3. Consider the following process, Xt = 0.7Xt-1-0.1Xt-2+Zt +20Zt-1-0² Z₁-2, where {Z} is a white noise with mean zero and variance o². (a) Is {X} stationary? Justify your answer. (b) Find the range of such that {X} is invertible. (c) Suppose that is in the range found in (b) so that Z₁ can be expressed as Z₁ = Σ TjX₁-j. j=0 i. Find the values of 0, 1 and 2 in terms of 0. ii. Write down a recursive formula of 7; for j≥ 3 in terms of 0. (d) Let = 0. Given that Var (X) = 0.5, calculate the variance of Zt, 0². (e) Given the observations X2022 = 1.6 and X2021 = 0.9, find the one-step, two-step and three-step ahead forecasts at t = 2022, when 0 = 0. Moreover, calculate the variance of these three forecast errors in terms of o².

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A: *Answer:

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