month sales Jan 3000 Feb 3400 Mar 3700 Apr 4100 May 4700 Jun

month    sales

Jan     3000

Feb     3400

Mar     3700

Apr    4100

May    4700

Jun   5700

Jul   6300

Aug   7200

Sept   6400

Oct   4600

Nov 4200

Dec   3900

a. Use a 3-month weighted moving average to forecast the sales for the months April through December. Use weights of (4/8), (3/8), and (1/8), giving more weight to the more recent data.

b. Use exponential smoothing with a=0.6 to forecast the sales for the months April through December. Assume that the initial forecast for January was $3200. Start error measurement in April.

c. Compare the performance of the two methods by using the mean absolute deviation as the performance criterion, with error measurement beginning in April. Which method would you recommend?

d. Compare the performance of the two methods by using the mean absolute percent error as the performance criterion, with error measurement beginning in April. Which method would you recommend?

e. Compare the performance of the two mthods by using th mean squared error as the performance criterion, which error measurement beginning in April. Which method would you recommend?

Solution

Table 1 forecasts using the Weighted Moving Average and Exponential smoothing. We have also calculated the errors and squared error which in turn helps us in finding the MSE or the Mean squared error.

This solves part a,b and e

Thus, on the basis on MSE,

Exponential smoothing gives a lower MSE and hence should be recommended.

Table 2 gives the absolute deviation and the Mean absolute deviation of the error. This is simply the modulus values of errors obtained.

Again over here as well, exponential smoothing with a = 0.6 turns out to be better.

Table 3 gives percentage errors in absolute terms i.e modulus values of error. An average of those errors is given as MAPE.

Even this method inclines towards exponential  smoothing for better results.

This thus solves part c and d.

Hope this helps.Ask if you have any doubts.