Page 307 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes Demerits of Semi-average Method

1. Extreme Values : This method is based on arithmetic mean. Therefore, it is greatly affected by
extreme values of the items.
2. Straight-line Relationship : This method assumes a straight-line relationship between the two
points plotted on the graph, regardless of the fact whether such relationship exists or not.
3. Influence of Cycle : In this method, there is no assurance that the influence of cycle is eliminated.
The danger is greater when the time period represented by average is small.
In short, despite of above demerits, this method is definitely better than freehand curve method.
Limitations of Semi-average Method

1. This method assumes straight line relationship between the plotted points regardless of the
fact whether that relationship exists or not.
2. The limitations of arithmetic average shall automatically apply. If there are extremes in either
half or both halves of the series, then the trend line is not a true picture of the growth factor.
This danger is greatest when the time period represented by the average is small. Consequently,
trend values obtained are not precise enough for the purpose either of forecasting the future
trend or of eliminating trend from original data.
For the above reasons if the arithmetic averages of the data are to be used in estimating the
secular movement, it is sometimes better to use moving averages than semi-averages.
Self-Assessment

1. Fill in the blanks:
(i) Graphic method is flexible and can be used for linear as well as ............ trends.
(ii) The values of the time series are plotted on a graph paper in the form of a ............ .
(iii) In graphic method, the seasonal and cyclical and irregular variations are ............ .
(iv) Semi-average means average of the two ............ of the series.
(v) Semi-average method is based on arithmetic ............ .
23.3 Summary

• Measuring a trend actually means computing the constants of the equation that we have chosen
to be representative of the trend in the data. However, it should be remembered that if we
choose a wrong curve for the data, then the constants of the equation computed would be
wrong, and any forecasting made on the basis of this equation would be wrong.
• Freehand method is also called the graphic method in the sense that the trend line is determined
by inspecting the graph of the series. According to this method, the trend values are determined
by drawing freehand straight line through the time series data that is judged by the analyst to
represent adequately the long-term movement in the series. Once the freehand trend line is
drawn, a trend equation for the line can be approximated. This is done by first reading off the
trend values of the first and the last period from the chart with reference to the freehand line.
For this purpose, the first period is usually considered the origin. Thus, the trend value for the
first period is the value of a for the equation. Then the difference between the trend values of
the first and the last period is obtained.
• The trend line for many series may be satisfactorily drawn provided the fluctuations around
the general drift are so small that the path of the trend is clearly defined. The main trouble with
this method is that it is too subjective. Even an expert in this subject may draw different lines at
different times for the same series. There is no formal statistical criterion whereby the adequacy
of such a line can be judged. Furthermore, although this method appears simple and direct, in

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