Estimated the trend value by 4 yearly moving averages method for the following data:

Question

Estimated the trend value by 4 yearly moving averages method for the following data:
Year 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
Value 12 18 26 32 40 60 76 94 100 108 98 90

Answer 1

In the whole data set of Years/ time and each subset of consecutive 4 years are to be considered and average of their corresponding values from the data set of values are to be derived. The frequency of moving average being 4, i.e., an even number, the average of of values corresponding to years in each subset of 4 consecutive years corresponds to 2.5 year intervals. Then the consecutive values corresponding to consecutive 2.5 years intervals are averaged. The resulting values correspond to every 3rd year of each subset of 4 consecutive years. It is derived as follows: 

 

 

Year      Value     MOVING AVERAGE                     CENTERED

1997       12

1998      18 

-------------------(12+18+26+32)/4 =22

1999       26 ________________________________(22+29)/2   =25.5

 -------------------(18+26+32+40)/4 =29

2000       32  ________________________________ (29+39.5)/2 =34.25

-------------------(26+32+40+60)/4 =39.5

2001       40 ________________________________  (39.5+52)/2 =45.75

-------------------(32+40+60+76)/4 =52

2002       60  ________________________________ (52+67.5)/2 =59.75

-------------------(40+60+76+94)/4 =67.5

2003       76 ________________________________ (67.5+82.5)/2=75

-------------------(60+76+94+100)/4 =82.5

2004       94 ________________________________ (82.5+94.5)/2=88.5
-------------------(76+94+100+108)/4 =94.5

2005      100 ________________________________ (94.5+100)/2=97.25
-------------------(94+100+108+98)/4 =100

2006      108  ________________________________ (100+99)/2=99.5
-------------------(100+108+98+90)/4 =99

2007        98 

2008        90

 

Final Table:

 

 

Year Value     CENTERED MOVING AVERAGE
1997 12
1998 18
1999 26 ------------- 25.5
2000 32 ------------- 34.25
2001 40 ------------- 45.75
2002 60 ------------- 59.75
2003 76 ------------- 75.0
2004 94 ------------- 88.5
2005 100 ------------97.25
2006 108 ------------99.5 
2007 98
2008 90