Question

Consider the accompanying time series.

a. Forecast the demand for each quarter in Year 4 using multiplicative decomposition.

b. Interpret the meaning of the seasonal components.

c. Calculate the MAD for this forecast.

Year_1_Quarter   Year_ 1_Demand   Year_2_Quarter   Year_2_Demand   Year_3_Quarter   Year_3_Demand
1 4 1 5 1 8
2 10 2 13 2 16
3 11    3 11 3 14
4 5 4 9 4    8

.

Answer 1

The MINITAB output is:

Method

Model type	Multiplicative Model
Data	Demand
Length	12
NMissing	0

Fitted Trend Equation

Yt = 5.46 + 0.593×t

Seasonal Indices

Period	Index
1	0.67690
2	1.47660
3	1.33477
4	0.51174

Accuracy Measures

MAPE	12.2786
MAD	0.9778
MSD	1.3145

Forecasts

Period	Forecast
13	8.9099
14	20.3116
15	19.1519
16	7.6460

a. Forecast the demand for each quarter in Year 4 using multiplicative decomposition.

Forecasts

Period	Forecast
13	8.9099
14	20.3116
15	19.1519
16	7.6460

b. Interpret the meaning of the seasonal components.

Quarter 2 has the highest demand, followed by Quarter 3, followed by Quarter 1 and then by Quarter 4.

c. Calculate the MAD for this forecast.

MAD

0.9778