Computation problems:

Q$1.$ Consider an N$-$span moving average where each observation is weighted by a constant, say, aj $0.$ Therefore, the weighted moving average at the end of period $T$ is

$M_T^w={\displaystyle \underset{t=T-N+1}{\overset{T}{}}}{a}_{T+1-t}{y}_t.$

Why would you consider using a weighted moving average?

Show that the variance of the weighted moving average is

${}^2{\displaystyle \underset{j=i}{\overset{N}{}}}{a}_j^2$