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

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

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

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*X _{t}*−

*φX*

_{t}_{−1}−

*φ*

_{2}

*X*

_{t}_{−2}=

*Z*{

_{t},*Z*} ∼ WN(0

_{t}*,σ*

^{2})

*.*

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

b. The following sample moments were computed after observing*X*_{1}, *. . . *,*X*_{200}:

* (*0*) *= 6*.*06*, * *(*1*) *= *.*687*.*

Find estimates of *φ *and *σ*^{2} by solving the Yule–Walker equations. (If you find more than one solution, choose the one that is causal.)