I learned that if a random process is WSS, its mean should be constant and the correlation only depends on time difference. Also, I learned that white noise is definitely WSS. I tried to simulate white noise in Matlab, it turns out that the mean fluctuates around 0 within the range [-0.5,0.5]. I understand that it is impossible to simulate a true white noise in computer, hence it makes me re-think the meaning of a WSS and its importance.
Thus, I have following questions:
1) Is WSS a way to characterise and identify a random process?
2) Is WSS an idealisation? Is that possible that a random process has a constant mean? When I try to solve the math questions, it is easy to identify whether the process is WSS. Yet, when it comes to real-life example, it seems the mean cannot be perfectly constant.
3) What if the mean is approximately constant? Can I claim that the process is WSS?
4) Can I have some examples on how people use WSS to analyse statistical problems?
I apologise if my question is too abstract.