Synthetic time series generation according to some distribution I'm trying to develop a change detection model that uses sliding windows. Given a time series with some features I've a sliding widows that analyses that time period and compares with a successive time window. If the distribution of data has changed than it is notified. Anyway, I don't have enough real data about my problem, so I need to generate some artificial time series but with different distributions, no matter what distributions, the important thing is that they are different, so that I can test when my model detects change in the data. How can I generate those data?
If I understand you correctly, I think I have a simple way and you do not need to overthink it.


Take a Gaussian (Normal) distribution random number generator, it could even be just downloading a set from https://www.random.org/gaussian-distributions/
Multiply by the desired standard deviation, add the desired mean.
From a certain timestamp, change the standard deviation and mean to a new value to simulate the distribution change. This is the same as concatenating smaller sets with different mean and standard deviation.
See if/when your model detects it.