Question

Consider the quarterly electricity production for years 1-4 :

year	1	2	3	4
Q1	99	120	139	160
Q2	88	108	127	148
Q3	93	111	131	150
Q4	111	130	152	170

a) Estimate the trend using a centered moving average

b) Using a classical addictive decomposition, calculate the seasonal component

c) Explain how you handled the end points.

Answer 1

Solution:

Part(a)

We ignore the end points and obtain the following result:

Year	Quarter	Obs	Simple MA	Centered MA
1	1	99
1	2	SS
			97.75
1	3	93		100.375
			103
1	4	111		105.5
			108
2	1	120		110.25
			112.5
2	2	108		114.875
			117.25
2	3	111		119.625
			122
2	4	130		124.375
			126.75
3	1	139		129.25
			131.75
3	2	127		134.5
			137.25
3	3	131		139.875
			142.5
3	4	152		145.125
			147.75
4	1	160		150.125
			152.5
4	2	148		154.75
			157
4	3	150
4	4	170

Part(b)

We know the Centered Moving Average (CMA) contains no seasonality, the seasonal component may be estimated by

Obs	Centered MA	Seasonal Component
93	100.375	0.9265
111	1055	0.1052
120	110.25	1.0884
108	114.875	0.9402
111	119.625	0.9279
130	124.375	l.0452
139	129.25	1.0754
127	134.5	0.9442
131	139.875	0.9366
152	145.125	1.0474
160	150.125	1.0658
148	154.75	0.9564

Part(c)

Ends points are ignored to compute the mentioned seasonal component.