IID Noise
Definition
$\{Z_t\}$ is iid noise if: independent, identically distributed, zero mean $E(Z_t) = 0$.
If $E(Z_t^2) = \sigma^2 < \infty$: write $\{Z_t\} \sim \text{IID}(0, \sigma^2)$.
Stationarity
Always strictly stationary. Also weakly stationary when $E(Z_t^2) < \infty$.