Question

Problem # 1

The monthly sales for Telco Batteries Inc. were as follows:

                        Sales

Month            (000 units)

January            20

February          21

March              15

April                14

May                 13

June                 16

July                 17

August            18

September       20

October           20

November       21

December        23

1. Plot the monthly sales data.
2. Forecast coming January sales using each of the following:
   1. The naïve approach
   2. A 6-month moving average
   3. A 6-month weighted average using 0.1, 0.1, 0.1, 0.2, 0.2 and 0.3, with the heaviest weights applied to the most recent months.
3. Calculate the mean absolute deviation (MAD) and the mean squared error (MSE) for each of the method above. Which is better among the three methods?

Answer 1

a. Monthly sales data -

b. Below are the forecasts for all 3 methods -

		Naive				Six month Moving Average				Six month Moving Average
Month	Sales (000 units)	Forecast	Error	Absolute error	Error Square	Forecast	Error	Absolute error	Error Square	Forecast	Error	Absolute error	Error Square
Jan	20
Feb	21	20	1	1	1
March	15	21	-6	6	36
April	14	15	-1	1	1
May	13	14	-1	1	1
June	16	13	3	3	9
July	17	16	1	1	1	16.5	0.5	0.5	0.25	15.8	1.2	1.2	1.44
August	18	17	1	1	1	16	2	2	4	15.9	2.1	2.1	4.41
September	20	18	2	2	4	15.5	4.5	4.5	20.25	16.2	3.8	3.8	14.44
October	20	20	0	0	0	16.33	3.67	3.67	13.44	17.30	2.70	2.70	7.29
November	21	20	1	1	1	17.33	3.67	3.67	13.44	18.20	2.80	2.80	7.84
December	23	21	2	2	4	18.67	4.33	4.33	18.78	19.40	3.60	3.60	12.96
			MAD =	1.73			MAD =	3.11			MAD =	2.70
			MSE=	5.36			MSE=	11.69			MSE=	8.06

And below are the formulas that are used -

c. Mean absolute deviation and Mean Square error has already been calculated above. Mean absolute deviation and Mean squared error is minimum for Naive forecast. Hence naive forecast gives better forecasts than other two methods.