Methods of Measuring Secular Trend in Time Series:
Secular Trends in a Time Series can be determined by the following methods:
1. Freehand curve method;
2. Moving Averages method;
3. Semi Averages method; and
4. Least Squares method.
1. Freehand Curve Method of measuring Secular Trends in Time Series –
In statistical analysis, the term “freehand” is used for any non-mathematical curve even if it is drawn with the aid of drafting tools. This is the simplest way for analysing the trend of a time series.
The free-hand curve method is a simple, quick, and easy way to measure secular trends. A well-fitted trend line (or curve) gives a close approximation to the trend based on a mathematical model.
♦ Procedure for drawing a freehand curve – The method for drawing a freehand curve is as follows:
- First plot the original data on graph paper.
- Then observe carefully the direction of the plotted data.
- Then draw a smooth line through the plotted points.
♦ Conditions for fitting a trend line by the freehand –
When fitting a trend line by the freehand curve method, make an effort to ensure that the fitted curve meets these conditions.
- The curve should be smooth either a straight line or a combination of long gradual curves.
- The trend line or curve should be drawn through the graph of the data in such a way that the areas below and above the trend line are equal to each other.
- The vertical deviations of the data above the trend line must equal to the deviations below the line.
- The sum of the squares of the vertical deviations of the observations from the trend should be minimum.
Example 1: Draw a time series graph relating to the following data and fit the trend by the freehand method:
Year |
Production of Sugar (million tonnes) |
2013 |
20 |
2014 |
22 |
2015 |
30 |
2016 |
28 |
2017 |
32 |
2018 |
25 |
2019 |
29 |
2020 |
35 |
2021 |
40 |
2022 |
32 |
Solution:
The trend line drawn by the freehand method can be extended to project future values. However, the free-hand curve fitting is too subjective and should not be used as a basis for prediction.
(Source – Various books from college library)
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