Your description of what you want to do is quite vague and the "not a regression" part is kind of contradictory. Therefore I'll take

"Is it possible to calculate the same model also for the range of dates on which I provided the data?"

part to formulate an answer.

Importing your data saved in TSV format

```
data = MapAt[DateString[{#, {"Day", "/", "Month", "/", "Year"}}] &,
Import["D:\\Analytics www.superinformati.com Panoramica del pubblico 20141201-20150303 - Sheet 1.tsv"][[3 ;;, {1, 2}]]
, {All, 1}]
```

Finding the SARIMA process

```
tsm = TimeSeriesModelFit[data]
```

One can use `RandomFunction`

to create multiple simulations assuming a random process. The following code produces 5 simulations. I use `Length@data - 30`

because your data looks like the real trend starts somewhere after 30 days.

```
rf1 = RandomFunction[tsm["BestFit"], {Length@data - 30}, 5]
```

Creating a plot of these simulations and of their mean

```
randomP1 =
DateListPlot[Transpose[{data[[30 ;;, 1]], #}] & /@ rf1["States"],
PlotStyle -> Opacity[1/2],
PlotRange -> {{data[[1, 1]], data[[-1, 1]]}, Automatic}]
meanP1 = DateListPlot[
Transpose[{data[[30 ;;, 1]], TimeSeriesThread[Mean, rf1]["PathStates"]}],
PlotStyle -> Red, PlotRange -> {{data[[1, 1]], data[[-1, 1]]}, Automatic}]
```

Putting everything into one plot

```
Show[{randomP1,
DateListPlot[data, PlotStyle -> Directive[Black, Thick]],
meanP1}]
```

Doing the same using a ARIMA model

```
tsm2 = TimeSeriesModelFit[data, "ARIMA"]
rf2 = RandomFunction[tsm2["BestFit"], {Length@data - 30}, 5]
randomP2 =
DateListPlot[Transpose[{data[[30 ;;, 1]], #}] & /@ rf2["States"],
PlotStyle -> Opacity[1/2],
PlotRange -> {{data[[1, 1]], data[[-1, 1]]}, Automatic}]
meanP2 = DateListPlot[
Transpose[{data[[30 ;;, 1]], TimeSeriesThread[Mean, rf2]["PathStates"]}],
PlotStyle -> Red, PlotRange -> {{data[[1, 1]], data[[-1, 1]]}, Automatic}]
Show[{randomP2,
DateListPlot[data, PlotStyle -> Directive[Black, Thick]],
meanP2}]
```

What is

stagionalization? – C. E. – 2015-03-26T12:05:57.623@Pickett: sorry, my english is terrible. I meant seasonalization, I will correct. Thanks for telling me. – Revious – 2015-03-26T12:28:00.907

1

I'm not sure what you mean with deseasonalized without making a regression. Do you mean filtering or smoothing? Or something like this, this or this, which are all different kinds of regressions?

– Karsten 7. – 2015-03-26T12:38:19.750@Karsten7. I am not sure if what I want can be achieved. I will edit the question. ps: how did you managed to get the 3 images? – Revious – 2015-03-26T13:44:55.683

1The last one was created using something like what I show in my answer. The other two were produced by fitting a function, that is not a straight line, to the data (, but this is still doing a linear regression). – Karsten 7. – 2015-03-26T15:31:25.137