Consider the AR(2) process { X t } satisfying

Consider the AR(2) process {Xt} satisfying

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Xt− φXt−1 − φ2Xt−2 = Zt , {Zt} ∼ WN(02).

a. For what values of φ is this  a causal process?

b. The following sample moments were computed after observingX1. . . ,X200:

 width= (0= 6.06 width= (1.687.

Find estimates of φ and σ2 by solving the Yule–Walker equations. (If you find more than one solution, choose the one that is causal.)

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