(Requires Appendix Material) Define the difference operator $\Delta = ( 1 - L )$, where $L$ is the lag operator, such that $L ^ { j } Y _ { t } = Y _ { t - j }$. In general, $\Delta _ { j } ^ { i } = \left( 1 - L ^ { j } \right) ^ { i }$, where $i$ and $j$ are typically omitted when they take the value of 1. Show the expressions in $Y$ only when applying the difference operator to the following expressions, and give the resulting expression an economic interpretation, assuming that you are working with quarterly data: (a) $\Delta _ { 4 } Y _ { t }$

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The Answer of (Requires Appendix Material) Define the difference operator $\Delta = ( 1 - L )$, where $L$ is the lag operator, such that $L ^ { j } Y _ { t } = Y _ { t - j }$. In general, $\Delta _ { j } ^ { i } = \left( 1 - L ^ { j } \right) ^ { i }$, where $i$ and $j$ are typically omitted when they take the value of 1. Show the expressions in $Y$ only when applying the difference operator to the following expressions, and give the resulting expression an economic interpretation, assuming that you are working with quarterly data: (a) $\Delta _ { 4 } Y _ { t }$

(Requires Appendix Material) Define the Difference Operator Δ=(1−L)\Delta = ( 1 - L )Δ=(1−L)

(Requires Appendix Material) Define the Difference Operator $\Delta = ( 1 - L )$