Question

Forecasts and actual sales of MP3 players at Just Say Music are as follows:

Month	Forecast	Actual Sales
March	150	170
April	220	229
May	205	192
June	256	241
July	250	238
August	260	210
September	270	225
October	280	179

Answer the following questions.

a. Plot the data and provide through insights about the time series. (Use Microsoft Excel and attach the time series graph.)

b. What is the forecast for November, using a two-period moving average?

c. What is the forecast for November, using a three-period moving average?

d. Compute mean square error (MSE) for the two- and three-period moving average models and compare your results. Which one is better?

e. Find the single exponential smoothing model by evaluating the MSE for Alpha 0.5. How does this model compare with the best moving average model found in 1d?

Answer 1

Answer a= From the graph, the time series seems to be quite stable.

Answer b= forecast for November, using a two-period moving average =(225+179)/2 =202

Answer c=forecast for November, using a three-period moving average==(210+225+179)/3 =204.7

Answer d=

Month	Actual Sales	2-month moving avearge Forecast	Errro	Square of error
March	170
April	229
May	192	199.5	-7.5	56.25
June	241	210.5	30.5	930.25
July	238	216.5	21.5	462.25
August	210	239.5	-29.5	870.25
September	225	224	1	1
October	179	217.5	-38.5	1482.25
			Sum	3802.25
	MSE=3802.25/6
	MSE=633.71

Month	Actual Sales	3-month moving avearge Forecast	Errro	Square of error
March	170
April	229
May	192
June	241	197.00	44.00	1936.00
July	238	220.67	17.33	300.44
August	210	223.67	-13.67	186.78
September	225	229.67	-4.67	21.78
October	179	224.33	-45.33	2055.11
			Sum	4500.11
	MSE=4500.11/5
	MSE=900

If we look at the result of MSE, the value of MSE is less for a 2-month moving average so it should be selected.