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Consider the quarterly electricity production for years 1-4: Year 1 2 3 4 Q1 99 120 139 160 Q2...

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Statistics

Consider the quarterly electricity production for years1-4:
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 theseasonal component.
(c) Explain how you handled the end points. - PLEASEPROVIDE ANSWER C !
Note: Explain all the steps and computations

Answer & Explanation Solved by verified expert
4.0 Ratings (472 Votes)

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.
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