Find the weights, showing all working, for the following centred smoothers:

2 x 6 MA

(ii) 3 x 3 MA

(iii) 3 x 7 MA

(iv) Indicate how many missing observations there will be at the start and end of each smoothed series in (i)-(iii).

(v) Identify each smoother in (i)-(iii) as a WMA-k. What is k?

(vi) Is each smoother in (i)-(iii) symmetric? Justify your answer

(vii) Devise a symmetric smoother that is an WMA 5 so that the weight on time t is 1.5 times the weight at times t-1 and t+1; and double the weight at times t-2, t+2

Show All working