HW7_Solutions - Solutions to HW 7 Exercise 12.1 VAR(1)...

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Solutions to HW 7 Exercise 12.1 VAR(1) model, 1 tt + t X XZ , where 10 . 5 0.2 0.7 Φ= , i.e., . ,1 1,1 ,2 1 . 5 0.2 0.7 XX ⎡⎤ =+ ⎢⎥ ⎣⎦ t t Z Z The model is non-stationary if there are roots of |() | | |0 BIB Φ =− Φ = incide the unit circle. 1 0 0.5 1 0.5 0 1 0.2 0.7 0.2 1 0.7 B BB B B B −− −Φ = = I B . 2 12 . 5 1 1.7 0.6 0 2, 0.8333 0.2 1 0.7 B B + = = . One root is inside the unit circle, therefore the model is non-stationary. Exercise 12.2 The model is stationary if all the roots of | | Φ are outside of the unit circle. Similar to 12.1, (a)
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