From Exponential Smoothing Model to an equivalent ARIMA

[FVidal]

Hello,

I would like to know if there is a method to obtain an ARIMA model that 'simulates' a particular Exponential Smoothing.

The problem is that, in some cases, I get a very good exponential smoothing model and in a particular month I need to add an event.

As far as I know, I can not add events in an ESM. So, then I have to change my model to an ARIMA...and with ARIMA I'm not getting a good model.

The question is: there is a way to obtain an 'equivalent' ARIMA?

Thanks,

Ferran

[PaigeMiller]

SImple exponential smoothing is ARIMA (0,1,1), does that help?

Other than that, I find this question is rather vague and lacking in details, as we don't know what exact model you are using, we don't know why you are having trouble matching the exponential smoothing, etc. etc.

[FVidal]

Hello PaigeMiller,

Thanks for you answer.

I find the problem with several models.

In SAS FS we have eight exponential smoothing models, isn't it? You said that Simple Exponential Smoothing is ARIMA (0,1,1).

There are equivalence for all ESM?

Double Exponential Smoothing

Linear Exponential Smoothing

Damped-trend Exponential Smoothing

Seasonal Exponential Smoothing

Multiplicative Seasonal Exponential Smoothing

Winters Method - Additive version

Winters Method - Multiplicative version

Regards,

Ferran

[PaigeMiller]

I am not aware if there is a difference between what you call "linear exponential smoothing" and "simple exponential smoothing", I think these are the same (but honestly, I have not heard of "linear exponential smoothing")

Double exponential smoothing is ARIMA (0,2,2)

As far as the others go, I'm sure your favorite search engine will find information on your question.