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# hw4 - ORIE 4630 D Ruppert Homework#4 This assignment will...

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ORIE 4630 — D. Ruppert Homework #4 This assignment will not be collected, but in will be covered in the Exam on Sep 24 To help you study for the Exam 1, I am giving the answer to these problems now. 1. Suppose you just ﬁt at AR(2) model to a time series Y t , t = 1 ,...,n , and the estimates were b μ = 100 . 1, b φ 1 = 0 . 5, and b φ 2 = 0 . 1. The last three observations were: Y n - 2 = 101 . 0, Y n - 1 = 99 . 5, and Y n = 102 . 3. What are the forecasts of Y n +1 , Y n +2 , and Y n +3 ? Answer: b Y n +1 = 101 . 14, b Y n +2 = 100 . 84, b Y n +3 = 100 . 574. Notice that Y n - 2 is not needed for forecasting with the AR(2) model. This problem can be done without the use of R but it is a little faster in R than by hand. The following R code computed the forecasts: mu = 100.1 phi1 = 0.5 phi2 = 0.1 y = c(99.5,102.3) yhat1 = mu + phi1*(y[2]-mu) + phi2*(y[1]-mu) yhat2 = mu + phi1*(yhat1-mu) + phi2*(y[2]-mu) yhat3 = mu + phi1*(yhat2-mu) + phi2*(yhat1-mu) yhat1 yhat2 yhat3 > yhat1 [1] 101.14

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hw4 - ORIE 4630 D Ruppert Homework#4 This assignment will...

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