Xt=Xt1+wt,wtWN(0,w2)and>1. Define the new process Yt=Xt1Xt1. 1 Show that Yt is white noise and find the variance of Yt. Hint: write Yt as a linear process of wt and show EYt+hYt=0 for all h=0. Notably, it suggests that Xt is the solution of the equation Xt(1/)Xt1=Yt whose AR polynomial 11/z has no root in z1..
Xt=Xt1+wt,wtWN(0,w2)and>1. Define the new process Yt=Xt1Xt1. 1 Show that Yt is white noise and find the variance of Yt. Hint: write Yt as a linear process of wt and show EYt+hYt=0 for all h=0. Notably, it suggests that Xt is the solution of the equation Xt(1/)Xt1=Yt whose AR polynomial 11/z has no root in z1..