the difference between non-stationary data and random data?

#1
what are the the difference between non-stationary data and random data? If we detrend a stationary data and make it non-stationary what will happen, will it be random?
 

BGM

TS Contributor
#2
Conceptually very different term.

A simple example: consider a sequence of i.i.d. random variables \( X_t \) with finite mean and variance. Then it is a stationary time series. Next if you "integrate" it to form a random walk, i.e. \( Y_t = Y_{t-1} + X_t \), then it is not a stationary time series. But both are random, right?