H4 - H4 HW2(due Jan 24 Exercise 3.9 from the textbook and...

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H4 HW2 (due Jan. 24). Exercise 3.9 from the textbook and Problem 1 Let { } 2 ~IID(0 , ) σ t Z , and let c be a constant. Consider the process 12 cos( ) sin( ) = + t X Zc t t t . Find the mean and autocovariance function and determine whether the process is stationary. Problem 2 Determine which of the following ARMA processes are causal and which of them are invertible. (a) 0.2 0.48 −− =− + + tt t X XX Z 2 t . (b) 1 1.9 0.88 0.2 0.7 ++ = t X Z Z Z t . (c) 11 0.6 1.2 + + t X XZ Z . (d) 1.8 0.81 = t t X Z 2 t . (e) 1.6 0.4 0.04 += −+ X Z Z . _______________________________________________________________________________________________________ Example 1 . Is the AR(2) process given by 0.5 t t X Z = q stationary? A process given by 1 1 p t p t t q t X Z ZZ φ φθ θ −−− = +⋅⋅⋅+ + + is said to be an autoregressive moving-average process of order (,) p q (ARMA p q ). Using the backward shift operator B , it may be presented in the form () B XB Z = . The conditions on the model parameters to make the process stationary and invertible are the same as for pure AR or pure MA process, namely, the process is invertible if the roots of the equation, , 1 () 1 0 q q BB B θθθ =+ + + =
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This note was uploaded on 09/23/2009 for the course MATH 200 taught by Professor Gur during the Spring '09 term at Accreditation Commission for Acupuncture and Oriental Medicine.

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H4 - H4 HW2(due Jan 24 Exercise 3.9 from the textbook and...

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