STA2604 Assignment 3 Solutions 2026

STA2604 Assignment 3 Solutions 2026
UNISA
ASSESSMENT 6

,QUESTION 1

The quarterly sales data are:

Year Quarter 𝑡 Sales 𝑦𝑡

1 1 1 18

1 2 2 23

1 3 3 33

1 4 4 42

2 1 5 26

2 2 6 32

2 3 7 41

2 4 8 46

3 1 9 30

3 2 10 35

3 3 11 44

3 4 12 49



1.1 Additive decomposition model

The general additive decomposition model is

𝑦𝑡 = 𝑡𝑟𝑡 + 𝑠𝑛𝑡 + 𝑖𝑟𝑡

where:

• 𝑦𝑡 = observed time-series value at time 𝑡

• 𝑡𝑟𝑡 = trend component

• 𝑠𝑛𝑡 = seasonal component

• 𝑖𝑟𝑡 = irregular/random component

Therefore, Observed = Trend + Seasonal + Irregular

, 1.2 Four-period moving averages and centred moving averages

The 4-period moving average is
𝑦𝑡 + 𝑦𝑡+1 + 𝑦𝑡+2 + 𝑦𝑡+3
𝑀𝐴𝑡 =
4


MA for first four observations
18 + 23 + 33 + 42
𝑀𝐴1 =
4
116
= = 29.00
4


Next
23 + 33 + 42 + 26
𝑀𝐴2 =
4
124
= = 31.00
4


Next
33 + 42 + 26 + 32 133
𝑀𝐴3 = = = 33.25
4 4


Next
42 + 26 + 32 + 41 141
𝑀𝐴4 = = = 35.25
4 4


Next
26 + 32 + 41 + 46 145
𝑀𝐴5 = = = 36.25
4 4


Next
32 + 41 + 46 + 30 149
𝑀𝐴6 = = = 37.25
4 4


Next
41 + 46 + 30 + 35 152
𝑀𝐴7 = = = 38.00
4 4