I have been running in circles with this problem and would greatly appreciate any help.

2. Originally Posted by Abby123
I have been running in circles with this problem and would greatly appreciate any help.
Apply the stepping rule repeatedly to reduce the $X_{t}$ to lower order to get:

$\Delta_{m,t}=\sum_{r=t-m+1}^t u_r$

As variance is additive you should be able to complete the first part from here.

For the second part regroup the terms to express $\Delta^*$ in terms of $\Delta$'s

RonL