Stationarity

Summary

A time series process $y_1,…,y_T$ is called stationary (in the weak sense or in the wide sense) if

• $E\left( y_t \right)=μ$ (does not depend on $t$ )
• $Var\left( y_t \right)=σ^2$ (does not depend on $t$ )
• $Cov(y_t,y_{t-s})$ depends only on $s$ (but not on $t$ )

If $y_1,…,y_T$ and $x_1,…,x_T$ are two stationary processes , then

• $cy_1,…,{cy}_T$ is stationary for any constant $c$
• $y_1+x_1,…,y_T+x_T$ is stationary