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4. The standard equation for an AR(1) model is: yt=a0+a1yt1+t (a) Show that an ...
4. The standard equation for an AR(1) model is: yt?=a0?+a1?yt?1?+?t? (a) Show that an equivalent representation is: yt?=1?a1?a0??+?t? where ?t?=a1??t?1?+?t? (7 points) ? (b) Consider the sequence: yt?=a0?+a1?yt?1?+a2?t+?t? where ?a1??<1 Is the above sequence stationary? Why or why not? (5 points)
![4. The standard equation for an \( \mathrm{AR}(1) \) model is:
\[
y_{t}=a_{0}+a_{1} y_{t-1}+\varepsilon_{t}
\]
(a) Show that](https://media.cheggcdn.com/media/aa2/aa206587-e73a-47cd-879a-785ccd087902/phpPR8v0X)