, I'd like to write a documentation page like this one so that other users won't repeat my mistake.

[ChadFulton]

this is not possibile with Holt: the filter method fails. I can find no other way to do this. I'd like to make it clear that I do not want to refit the parameters, instead I wish to keep the same ones from the train fit.

I suggest using the new exponential smoothing class, sm.tsa.ETSModel. For example, you could do:

import statsmodels.api as sm

data = load_data_from_somewhere()
n = data.size
n_train = int(0.8 * n)
train = data[:n_train]
test = data[n_train:]
mod = sm.tsa.ETSModel(train, trend='add')
with mod.fix_params({'smoothing_level': 0.5, 'smoothing_trend': 0.05}):
    fitted_mod = mod.fit()
fitted_mod.summary()

and then

complete_mod = sm.tsa.ETSModel(data, trend='add')
fitted_complete_mod = complete_mod.smooth(fitted_mod.params)
pred = fitted_complete_mod.predict(start=n_train)
# then compute metrics like MSE between pred and train

[ChadFulton]

The Hold instance provided here should be of class statsmodels.tsa.holtwinters.Holt, but is of type statsmodels.tsa.statespace.structural.UnobservedComponents instead. I do not now how this behaviour is possible and generates inconsistency, because fitted_complete_mod is of type statsmodels.tsa.holtwinters.results.HoltWintersResultsWrapper, instead of the statsmodels.tsa.statespace.structural.UnobservedComponentsResultsWrapper one would expect as output of the fit method of an UnobservedComponents.

I think that this is probably some error in your code. The Holt and UnobservedComponents classes have nothing to do with each other.

[ChadFulton]

Closing as answered, but feel free to follow up with comments if you have additional questions.

[dtoniolo]

Thanks you, really. The class issue was really a problem of my code, so no bug in the library. I'm sorry for opening a useless issue report, I'll check my code better next time, and I'll use the sm.tsa.ETSModel class from now on.

Thank you for your awesome work for statsmodels, being able to ditch R and have basically all the statistical tools I need in one package, with consistent syntax, is priceless.

[ChadFulton]

No problem. Also, I think the idea of an example notebook showing forecasting with exponential smoothing models is a great idea. If you happen to write something up (ideally using ETSModel), I think that could make a nice addition to the documentation.