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