Question $7(8$ points$)$

Suppose $w_{t}N(0,1).$

$($:$x_t=\frac{1}{3}o{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{w}_t+w_{t-1}+w_{t-2}\}$

The R code to implement this is:

sides $=$

filter $=$ rep$($

Suppose $w_{t}N(0,1)$

Let $x_t=\frac{1}{3}(w_t+w_{t-1}+w_{t-2}).$

The R code to implement this is:

sides $=$

filter $=$ rep$($