Statistics >> Measurement of Trend
To measure the secular trend, the short-term variations should be removed and irregularities should be smoothed out. The following are the methods of measuring trend.
1. Graphic (or free hand curve) method
2. Semi-average method
3. Moving average method
4. Least squares method
GRAPHIC METHOD
The values of the time series are plotted on a graph paper with the time (t) along x-axis and the values of the variable (y) along y-axis. A freehand curve is drawn through these points in such a manner that it may show a general trend. A free hand curve removes the short-term variations and irregular movements.
It is the simplest method, Time and labour is saved. It is very flexibe method as it represents both linear and non-linear trends.
The main drawback of this method is that it is highly subjective as different persons will draw different free hand curves. Because of its subjective nature it is useless in forecasting.
Semi-Average Method
This method is sometimes used when a straight line appears to be an adequate expression of trend. In this method, the original data are divided into two equal parts. The averages of each part are then calculated. The average of each part is centred in the period of the time of the part from which it has been computed and then plotted on the graph paper. In this way, a line may be drawn to pass through the plotted points which gives the trend line. In case of odd number of years, the mid-year is eliminated while dividing the data into two equal parts.
This method is not subjective and ·everyone gets the same trend line. It is possible to extend the trend line both the ways to estimate future or past values. But the method assumes the presence of linear trend which may not exist.
Moving Average Method
Method of moving average consists in calculating a series of arithmetic means of some overlapping groups of the time series. There is no hard and fast rule for decision regarding period of moving average and the selection of period depends upon the objective that has to be attained from the figures of trend. The averaging process removes ups and downs in the data. If y1, y2, y3, ........ are the values of the time series for time periods t1, t2, t3 ........... then.
1st moving average of period In 1/m(y1+y2+-----+ym )
2nd moving average of period m 1/m(y2+y3+----+ym+1
3rd moving average of period m 1/m(y3+----+ym+2
Now, if the period m is odd, then the moving average values are placed against the middle values of the time periods. Again if the period m is even, then the moving average values are placed in between two middle time periods. After that, method of centering is applied to adjust the data with the original time periods.
The moving average values plotted against time give the trend line.
Merits and Demerits of Moving Average Method
Merits:
(i) This method is easy to understand and calculate.
(ii) This method is not subjective.
(iii) This method is flexible in the sense that a few more observations may be included of moving average is equal to or multiple of the cycle of a cyclical..
Demerits:
(i) Moving average can not be obtained for all the years.
(ii) There is no definite rule for fixing the period of moving average.
(iii) This method is suitable only when the trend is liner.
(iv) This method is not suitable for forecasting.
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