EQC7006 : Time Series Analysis 2017/2018
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ACADEMIC SESSION 2017/2018: SEMESTER II
EQC7006: Time Series Analysis
1. The following table gives a quarterly time series data and the results of classical decomposition using multiplicative decomposition approach.
|
Year |
Quarter |
Yt |
Trend (Tt) |
De- trend |
Seasonal indices (St) |
Normalized (St) |
Revised irregular (Et) |
Seasonally adjusted
( |
|
1 |
1 |
362 |
|
|
|
|
|
|
|
2 |
385 |
|
|
|
|
|
|
|
|
3 |
432 |
382.50 |
1.13 |
1.14 |
|
|
|
|
|
4 |
341 |
388.00 |
0.88 |
0.86 |
|
|
|
|
|
2 |
1 |
382 |
399.25 |
0.96 |
|
|
|
|
|
2 |
409 |
413.25 |
0.99 |
|
|
|
|
|
|
3 |
498 |
430.38 |
1.16 |
|
|
|
|
|
|
4 |
387 |
454.75 |
0.85 |
|
|
|
|
|
|
3 |
1 |
473 |
478.25 |
0.99 |
|
|
|
|
|
2 |
513 |
499.63 |
1.03 |
|
|
|
|
|
|
3 |
582 |
|
|
|
|
|
|
|
|
4 |
474 |
|
|
|
|
|
|
a) Compute seasonal indices (
1 and 
2 ), normalized seasonal indices ( 
1 , 
2 , 
3 and 
4 ), and revised irregular component 
3, 
4, 
5 and 
6 values.
(6 marks)
b) Compute seasonally adjusted series (
1, 
2, 
3 and 
4 ) using normalized 
obtained in (a).
(2 marks)
c) Give an example of situation that requires us to analyse seasonally adjusted series instead of the seasonally unadjusted series.
(0.5 mark)
(Total: 8.5 marks)
2. The following table gives a quarterly time series data and the results of Holt-Winters multiplicative exponential smoothing approach. (
= 
= 
= 0.3).
|
Year |
Quarter |
Yt |
|
|
|
|
|
1 |
1 |
362 |
|
|
|
|
|
2 |
385 |
|
|
|
|
|
|
3 |
432 |
|
|
|
|
|
|
4 |
341 |
|
|
|
|
|
|
2 |
1 |
382 |
|
|
|
|
|
2 |
409 |
403.83 |
10.74 |
|
|
|
|
3 |
498 |
421.62 |
12.86 |
1.15 |
|
|
|
4 |
387 |
433.51 |
12.57 |
0.90 |
|
|
|
3 |
1 |
|
|
|
|
|
|
2 |
|
|
|
|
|
|
|
3 |
|
|
|
|
|
|
|
4 |
|
|
|
|
|
2022-05-19