3. Let X= 3 +0,3X, +0.1X,-, +, where e, is a white noise process with variance equal to o? (a) Use backshift operators a

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3 Let X 3 0 3x 0 1x Where E Is A White Noise Process With Variance Equal To O A Use Backshift Operators A 1 (21.54 KiB) Viewed 18 times

3. Let X= 3 +0,3X, +0.1X,-, +, where e, is a white noise process with variance equal to o? (a) Use backshift operators and show that E(X) = 5. Hint: rewrite X, as Στε, X = a + 1+B and then take the expectations on both sides. B is the backshift operator defined as B'N, EN (b) Calculate the values of a, b, and c. (e) Show that X, is weakly stationary of order two. Hint: Consider rewriting X, as X, - 5 = 0.3(X - 5) +0.1(X - 5) + €, 2,-0.32, +0.12., +, (d) Show P. for k = 0 0.3p., +0.12., fork > 1