Page 328 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 25 : Methods of Moving Averages

25.3 Summary Notes

This method may be considered as an artificially constructed time series in which each periodic
figure is replaced by the mean of the value of that period and those of a number of preceding
and succeeding periods. The computation of moving averages is simple and straight-forward.
• Moving average method is quite simple and is used for smoothing the fluctuations in curves.
The trend values obtained by this method are very much accurate. Like semi-average method,
this method also employs arithmetic means of items. But here we find out the moving averages
from the time series. A moving average of a time series is a new series obtained by finding out
successively the average of a number of the original successive items choosen on the basis of
periodicity of fluctuations, dropping off one item and adding on the next at each stage.
• The most important point in the average method is the selection of period. The selection of
period depends upon the periodicity of data.
• Odd period is the period of three, five, seven, nine years and so on. In case of odd period
moving average, no difficulty is faced while placing the computed average.
• The procedure of calculation of moving average of even number of years, say, four, six, eight,
and so on, is different from the procedure of odd number of years. Suppose moving average is
to be calculated for four years. We will take the total of first four years and will be placed in
between second and third years, i.e., in the middle of four years. Leaving the first year, calculate
the total of next four years and so on. It is important to note that these calculated totals are
placed between two years. Then we adjust these moving totals. For this we compute two yearly
moving totals of four yearly moving totals. We take the total of first and second four years
moving totals and write against the third year and then the second and third four yearly moving
totals are totalled and written against the fourth year and so on. The two yearly moving totals
of four yearly moving totals are then divided by eight and this gives us the centered four yearly
moving average. The series so obtained is known as an estimate of the trend.
• No particular period of a moving average will eliminate the fluctuations completely. But greater
the period, the greater will be the reduction in the irregular fluctuations. Because the duration
of business cycles always remain changing.
• This method is highly flexible in the sense that if a few more figures are added to the series,
entire calculations are not changed. Only thing, we have to do is to extend the process so as to
calculate further trend values.
• The main limitation or demerit of this method is that it is difficult to determine the proper
period of moving average. If a wrong period is selected, there is every likelihood that conclusions
may be misleading.
• The main limitation or demerit of this method is that it is difficult to determine the proper
period of moving average. If a wrong period is selected, there is every likelihood that conclusions
may be misleading.
• In this method, moving averages are calculated by using the arithmetic average. Thus, like
arithmetic average it is also affected by extreme values of the series.
• Trend values cannot be computed for all the years. The longer the period of moving average,
the greater the number of years for which trend values cannot be obtained. For example, in a
three-yearly moving average, trend value cannot be obtained for the first year and last year, in
a five-yearly moving average for the first two years and the last two years, and so on. It is often
these extreme years in which we are most interested.
• Although theoretically we say that if the period of moving average happens to coincide with
the period of cycle, the cyclical fluctuations are completely eliminated, but in practice. Since the
cycles are by no means perfectly periodic, the lengths of the various cycles in any given series
will usually vary considerably and, therefore, no moving average can completely remove the
cycle. The best results would be obtained by a moving average whose period is equal to the

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