Question

Year	Qtr	t	revenue ($M)
2011	1	1	5.889
	2	2	6.141
	3	3	8.272
	4	4	9.302
2012	1	5	6.436
	2	6	6.932
	3	7	8.987
	4	8	10.602
2013	1	9	7.517
	2	10	7.731
	3	11	9.883
	4	12	12.098
2014	1	13	8.487
	2	14	8.685
	3	15	11.559
	4	16	15.221
2015	1	17	11.132
	2	18	11.203
	3	19	13.83
	4	20	16.979
2016	1	21	12.312
	2	22	13.452
	3	23	17.659
	4	24	21.655
2017	1	25	17.197
	2	26	19.05
	3	27	22.499
	4	28	25.629

State the method ( Winter's additive or multiplicative) which is the most accurate to forecast for 2018 according to the data set?

Answer 1

From the scatter plot, increase the value of time, increases the corresponding value of revenue as a whole. Hence, this data presence the trend component. Also, there is a repeating short-term cycle with this series for every four data points. Hence, it also presence the seasonal component. Therefore, the most suitable model is to include both the trend and seasonal component in the model.

Arrange the given data as

Year	Qtr	t	revenue	Q1	Q2	Q3
2011	1	1	5.889	1	0	0
	2	2	6.141	0	1	0
	3	3	8.272	0	0	1
	4	4	9.302	0	0	0
2012	1	5	6.436	1	0	0
	2	6	6.932	0	1	0
	3	7	8.987	0	0	1
	4	8	10.602	0	0	0
2013	1	9	7.517	1	0	0
	2	10	7.731	0	1	0
	3	11	9.883	0	0	1
	4	12	12.098	0	0	0
2014	1	13	8.487	1	0	0
	2	14	8.685	0	1	0
	3	15	11.559	0	0	1
	4	16	15.221	0	0	0
2015	1	17	11.132	1	0	0
	2	18	11.203	0	1	0
	3	19	13.83	0	0	1
	4	20	16.979	0	0	0
2016	1	21	12.312	1	0	0
	2	22	13.452	0	1	0
	3	23	17.659	0	0	1
	4	24	21.655	0	0	0
2017	1	25	17.197	1	0	0
	2	26	19.05	0	1	0
	3	27	22.499	0	0	1
	4	28	25.629	0	0	0

1) Forecast for 2018 with Qtr=1

revenue = 7.1955 + 0.54569*29 - 4.4366*1 - 4.3789*0 - 2.1396*0 =$18.5839

2)

Forecast for 2018 with Qtr=2

revenue = 7.1955 + 0.54569*30 - 4.4366*0 - 4.3789*1 - 2.1396*0 =$19.1873

3)

Forecast for 2018 with Qtr=3

revenue = 7.1955 + 0.54569*31 - 4.4366*0 - 4.3789*0 - 2.1396*1 = $ 21.9723

4)

Forecast for 2018 with Qtr=4

revenue = 7.1955 + 0.54569*32 - 4.4366*0 - 4.3789*0 - 2.1396*0 = $24.6576