The following time series shows the sales of particular prod

The following time series shows the sales of particular product over the past 7 months.

Month Sales

1 105

2 135

3 120

4 105

5 90

6 120

7 130

A. Use A=0.3 to compute the exponential smoothing values for the time series

B. Compute MAD and state your idea about MAD

Please show your work

Solution

A. Exponential smoothing using alpha of 0.3

The formula for obtaining the output for exponential smoothening is:

The most recent period’s sales multiplied by the smoothing factor.
PLUS
The most recent period’s forecast multiplied by (one minus the smoothing factor).

OR

(S*A)+(F*(1-A))

Where

S = most recent period’s sales
A = the smoothing factor represented in decimal form = 0.3
F = the most recent period’s forecast (the output of the smoothing calculation from the previous period).

B. MAD: mean absolute deviation

= sum of absolute value of deviations of sales figure from mean/(number of observation)

Sum of deviations = 90

No. of observations = 7

MAD = 90/7 = 12.85. MAD shows the average distance between each data value and the mean. The lower the MAD the better it is. The larger the MAD, the greater variability there is in the data (the data is more spread out).