Method of Moving Averages
Suppose that there are times periods denoted by and the corresponding values of variable are . First of all we have to decide the period of the moving averages. For short time series, we use period of 3 or 4 values. For long time series, the period may be 7, 10 or more. For quarterly time series, we always calculate averages taking 4quarters at a time. In monthly time series, 12monthly moving averages are calculated. Suppose the given time series is in years and we have decided to calculate 3years moving average. The moving averages denoted by are calculated as below:
Years (t)

Variable (Y)

3Years moving totals

3Years moving averages





































The average of the first 3 values is and is denoted by. It is written against the middle year . We leave the first value and calculate the average for the next three values. The average is and is written against the middle years. The process is carried out to calculate the remaining moving averages. 4years moving averages are calculated as under:
Years (t)

Variable (Y)

3Years moving averages

3Years moving averages centered




























The first average is which is calculated as
. It is written against the middle of and . The two averages and are further averaged to get an average , which refers to the center of and is written against . This is called centering of the 4years moving averages. The process is continued till the end of the series to get 4years moving average centered. The moving averages of some proper period smooth out the short term fluctuations and the trend is measured by the moving averages.
Example: Compute 5years, 7years and 9years moving averages for the following data.
Years 
1990

1991

1992

1993

1994

1995

1996

19997

1998

1999

2000

Values 
2

4

6

8

10

12

14

16

18

20

22

Solution:
The necessary calculations are given below:


5Years Moving

7Years Moving

9Years Moving


Years

Values

Total

Average

Total

Average

Total

Average

1990

2













1991

4













1992

6

30

6









1993

8

40

8

56

8





1994

10

50

10

70

10

90

10

1995

12

60

12

84

12

108

12

1996

14

70

14

98

14

126

14

1997

16

80

16

112

16




1998

18

90

18









1999

20













2000

22













Example: Compute 4years moving average centered for the following time series:
Years 
1995

1996

1997

1998

1999

2000

2001

2002

Production 
80

90

92

83

87

96

100

110

Solution:
The necessary calculations are given below:
Year

Production

4Years Moving Total

4Years Moving Average

2values Moving Total

4years Moving
Average Centered 
1995

80









1996

90

345

86.25





1997

92

352

88.00

174.25

87.125

1998

83

358

89.50

177.50

88.750

1999

87

366

91.50

181.00

90.500

2000

96

393

98.25

189.75

94.875

2001

100









2002

110








