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

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( 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
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  • Spring '12
  • Smith
  • Zagreb, BMW Sports Activity Series, BMW vehicles, All wheel drive vehicles

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