MEASUREMENT OF TREND COMPONENT OF A TIME SERIES

A time series is a set of observations recorded at successive intervals of time. The simplest and more commonly employed methods to measure Trend Component of a Time Series are: 

1.      Graphic or Free hand Method:   First of all the data is plotted on a graph paper and the trend line is fitted by a line or a freehand curve by just inspecting and following the graph of the series.  The curve need to be smooth and with almost equal number of points above and below it.  By eye estimate, the sum of the vertical deviations of the given points above the trend line should approximately equal to the sum of the vertical deviations of the given points below the trend line. Also the sum of the squares of the vertical deviations of the given points from the trend line should be minimum possible. 

2.      Moving Average Method:  This method comprise of taking arithmetic means of the data/values for a certain span and then placing the value so calculated against the middle of the time span.  The time span should be equal to the average fluctuation period.  If this span is of period k, then the moving averages obtained by averaging k at a time are called Moving Averages of period or extent k.   If k is even, the successive values of moving averages are placed in the center/middle of the period/span of time.