Freehand Curve Method of measuring Secular Trends in Time Series

Lata Agarwal Business Statistics & Statistics

time series in statistics — Image Source - AT&T Reports

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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About Lata Agarwal 270 Articles

M.Phil in Mathematics, skilled in MS Office, MathType, Ti-83, Internet, etc., and Teaching with strong education professional. Passionate teacher and loves math. Worked as a Assistant Professor for BBA, BCA, BSC(CS & IT), BE, etc. Also, experienced SME (Mathematics) with a demonstrated history of working in the internet industry. Provide the well explained detailed solutions in step-by-step format for different branches of US mathematics textbooks.