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 
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 
 
 
 
 