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Why the series to the power of two differs from the expanded AR(2) equation?

I am trying to rewrite the series $\tilde{R}_{t}=\beta_{2}\left(\sum_{s=0}^{\infty}\frac{U_{t-s}}{\phi^{s+1}}\right)^{2}$ as an $AR(2)$ using lag operators $L$. I expand the series, define $\alpha=\...
Edoardo Baldoni's user avatar