Measurement of Trend: Graphical (Freehand Curve) Method

The simplest way to show the trend of a time series is to draw it. In the graphical (freehand curve) method we plot the given values against time and then draw a smooth curve or straight line, by hand and by eye, that passes through the middle of the plotted points — smoothing out the short-term seasonal, cyclical and irregular ups and downs and leaving only the long-term movement.

Steps.

1. Take time (years) on the horizontal $X$-axis and the values of the variable on the vertical $Y$-axis, choosing suitable scales.
2. Plot each observation $(t_i, y_i)$ as a point and join the points to obtain the actual (historigram) curve.
3. Draw a smooth freehand curve — or a straight line — through the general middle of these points, so that it lies as evenly as possible among them (roughly as many points above the line as below).
4. This smooth freehand curve is the trend.