Question 4 [12 marks]. Let {Zt} be a white noise process with mean 0 and variance 1. For the following processes, comput

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Question 4 [12 marks]. Let {Zt} be a white noise process with
mean 0 and variance 1. For the following processes, compute the
partial autocorrelation function (PACF) at lag 3:
(a) Xt = 0.45Xt−1 + 0.05Xt−2 − 0.35Xt−3 + Zt . [2]
(b) Xt = 0.7Xt−1 − 0.4Xt−2 + 0.5Xt−3 + Zt − 0.7Zt−1 + 0.4Zt−2 −
0.5Zt−3. [3]
(c) Xt = Zt − 0.75Zt−1. [3]
(d) Xt = 41 36 Xt−1 − 2 3 Xt−2 + 1 9 Xt−3 + Zt − 1 4 Zt−1.
[4]