Question

Consider the following time series data.

Quarter	Year 1	Year 2	Year 3
1	4	6	7
2	2	3	6
3	3	5	6
4	5	7	8

Compute seasonal indexes and adjusted seasonal indexes for the four quarters (to 3 decimals).

Quarter	Seasonal Index	Adjusted Seasonal Index
1	(___)	(___)
2	(___)	(___)
3	(___)	(___)
4	(___)	(___)
Total	(___)

Consider the following time series data.

Quarter	Year 1	Year 2	Year 3
1	5	5	6
2	2	4	5
3	4	6	6
4	7	5	8

b. Show the four-quarter and centered moving average values for this time series (to 3 decimals if necessary).

Year	Quarter	Time Series Value	Four-Quarter Moving Average	Centered Moving Average
1	1	5
	2	2
			(___)
	3	4		(___)
			(___)
	4	7		(___)
			(___)
2	1	5		(___)
			(___)
	2	4		(___)
			(___)
	3	6		(___)
			(___)
	4	5		(___)
			(___)
3	1	6		(___)
			(___)
	2	5		(___)
			(___)
	3	6
	4	8

c. Compute seasonal indexes and adjusted seasonal indexes for the four quarters (to 3 decimals).

Quarter	Seasonal Index	Adjusted Seasonal Index
1	(___)	(___)
2	(___)	(___)
3	(___)	(___)
4	(___)	(___)
Total	(___)

Answer 1

Answer :

By using Excel

Path :Data < Data analysis

a) we have to obtain seasonal index and adjusted seasonal index

For seasonal index ,

			year
		1	2	3
	1	4	6	7
Quarter	2	2	3	6
	3	3	5	6
	4	5	7	8
	total	14	21	27
	average	3.5	5.25	6.75

Seasonal index = average ( actual value / average of of year)

eg.

1. SI= 4 / 3.5 = 1.107

			year
		1	2	3	Seasonal index
	1	1.142857	1.142857	1.037037	1.107
Quarter	2	0.571429	0.571429	0.888889	0.677
	3	0.857143	0.952381	0.888889	0.899
	4	1.428571	1.333333	1.185185	1.315
				total=	4

For adjusted seasonal index,

Adjusted seasonal index = Actual value / seasonal index

			year
		1	2	3
	1	3.611	5.417	6.320
Quarter	2	2.953	4.429	8.859
	3	3.335	5.558	6.670
	4	3.800	5.320	6.080

b) we obtain four year moving average and centering moving average,

  

Quarter	year	Four year moving average	centered moving average
1	5
2	2
3	4
4	7	4.5
1	5	4.5	4.5
2	4	5	4.75
3	6	5.5	5.25
4	5	5	5.25
1	6	5.25	5.125
2	5	5.5	5.375
3	6	5.5	5.5
4	8	6.25	5.875