Solutions to HW 7 Exercise 12.1 VAR(1) model, 1tt−=Φ+tXXZ, where 10.50.20.7⎡⎤Φ=⎢⎥⎣⎦, i.e., . ,11,1,184.108.40.206XX−−⎡⎤⎡⎤⎡=+⎢⎥⎢⎥⎢⎣⎦⎣⎦⎣ttZZ⎤⎥⎦The model is non-stationary if there are roots of |()|||0BIBΦ=−Φ =incide the unit circle. 100.510.5010.20.70.210.7BBBBBB−−⎡⎤⎡−Φ =−=⎢⎥⎢⎣⎦⎣IB⎤⎥⎦. 212.51 1.70.602,0.83330.210.7BB+==≈. 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 ||Φare outside of the unit circle. Similar to 12.1, (a)
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