Non-Stationary Series and Standard Deviation


I am trying to model a non-stationary series for the purpose of outlier detection. The series is not labeled as normal and abnormal, which is a part of the problem.

In the first step to model it, I figured out the seasonal dynamics which were at 1 min and 60 min. You can see the AC and PAC of the series before and after removing the dynamics in the photo that I've attached. The AC of the differentiated series does not have any peaks after lag 61.

My problem is here: I am expecting the standard deviation of the \(\nabla\nabla_{60}x_t\) stay almost the same on a moving window of size 24 hours. But, this does not happen.

I was wondering if there is any explanation for this, or I am simply doing something wrong.

I appreciate your comments.