It is a process consisting of a sequence of uncorrelated identically distributed random variables, with zero mean and variance σε2.
The auto-covariance expression can be represented as:
therefore we can assume that is a weakly stationary process; furthermore, the autocorrelation function will be:
If εt has normal distribution N(0,σε2), it will be a strongly stationary process and takes the name of Gaussian white noise.
Editor: Giuliano DI TOMMASO