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I've a doubt in the application of the exponential smoothing for pure forecasts. I'm using this type of model in these days, for the automatization of some algorithms. This time i'm working on non-seasonal data, year population, but the fitted value of my models seems shifted in some cases, as in this example:

enter image description here

How can i solve this shift of the fitted values (in red)? the forecast works very good, but sometime i have this strange result. Thanks a lot.

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  • $\begingroup$ Where is the picture? $\endgroup$ – Richard Hardy Feb 18 '17 at 20:03
  • $\begingroup$ i'm sorry, i've uploded it but maybe it doesn't worked. I'll try again $\endgroup$ – Enzo D'Innocenzo Feb 18 '17 at 20:05
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This is to be expected with ordinary running averages (including weighted) and so impacts exponential smoothing

Consider what happens when you smooth a linear trend:

Plot showing exponential smoothing fit lagging a trend

If you want a smoother to "follow" a trend you need a more sophisticated smoother than simple exponential smoothing. If you introduce suitable negative weights you can get running weighted-average smoothers that follow linear, quadratic or cubic trends for example.

Such methods were widely used many decades past but are less commonly used now (partly because the simpler forecasting methods generally produce better forecasts rather than better fits); nonetheless if you know before the fact your data will have a certain form of trend you can choose a smoothing approach that will take account of that trend and predict accordingly.

Or you could look at say double exponential smoothing, which would be suitable for some situations

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  • $\begingroup$ Thanks. So, as a first solution i've worked in this way. I've take into account the estimated "level" and "slope" and since i'm using a multiplicative damped trend i've simply multiplied this two factors. The exponential smoothing now follows very good the real data. Can be a good approach? thanks a lot for your answare. $\endgroup$ – Enzo D'Innocenzo Feb 19 '17 at 8:46
  • $\begingroup$ I'm sorry I am not 100% sure I quite follow what you're asking, but if I guessed what you mean correctly, that might work. I also just noticed I accidentally left the word "double" out of my last paragraph, which meant it couldn't have been much help to you. I've corrected that. $\endgroup$ – Glen_b Feb 19 '17 at 8:58

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