Question

Consider the following time series data.

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

a. Which of the following is a time series plot?

- Select your answer -time series plot #1time series plot #2time series plot #3Item 1

What type of pattern exists in the data?

- Select your answer -upward linear trendnonlinear trend and a seasonal patternlinear trend and a seasonal patternslight curvaturedownward linear trendItem 2

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	3
	2	4
			_________
	3	1		_____
			__________
	4	5		_________
			__________
2	1	6		______
			________
	2	1		_______
			______
	3	7		_______
			________
	4	7		________
			________
3	1	7		__________
			________
	2	8		________
			________
	3	5
	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

a) The time seres plot is given by,

The type of pattern exists in the data is seasonal pattern upward linear trend.

Year	Quater	Time series	4 point moving total	4 point oving average	Centered moving average
1	1	3
	2	4
			13	3.25
	3	1			3.625
			16	4
	4	5			3.625
			13	3.25
2	1	6			4
			19	4.75
	2	1			5
			21	5.25
	3	7			5.375
			22	5.5
	4	7			6.375
			29	7.25
3	1	7			7
			27	6.75
	2	8			6.875
			28	7
	3	5
	4	8

c) Seasonal indexes and adjusted seasonal indexes for the four quarters.

Year	Quater	Time series	centered moving average	Seasonal Irregular component
1	1	3
	2	4
	3	1	3.625	0.276
	4	5	3.625	1.379
2	1	6	4	1.500
	2	1	5	0.200
	3	7	5.375	1.302
	4	7	6.375	1.098
3	1	7	7	1.000
	2	8	6.875	1.164
	3	5
	4	8

Seasonal Index :

Total: 1.250 + 0.682+ 0.789+ 1.238 = 3.959

Adjusted Seasonal Index :

****If you have any queries or doubts please comment below, if you're satisfied please give a like. Thank you!