It is a process consisting of a sequence of uncorrelated identically distributed random variables, with zero mean and variance σε ².

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,σ_ε²), it will be a strongly stationary process and takes the name of Gaussian white noise.

Editor: Giuliano DI TOMMASO