Discrete Gaussian white noise (${\epsilon }_t\stackrel{\mathrm{iid}}{\sim }N(0,{\sigma }^2)$)

Discrete Gaussian white noise is a jointly Gaussian sequence with expected value zero and covariance ${\sigma }^2$ at lag zero and zero at other lags. Joint normality makes the components independent. This is a sequence of ordinary random variables, unlike the generalized continuous-time white-noise process.