how to detect anomalies in data I want to get ideas of how to approach this problem and what is the different  effect of each one.
Assume you have a set of time series (several variables measured always at the same time) and you want to detect anomalies in these time series.
Assuming each time series varies slowly in time, so changes are seen as a smooth variation in the observations, how would I develop a system to detect anomalies?
But now let me assume instead that the time series varies faster than our measurement of them. Changes are discontinuous. Does this change the answer?
I would really appreciate it if you can give me feedback as I am new to anomaly detection.

Your question is a little underspecified.
However, it seems that the left Matrix-Profile could solve this: see [a].
Moreover, it is easy to implement, incredibly fast, and parameter light.
[a] https://www.cs.ucr.edu/~eamonn/DAMP_long_version.pdf
