I have some SKUs and I'd like to do a forecast using single exponential smoothing as a forecasting method, when should we go for small value of alpha (.05,.1,...) and when for bigger values(.8,.9,...)? Does it depend on the characteristics of the series?
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The data will tell you what coefficient is appropriate for your assumed model. The SES model is just one model from an infinite set of models. Just simply estimate the optimal coefficient for that model. This will be sufficient IFF this is the best ARIMA model AND IFF there are no outliers/inliers/pulses AND no level/step shifts AND no Seasonal Pulses AND no Local Time Trends AND the parameter is constant over time and the error variance is constant over time. IFF all of these are true you should be good to go !
I second IrishStats advice. Method of analysis should be dependent on characteristics of the series. When doing time series analysis or statistical analysis in general the methodology you use should be dictated by (1) basic knowledge of the subject matter that suggests model form and (2) models that seem to fit well with data. Exponential smoothing used to be looked at a a general forecasting method and modifications to it were used to compensate when simple exponential smoothing did not work well.
In the first edition of their book Box and Jenkins pointed out that single exponential was just one example of the broad class of ARIMA models, namely the IMA(1,1) model. So rather than taking an approach that uses an extension of single exponential smoothing it might be better to pick a model based on the data out of the ARIMA class.
When I worked for the US Army in the early 1970s I showed that exponential smoothing did a lot better than what the supply depots were using. They did not base their forecasts based on a mathemtical formula that used historical data. So it was easy for any method based on patterns in historical data to make sense. The fact that it is a special case of Box-Jenkins Arima models was brought to my attention and so began my interest in time series analysis.
After that I began using the Box-Jenkins approach. When I took time series from Box and Tiao, George Tiao would mrntion that it was common for exponential smoothing to be the optimal form for the model. So as IrishStat mentioned, first identify the best form of your model. If it turns out that exponential smoothing is the best form for the model then the estimated moving average parameter determines the smoothing constant.