Question

Consider the following time series data.

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

1. Which of the following is the correct time series plot?
   

   a.	$appletImage?dbid=556868570$
   b.	$appletImage?dbid=409718475$
   c.	$appletImage?dbid=1845446929$

   
   
2. 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	4
   	2	2
   	3	3
   	4	5
   2	1	6
   	2	4
   	3	5
   	4	7
   3	1	7
   	2	6
   	3	7
   	4	8

3. 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

question (a)

Convert the following matrix (quarter x year) into single column

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

Year	Quarter	Period	Value
1	1	1	4
1	2	2	2
1	3	3	3
1	4	4	5
2	1	5	6
2	2	6	4
2	3	7	5
2	4	8	7
3	1	9	7
3	2	10	6
3	3	11	7
3	4	12	8

so option c (the last graph) is the correct answer

question (b)

Four-Quarter Moving Average

X-4+Xt-2+ Xt-1Xt MAt 4 not be defined therefore for t 1, 2, and 3

Centered Moving Average

Xt-2+Xt-1XXt+1 MAt 4 MAXt-1 X Xt+1Xt2 4 it can not be defined therefore for t 1, and n

Year	Quarter	Period	Value	Four-Quarter Moving Average	Centered Moving Average
1	1	1	4	-	-
1	2	2	2	-	3.500
1	3	3	3	-	4.000
1	4	4	5	3.500	4.500
2	1	5	6	4.000	5.000
2	2	6	4	4.500	5.500
2	3	7	5	5.000	5.750
2	4	8	7	5.500	6.250
3	1	9	7	5.750	6.750
3	2	10	6	6.250	7.000
3	3	11	7	6.750	7.000
3	4	12	8	7.000	-