# Φ 2 1 now by definition of w t we have γ w h cov w

• Notes
• 4

This preview shows page 4 out of 4 pages.

( φ 2 - 1) . Now by definition of W t ,we have γ W ( h ) = Cov ( W t + h , W t ) = Cov ( X t + h - 1 φ X t + h - 1 , X t - 1 φ X t - 1 ) = γ X ( h ) - 1 φ γ X ( h + 1) - 1 φ γ X ( h - 1) 1 φ 2 γ X ( h ) = σ 2 φ 2 if h = 0 0 otherwise. Then W t is a white noise WN (0 , σ 2 φ 2 ). These calculations show that X t is also a solution of the causal AR(1) equation X t - 1 φ X t - 1 = W t . 4
You've reached the end of this preview.
• Spring '12
• Smith
• Zagreb, BMW Sports Activity Series, BMW vehicles, All wheel drive vehicles

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern