Project Planning
1
Describe the Moving Average Method of time series projection:
A moving average is defined as an average of fixed number of items in the time series which
move through the series by dropping the top items of the previous averaged group and adding
the next in each successive average. This method is based on the principle that the total effect
of periodic variations at different points of time in its cycle gets completely neutralized. In the
method of moving average, successive arithmetic averages are computed from overlapping
groups of successive values of a time series. Each group includes all the observations in a given
time interval, termed as the period of moving average. The next group is obtained by replacing
the oldest value by the next value in the series. The averages of such groups are known as the
moving averages. The moving averages of a group are always shown at the centre of its period.
Moving Average when the period is Odd:
By three-yearly moving averages, we shall obtain average of first three consecutive years and
place it against time t=2; then the average of the next three consecutive years and place it
against time t=3, and so on.
Time (t)
Observations (Yt)
Moving Total
Moving Average (3 years)
1
Y1
2
Y2
Y1+Y2+Y3
(Y1+Y2+Y3 )1/3
3
Y3
Y2+Y3+Y4
(Y2+Y3+Y4) 1/3
4
Y4
Y3+Y4+ Y5
(Y3+Y4+ Y5) 1/3
5
Y5
It should be noted that for odd period moving average, it is not possible to get the moving
averages for the first and the last periods.
Moving Average when the period is Even:
For an even order moving average, two averaging processes are necessary in order to centre
the moving average against periods rather than between periods. For example, for a four –
yearly moving average we shall first obtain the average Y1=1/4(Y1 + Y2 + Y3 + Y4) of the first
four years and place it in between t =2 and t=3 then the average Y2 = 1/4(Y2 + Y3 + Y4 + Y5)
of the next four years is and place it in between t=3 and t=4.
Merits:
1. This method is easy to understand and easy to use because there are no mathematical
complexities involved.
2. It is an objective method in the sense that anybody working on a problem with the method
will get the same trend values. It is in this respect better than the free hand curve method.
3. It is a flexible method in the sense that if a few more observations are added, the entire
calculations are not changed. This not with the case of semi-average method.
4.When the period of oscillatory movements is equal to the period of moving average, these
movements are completely eliminated.
5. By the indirect use of this method, it is also possible to isolate seasonal, cyclical and random
components.
Demerits:
1. It is not possible to calculate trend values for all the items of the series. Some information is
always lost at its ends.
2. This method can determine accurate values of trend only if the oscillatory and the random
fluctuations are uniform in terms of period and amplitude and the trend is, at least,
approximately linear. However, these conditions are rarely met in practice. When the trend is
not linear, the moving averages will not give correct values of the trend.
3. The trend values obtained by moving averages may not follow any mathematical pattern i.e.,
fails in setting up a functional relationship between the values of X(time) and Y(values) and
thus, cannot be used for forecasting which perhaps is the main task of any time series analysis.
4. The selection of period of moving average is a difficult task and a great deal of care is needed
to determine it.
5. Like arithmetic mean, the moving averages are too much affected by extreme values.
2
For the data given above, set n equal to 3 and develop forecasts for the periods 4 to 12 using
Moving Average Method of demand forecasting.
t
1
2
3
4
5
6
7
8
9
10
11
12
Sale
750
1150
1000
900
1300
1400
1550
1900
1850
1900
2200
2400
Forecast
Ft
966.6667
1016.667
1066.667
1200
1416.667
1766.667
1883.333
1983.333
Forecast for t+1
Ft+1=(St+St-1 +St-2 +…+St-n+1 )/n
(If n is set equal to 3 i.e. 3 yr M.A.)
F4= (750+1150+1000)/3
F5= (900+1000+1150)/3
F6= (1300+900+1000)/3
F7= (1400+1300+900)/3
F8= (1550+1400+1300)/3
F9= (1900+1550+1400)/3
F10= (1805+1900+1550)
F11= (1900+1850+1900)/3
F12= (2200+1900+1850)/3