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1.4 Consider the time series Xt = Bo + B1t + Wt, where Bo and B1 are regression coefficients, and Wt is a white noise process with variance of (a) Determine whether Xt is stationary. (b) Show that the process Yt = Xt - Xt-1 is stationary. (c) Show that the mean of the moving average = 1 is 80 + B1t. 3.1 For an MA(1), Xt = Wt + Owt-1, show that Px (1) I 1/2 for any number 0. For which values of 0 does Px (1) attain its maximum and minimum? 3.3 Using Example 3.6 as a guide, identify the following models as ARMA(p, q) models (watch out for parameter redundancy), and determine whether they are causal and/or invertible. If the model is causal, use R to find the first 10 1-weights, and if the model is invertible, use R to find the first 10 Tt-weights. (a) xt = .80xt_ 1 - .15xt-2 + Wt - .30wt_1. (b) Xt = Xt-1 - 50xt-2 + Wt - Wt-1- - .

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