Question: Consider the following process, Xt + 0.2Xt1 + 0.7Xt2 = at at1 2 at2, where {at} is a white noise with mean zero and variance

Consider the following process, Xt + 0.2Xt1 + 0.7Xt2 = at at1 2 at2, where {at} is a white noise with mean zero and variance 2 a .

(a) Is {Xt} stationary? Justify your answer. [4 marks]

(b) Find the range of such that {Xt} is invertible. [10 marks]

(c) Suppose that is in the range found in (b) so that at can be expressed as at = P j=0 bjXtj .

i. Find the values of b0, b1 and b2 in terms of . [4 marks]

ii. Write down a recursive formula of bj for j 3 in terms of . [2 marks]

(d) Find the autocovariances 0, 1 and 2 of the process when = 0.

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