Question

Costello Music Company has been selling electronic organs over the past 5 years. Sales were initially low but have grown over time. Ray Costello, the owner of the company, wants to predict the sales for the upcoming year using the number of sales that Costello Music Company has experienced. The sales totals are given in the following table.

Year	Q1	Q2	Q3	Q4	Total
1	4	2	1	5	12
2	6	4	4	14	28
3	10	3	5	16	34
4	12	9	7	22	50
5	18	10	13	35	76

a) Using the centered moving average approach (CMA) what are the seasonal indexes for the four quarters?

b) In which quarter does Costello Music Company experience their largest seasonal effect? Does this result seem reasonable? Explain your answer.

c) Using multiplicative decomposition predict the level of sales for each quarter next year. Report your results.

Answer 1

solution:

Given data:

a)

i) First calculate Centered Moving Average ( CMA )

For Year-1 and Q3 :

((4+2+1+5)/4)+((2+1+5+6)/4)

= 3.250

ii) Calculate combined seasonal-irregular value.

For Year-1 and Q3 :

1/3.25 = 0.308

Year	Quarter	Sales	CMA	Seasonal-Irregular-value
1	Q1	4
1	Q2	2
1	Q3	1	3.250	0.308
1	Q4	5	3.750	1.333
2	Q1	6	4.375	1.371
2	Q2	4	5.875	0.681
2	Q3	4	7.500	0.533
2	Q4	14	7.875	1.778
3	Q1	10	7.875	1.270
3	Q2	3	8.250	0.364
3	Q3	5	8.750	0.571
3	Q4	16	9.750	1.641
4	Q1	12	10.750	1.116
4	Q2	9	11.750	0.766
4	Q3	7	13.250	0.528
4	Q4	22	14.125	1.558
5	Q1	18	15.000	1.200
5	Q2	10	17.375	0.576
5	Q3	13
5	Q4	35

iii) Calculate Seasonal Index

Summarize the Seasonal Irregular value in to the following table.

Seasonal Index for Q1 = ( 1.371+1.270+1.116 )/3 = 1.253

Similarly, calculate for Q2, Q3, and Q4

Quarter	Seasonal-Irregular-value			Seasonal Index	Adjusted Seasonal Index
1	1.371	1.270	1.116	1.253	1.234
2	0.681	0.364	0.766	0.603	0.595
3	0.533	0.571	0.528	0.544	0.536
4	1.778	1.641	1.558	1.659	1.635
			Total	4.059	4.000

b)

  Costello Music Company experience their largest seasonal effect in Q4 ( Seasonal Index 1.635 )

i.e. : the sales averaging 63.5% above the trend estimate

It is reasonable because as per data, every year Q4 sales were much more than other three quarters.

c)

Quarter	Forecast
1	25.28308
2	12.77557
3	12.05948
4	38.38021

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