Which mathematical model is used in AF to calculate (predict) future data?
Basically the PI system does not predict or forecast data. However, you can use PI Analytics to calculate forecast data and save it with a timestamp in future. For example, you could calculate the average daily production number from data of the past 7 days and set this is to be the forecast for tomorrow. To store a value with a timestamp in the future, apply the "Relative to Trigger Time" option with a value of e.g. "*+24h" from the Analysis Advanced Options.
but still it is not clear to me... like you can see in my diagram (picture), how are calculated marked data ("future" data, *+2h)?
Where did you get the screenshot from? That system will be able to disclose how the value of "Future" is calculated.
Basically Gerhard is right, analytics can do some forecasting, but there are other ways.
this screenshot is from PI Vision.
Blue is realtime data, and orange data *+2h calculated in analysis.
Retrieving data ...