# Xt=Xt1+wt,wtWN(0,w2)�and�1. Define the new process Yt=Xt1Xt1. 1 Show .pdf

A

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..

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### Xt=Xt1+wt,wtWN(0,w2)�and�1. Define the new process Yt=Xt1Xt1. 1 Show .pdf

• 1. 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.
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