Let (left{x_{t} ight}) and (left{y_{t} ight}) be univariate random walk processes with (operatorname{Cor}left(x_{s}, y_{t} ight)=0) for all

Let \(\left\{x_{t}\right\}\) and \(\left\{y_{t}\right\}\) be univariate random walk processes with \(\operatorname{Cor}\left(x_{s}, y_{t}\right)=0\) for all \(s\) and \(t\). Now for a constant \(a\), let \(z_{t}=a x_{t}+y_{t}\). Show that \(\left\{z_{t}\right\}\) is a random walk process.