White Noise

Definition

A White Noise is a stochastic process $\{e_t\}$ that is:

1. Consisting of uncorrelated random variables
2. Mean 0
3. Constant variance ${\sigma }_e^2$

Properties

Property	Expression
Mean (${\mu }_t$)	$0$
Variance	${\sigma }_e^2$
Autocovariance ${\gamma }_k$	$\{\begin{array}{ll}{\sigma }_e^2& ,k=0\\ 0& ,k\ne 0\end{array}$
Autocorrelation ${\rho }_k$	$\{\begin{array}{ll}1& ,k=0\\ 0& ,k\ne 0\end{array}$
Stationarity	strictly and weakly