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**1. Show that applying a second-order weighted moving average to a cubic polynomial will not change anything.**

[tex]X_t = a_0 + a_1t + a_2t^2 + a_3t^3[/tex] is our polynomial

Second-order weighted moving average: [tex]\sum_{i=-L}^{i=L} B_iX_{t+i}[/tex]

where [tex]B_i=(1-i^2I_2/I_4)/(2L+1-I_2^{2}/I_4)[/tex]

where [tex]I_2=\sum_{i=-L}^{i=L} i^2[/tex]

**2. I did a similar problem where applying a linear moving average to a linear equation returns the same thing, but I'm not sure how to proceed here.**