What is the tracking signal for the 5 month moving average M

What is the tracking signal for the 5 month moving average?

Month...Sales

January 9.00

Feb 7.00

March 10.00

April 8.00

May 7.00

June 12.00

July 10.00

August 11.00

September 12.00

October 10.00

November 14.00

December 16.00

January ---

Please show how to do each step of the problem.

Solution

To calculate the tracking signal we have to first calculate the five months moving average forecast, forecast errors and mean absolute deviation.

Using the five months moving average method the forecast is calculated as the average of the actual value for the previous five months. This can be calculated using the following formula :Sum of the actual value for the previous five months / 5.So using the five months moving average the forecast for June through January are

Then we have to calculate the mean absolute deviation(MAD) which is : Sum of the absolute deviation for all the periods / number of periods.

Where, deviation = actual value - forecasted value

Absolute deviation = absolute value of deviation

So using the above formula the deviation and absolute deviation for all the months are :

MAD = (3.8+1.2+1.6+2.4+0.4+0.25+4.6) / 7 = 14.25/7 = 2.04

Accumulated forecast errors = Sum of the deviations for all the periods = 3.8+1.2+1.6+2.4+(-0.4)+0.25+4.6 = 13.85-0.4 = 13.45

Tracking signal = Accumulated forecast errors / MAD

= 13.45 / 2.04

= 6.59