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 additive decomposition, calculate the seasonal component.
(c) Explain how you handled the end points. - PLEASE PROVIDE ANSWER C !
Note: Explain all the steps and computations

Answer 1

a) If the end-points are ignored, we obtain the following results:

Year	Quarter	Obs	Simple MA	Centred MA
1	1	99
1	2	88
			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

b)I Because the centered moving average (CMA) contains no seasonality and no or little irregularity, the seasonal component may be estimated by

For example,Seasonal component =93/100.375=0.9265 and calculate other values

Obs	Centred MA	Seasonal component
93	100.375	0.926525529
111	1055	0.10521327
120	110.25	1.088435374
108	114.875	0.940152339
111	119.625	0.927899687
130	124.375	1.045226131
139	129.25	1.075435203
127	134.5	0.944237918
131	139.875	0.936550492
152	145.125	1.047372954
160	150.125	1.065778518
148	154.75	0.95638126

c) End points ignored. Other approaches are possible.