discrete white noise

The stochastic process $\{Z_t,t\in T\}$,where T is the set of natural integers $\mathbb{N}$ or the set of all integers $\mathbb{Z}$, is said to be white noise with mean 0 and variance ${\sigma }^2$, written$\{Z_t\}\sim WN(0,{\sigma }^2)$, if and only if $\{Z_t\}$ has zero mean and autocovariance function