Trend Values Computation

For any given long term series, we wish to know and present the direction which it takes-Is it growing or declining? There are two most important reasons for trend measurement:

(i) To find out the trend specifications or characteristics in and of themselves: in studying a trend in and of itself, we can ascertain the growth factor. For e.g., we can compare the growth in the textile industry with the growth in the economy as an entire or with the growth in the other industries, or we can compare the growth in one firm for the textile industry with the growth in the industry as an entire. Moreover, we can compare through trend characteristics the growth for the textile industry in India with that of other countries. The growth factor helps us in predicting the future behavior of the data. If a trend can be known, the rate of change can be ascertained and tentative estimates concerning future is made accordingly.

(ii) To enable us the estimate trend in order to study other elements: the elimination of trend leaves is with cyclical, seasonal and irregular factors. We then, in two or more series, compare or use the impact of these three relatively short-term elements divorced from the long term factor. The different methods that can be used for determining trend are as follows:

1. Freehand or graphic method

2. Semi-average method

3. Moving average method

4. Method of least squares

Computation of trend values

Illustration: - the sale of a commodity in million tones varied from January 2009 to December 2009 in the following manner;

Fit a trend line by the method of semi-averages.

Solution: -

Average of the first half = 1650/6 = 275 tonnes.

Average of the second half = 1290/6 = 215 tonnes.

These two figures, viz. 275 and 215, should be plotted at the middle of their respective periods, at the middle of March-April & that of September-October, 2009 by joining these two points, we get a trend line which describes the given data.