Consider the simple moving average model Xt = 0.02 + Wt − 0.4Wt−1, where Wt is...
Consider the simple moving average model Xt = 0.02 + Wt − 0.4Wt−1, where Wt is a sequence of i.i.d. normal random variables with mean zero and variance 4. What is the mean of Xt? What is the variance of Xt. Show working
Homework Answers
Consider the simple moving average model Xt = 0.02 + Wt − 0.4Wt−1, where Wt is a sequence of i.i.d. normal random variables with mean zero and variance 4. What is the mean of Xt? What is the variance of Xt. Show working
Xt = 0.02 + Wt − 0.4Wt−1
Wt ~ N(0,4)
mean of Xt= E(Xt)
=E( 0.02 + Wt − 0.4Wt−1)
=E(0.02)+E(Wt)-0.4*E(Wt-1)
=0.02+0-0.4*0 since E(constant)=constant
=0.02
mean of Xt=0.02
Variance of Xt= V(Xt)
=V( 0.02 + Wt − 0.4Wt−1)
=V(0.02)+V(Wt)-V(0.4*Wt-1)
=0+4+0.4^2*4 since Var(constant)=0
=4+0.64
=4.64
Answer:
mean of Xt=0.02
Variance of Xt = 4.64
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Consider the simple moving average model Xt = 0.02 + Wt −
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We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
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Consider the time series of X-Xi-1+Wi, whereW are i.i.d and W N(0, σ2) and Xo 0. Let X = n Σ, Derive the general form for var(X). (Hint: Σ i- n(n+1)(2n+1))
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We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
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