Moving average table?

Question

Given the data

t: 1 2 3 4 5 6

x: 6 8 7 8 9 9

Construct the moving average table with N = 3.

Construct a table for single exponential smoothing with 'a = 0.5' ('a' is an alpha sign)

The exponential smoothing is the most important part of this question.

Thank you

Answer 1

Simple exponential smoothing is nothing more than alpha times the actual value for the period, plus 1-alpha times the smoothed value of the previous period.

This presents a problem at the initial period, as there is no previous smoothed value. I used the actual value as the initial smoothed value for period 1. Sometimes this is done, and sometimes the average for some number (or all) periods is used. You should use whatever your text recommends.

1 6: 6  [just the actual value]

2 8: 7  [a*8 + (1-a)*6]

3 7: 7  [.5*7 + .5*7]

4 8: 7.5 [.5*8 + .5*7]

5 9: 8.25 [.5*9 + .5*7.5]

6 9: 8.625 [.5*9 + .5*8.25]