Question

Orchard Relief is a product that is designed to improve sleep at night. The company, Eli Orchard, is guessing that sales of the product is somewhat related to sleeping patterns of customers over the days of the week. Before mass production of the product, Eli Orchid has market-tested Orchid Relief in only Orange County over the past 8 weeks. The weekly demand is recorded. Eli Orchid is now trying to use the sales pattern over the past 8 weeks to predict sales in US for the upcoming few weeks, especially for days 57 and 60. An accurate forecast would be helpful in arrangements for the company’s production processes and design of price promotions over each week.

To solve the following problem, use a de-seasonalized time series for the last 7 days:

What is a de-seasonalized forecast for day 57 using the exponential smoothing method with smoothing constant 0.7? (Hint: Use de-seasonalized data on day 50 as your de-seasonalized forecast for day 51.)

Number of Days	Daily Demand
1	297
2	293
3	327
4	315
5	348
6	447
7	431
8	283
9	326
10	317
11	345
12	355
13	428
14	454
15	305
16	310
17	350
18	328
19	366
20	460
21	427
22	291
23	325
24	354
25	322
26	405
27	442
28	450
29	318
30	298
31	355
32	355
33	374
34	447
35	463
36	291
37	319
38	333
39	339
40	416
41	475
42	459
43	319
44	326
45	356
46	340
47	395
48	465
49	453
50	307
51	324
52	350
53	348
54	384
55	474
56	485

Answer 1

answer is 472.5686

What is a de-seasonalized forecast for day 57 using the exponential smoothing method with smoothing constant 0.7? (Hint: Use de-seasonalized data on day 50 as your de-seasonalized forecast for day 51.)

the forecast for day 57 =F₅₇ is= 472.5686

since the hint has been given as data on day 50 is the forecast value of day 51, so accordingly following information has been generated.

smoothing constant=	alpha=	0.7
t	Yt	Ft=alpha*Y(t-1)+(1-alpha)*F(t-1)	forecast error	squared forecast error
50	307
51	324	307.0000	17.0000	289.0000
52	350	318.9000	31.1000	967.2100
53	348	340.6700	7.3300	53.7289
54	384	345.8010	38.1990	1459.1636
55	474	372.5403	101.4597	10294.0707
56	485	443.5621	41.4379	1717.1004
57		472.5686	total=	14780.2736
			MSE=	49.6324