Question

1. A popular brand of skate board has had the following sales history for the past 36 periods.

Period	Sales	Period	Sales	Period	Sales
1	437	13	395	25	527
2	582	14	512	26	537
3	646	15	535	27	477
4	499	16	556	28	474
5	422	17	725	29	709
6	381	18	597	30	663
7	423	19	442	31	748
8	397	20	408	32	698
9	519	21	478	33	609
10	655	22	526	34	530
11	538	23	625	35	550
12	518	24	681	36	609

1. Plot the above sales data. What type of pattern (e.g. level, linear trend, nonlinear trend, seasonal, intermittent) does this data exhibit?
2. Use the first 36 past sales data to initialize a Winter’s Multiplicative Seasonal forecasting model. Use linear regression (regression line fitted using all 36 periods) to initialize your model.
3. Forecast the skate board sales for periods 37 through 49 using your part b model; i.e. at the end of period 36, forecast the demand for the next 13 periods.
4. Now suppose the actual demand in period 37 is 621. Update your Winter’s Multiplicative Seasonal forecasting model parameters using α = 0.20, β = 0.25, γ = 0.15. Forecast the skate board sales for periods 38 through 49 using your updated forecasting model parameters; i.e. at the end of period 37, forecast the demand for the next 12 periods.

Answer 1

Plot the above sales data. What type of pattern (e.g. level, linear trend, nonlinear trend, seasonal, intermittent) does this data exhibit?

There is a seasonal pattern in the data.

Use the first 36 past sales data to initialize a Winter’s Multiplicative Seasonal forecasting model. Use linear regression (regression line fitted using all 36 periods) to initialize your model.

Yt = 468.8 + 4.13×t

Forecast the skate board sales for periods 37 through 49 using your part b model; i.e. at the end of period 36, forecast the demand for the next 13 periods.

Period	Forecast
37	621.608
38	625.737
39	629.866
40	633.995
41	638.124
42	642.253
43	646.382
44	650.511
45	654.640
46	658.769
47	662.898
48	667.026
49	671.155

Now suppose the actual demand in period 37 is 621. Update your Winter’s Multiplicative Seasonal forecasting model parameters using α = 0.20, β = 0.25, γ = 0.15. Forecast the skate board sales for periods 38 through 49 using your updated forecasting model parameters; i.e. at the end of period 37, forecast the demand for the next 12 periods.

Forecasts

Period	Forecast	Lower	Upper
38	635.065	392.478	877.652
39	635.240	386.005	884.474
40	622.083	365.462	878.705
41	634.386	369.701	899.070
42	639.272	365.907	912.637
43	639.441	356.835	922.047
44	626.191	333.837	918.545
45	638.568	336.008	941.127
46	643.479	330.300	956.658
47	643.642	319.471	967.813
48	630.299	294.800	965.798
49	642.750	295.619	989.880