Freehand Curve Method of measuring Secular Trends in Time Series

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:

Freehand Curve Method of measuring Secular Trends in Time Series

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.

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