$$\text { Consider the standard AR(1) } Y _ { t } = \beta _ { 0 } + \beta _ { 1 } Y _ { t - 1 } + u _ { t } \text {, where the usual assumptions hold. }$$ (a) Show that $y _ { t } = \beta _ { 1 } y _ { t - 1 } + u _ { t }$, where $y _ { t }$ is $Y _ { t }$ with the mean removed, i.e., $y _ { t } = Y _ { t } - E \left( Y _ { t } \right)$. Show that $E \left( y _ { t } \right) = 0$.

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The Answer of $$\text { Consider the standard AR(1) } Y _ { t } = \beta _ { 0 } + \beta _ { 1 } Y _ { t - 1 } + u _ { t } \text {, where the usual assumptions hold. }$$ (a) Show that $y _ { t } = \beta _ { 1 } y _ { t - 1 } + u _ { t }$, where $y _ { t }$ is $Y _ { t }$ with the mean removed, i.e., $y _ { t } = Y _ { t } - E \left( Y _ { t } \right)$. Show that $E \left( y _ { t } \right) = 0$.

(A) Show That yt=β1yt−1+uty _ { t } = \beta _ { 1 } y _ { t - 1 } + u _ { t }yt​=β1​yt−1​+ut​

(A) Show That $y _ { t } = \beta _ { 1 } y _ { t - 1 } + u _ { t }$