(a) Write down the MA(1) representation of a causal ARMA(1, 1). (b) Suppose we observe X1,X2, . . . ,Xn from the causal ARMA(1, 1) in part (a). Write down the minimum mean square error predictor Xn+1(head) and Xn+2(head) along with their respective mean square error of prediction. (c) Simulate n = 102 observations from a causal ARMA(1, 1) of your choice. Use only the first 100 of these to construct 95% prediction intervals for X101 and X102. How did these intervals do with the actual values? Solution 1. http://www.economics.ox.ac.uk/members/jennifer.castle/teachingwebpage/JLCARMAnotes_09. pdf 2. http://www.pstat.ucsb.edu/faculty/feldman/174-03/lectures/l7.pdf.

1. (a) Write down the MA(1) representation of a causal ARMA(1, 1).
(b) Suppose we observe X1,X2, . . . ,Xn from the causal ARMA(1, 1) in part (a). Write down the
minimum mean square error predictor Xn+1(head) and Xn+2(head) along with their respective
mean square
error of prediction.
(c) Simulate n = 102 observations from a causal ARMA(1, 1) of your choice. Use only the first
100 of these to construct 95% prediction intervals for X101 and X102. How did these intervals
do
with the actual values?
Solution
1.
http://www.economics.ox.ac.uk/members/jennifer.castle/teachingwebpage/JLCARMAnotes_09.
pdf 2. http://www.pstat.ucsb.edu/faculty/feldman/174-03/lectures/l7.pdf