In continuation of our posts on ‘Time Series’, today we will discuss how trends are measured and give you an example of the graphic model used to measure trends.
In the first post on Time Series, Introduction to Time Series Analysis, we discussed that “Trend” is the tendency. The reasons for the measurement of Trend, is to study the behaviour of the variable in the long run. This study is only possible when the Time Series is devoid of all the other components.
Trend is also measured to study the regular or irregular variation, which is possible only when Trend values are isolated.
We can measure trend with the help of any of the following methods:
a> Graphic model
b> Semi-average method
c> Moving average method
d> Curve- fitting by method of least squares
Let’s discuss the graphic method first.
Amongst the four, this is the simplest. Reason?
It is free from mathematical calculations!
Initially points are to be plotted on a graph paper. On the horizontal axis, year marks are to be plotted, and on the vertical axis, data is plotted. Then simply by inspection a line is to be drawn so that the fluctuations on one direction become approximately equal to those on the other direction. This trend line needs to be drawn with utmost care, so that the following conditions get fulfilled:
i. It should be smooth
ii. The sum of the vertical deviations from the trend line of the points above the line should be more or less equal to the sum of the vertical deviations of the points below the line.
iii. Sum of the squares of the vertical deviations of all points from the trend line should be minimum.
We will now use an example.
This is a small data of the number of eggs sold by a poultry-merchant in a year, month-wise.
We will now plot this data in a graph:
A vertical line going through the zigzag curve makes the diagram complete.
Now, we will discuss the merits and demerits of this method.
a> As stated earlier, this method is simple and needs no mathematical calculations.
b> For an experienced statistician, it is a time-saving method. He can easily set the line at a glance.
a> For beginners it is difficult to draw the line with eye estimation.
b> It is crude and subjective method. It depends purely on the judgement of the statistician.
c> Further prediction may be far from the proper estimate as it is fully dependent on eye estimation.
d> It requires a lot of experience and expertise to draw the line.
In our next few article on Time Series, we will describe the other methods used to measure trend.