Question

Barbara Lynch, the product manager for a line of skiwear produced by HeathCo Industries, has been working on developing sales forecasts for the skiwear that is sold under the Northern Slopes and Jacque Monri brands. She has had various regression-based forecasting models developed. Quarterly sales for 1988Q1 through 1997Q4 are as follows:

	Sales
Year	Q1	Q2	Q3	Q4
1988	72,962	81,921	97,729	142,161
1989	145,592	117,129	114,159	151,402
1990	153,907	100,144	123,242	128,497
1991	176,076	180,440	162,665	220,818
1992	202,415	211,780	163,710	200,135
1993	174,200	182,556	198,990	243,700
1994	253,142	218,755	225,422	253,653
1995	257,156	202,568	224,482	229,879
1996	289,321	266,095	262,938	322,052
1997	313,769	315,011	264,939	301,479

a) Prepare a time-series plot of the data, and on the basis of what you see in the plot, write a brief paragraph in which you explain what patterns you think are present in the sales series.

b) Smooth out seasonal influences and irregular movement by calculating the center moving averages. Add the centered moving averages to the original data you plotted in part a. Has the process of calculating center moving averages been effective in smoothing out the seasonal and irregular fluctuations in the data? Explain.

c) Determine the degree of seasonality by calculating seasonal indexes for each quarter of the year.

d) Develop a forecast for Ms Lynch for the four quarters of 1998.

Answer 1

(a) The time-series plot is:

There is a seasonality in the data.

(b)

				Centered
				Moving
t	Year	Quarter	Data	Average
1	1	1	72,962
2	1	2	81,921
3	1	3	97,729	107772.000
4	1	4	1,42,161	121251.750
5	2	1	1,45,592	127706.500
6	2	2	1,17,129	130915.375
7	2	3	1,14,159	133109.875
8	2	4	1,51,402	132026.125
9	3	1	1,53,907	131038.375
10	3	2	1,00,144	129310.625
11	3	3	1,23,242	129218.625
12	3	4	1,28,497	142026.750
13	4	1	1,76,076	156991.625
14	4	2	1,80,440	173459.625
15	4	3	1,62,665	188292.125
16	4	4	2,20,818	195502.000
17	5	1	2,02,415	199550.125
18	5	2	2,11,780	197095.375
19	5	3	1,63,710	190983.125
20	5	4	2,00,135	183803.250
21	6	1	1,74,200	184560.250
22	6	2	1,82,556	194415.875
23	6	3	1,98,990	209729.250
24	6	4	2,43,700	224121.875
25	7	1	2,53,142	231950.750
26	7	2	2,18,755	236498.875
27	7	3	2,25,422	238244.750
28	7	4	2,53,653	236723.125
29	8	1	2,57,156	234582.250
30	8	2	2,02,568	231493.000
31	8	3	2,24,482	232541.875
32	8	4	2,29,879	244503.375
33	9	1	2,89,321	257251.250
34	9	2	2,66,095	273579.875
35	9	3	2,62,938	288157.500
36	9	4	3,22,052	297328.000
37	10	1	3,13,769	303692.625
38	10	2	3,15,011	301371.125
39	10	3	2,64,939
40	10	4	3,01,479

The plot is:

The data has smoothed efficiently.

(c)

				Centered
				Moving	Ratio to	Seasonal
t	Year	Quarter	Data	Average	CMA	Indexes
1	1	1	72,962			1.079
2	1	2	81,921			0.946
3	1	3	97,729	107772.000	0.907	0.909
4	1	4	1,42,161	121251.750	1.172	1.066
5	2	1	1,45,592	127706.500	1.140	1.079
6	2	2	1,17,129	130915.375	0.895	0.946
7	2	3	1,14,159	133109.875	0.858	0.909
8	2	4	1,51,402	132026.125	1.147	1.066
9	3	1	1,53,907	131038.375	1.175	1.079
10	3	2	1,00,144	129310.625	0.774	0.946
11	3	3	1,23,242	129218.625	0.954	0.909
12	3	4	1,28,497	142026.750	0.905	1.066
13	4	1	1,76,076	156991.625	1.122	1.079
14	4	2	1,80,440	173459.625	1.040	0.946
15	4	3	1,62,665	188292.125	0.864	0.909
16	4	4	2,20,818	195502.000	1.129	1.066
17	5	1	2,02,415	199550.125	1.014	1.079
18	5	2	2,11,780	197095.375	1.075	0.946
19	5	3	1,63,710	190983.125	0.857	0.909
20	5	4	2,00,135	183803.250	1.089	1.066
21	6	1	1,74,200	184560.250	0.944	1.079
22	6	2	1,82,556	194415.875	0.939	0.946
23	6	3	1,98,990	209729.250	0.949	0.909
24	6	4	2,43,700	224121.875	1.087	1.066
25	7	1	2,53,142	231950.750	1.091	1.079
26	7	2	2,18,755	236498.875	0.925	0.946
27	7	3	2,25,422	238244.750	0.946	0.909
28	7	4	2,53,653	236723.125	1.072	1.066
29	8	1	2,57,156	234582.250	1.096	1.079
30	8	2	2,02,568	231493.000	0.875	0.946
31	8	3	2,24,482	232541.875	0.965	0.909
32	8	4	2,29,879	244503.375	0.940	1.066
33	9	1	2,89,321	257251.250	1.125	1.079
34	9	2	2,66,095	273579.875	0.973	0.946
35	9	3	2,62,938	288157.500	0.912	0.909
36	9	4	3,22,052	297328.000	1.083	1.066
37	10	1	3,13,769	303692.625	1.033	1.079
38	10	2	3,15,011	301371.125	1.045	0.946
39	10	3	2,64,939			0.909
40	10	4	3,01,479			1.066

(d)

Forecast

309383.3

314776.6

320169.9

325563.2