SKEDSOFT

Measurement of Secular Trend:

Trends are measured by the following methods:

1. Free hand graphic method

2. Method of semi averages

3. Method of moving averages

4. Method of least squares.

Method of Semi Averages:

The methods of fitting a linear trend with the help of semi-average method are as follows:

1. The number of years is even: The data of the time series are divided into two equal parts. The total of the items in each as the part is done and it is then divided by the number of items to obtain arithmetic means of the each part. Each average is then plotted at mid-point of the interval from which it has been computed. A straight line is drawn passing through these points. This is the required trend line.

2. The number of years is odd: When the number of years is odd, the value of the middle year is omitted to divide the time series into equal parts. Then follow the same procedure as for even numbers.Mathematical form of the trend line. The straight line passing through the two points (t₁ − y₁) and (t₂ − y₂),

Method of Moving Average:

To determine trend with the following steps is called the method of moving averages:

1. We take the first m consecutive values of the series and calculate these average, m is a number to be decided by us and is called the time-interval or period for computing the moving average. This average is taken as the trend value for the time failing at the middle of the period covered in the computation of average. When the time id odd it is all right. But when the time period is even, the moving average fall mid way between the two observations, because the mid term will not coincide with a point of the series. To avoid this difficulty we calculate further twoitem moving averages so that the mid-points now may coincide with the given time periods. This process is known as centering of the moving averages.

2. We drop the first observation in the series and include the (m 1)th observation and calculate their average and place it at the middle of the period covering second to (m 1)th values.

3. Now leave the first two values and include the (m 1)th value and calculate their average and place it a the middle of the period covering third to (m 2)th values. This process will go on till the and of the series. Symbolically, suppose the time series is given

4. Time:

Let m = 3 (Odd case), then

First moving average;

Second moving average;

Third moving average;

The quantities v₁, v₂, v_3, .. etc are called 3-yearly moving average. Now again let m = 4 (Even case)

First moving average v₁ = y₁ y₂ y₃ y₄/4 against t₂.

Second moving average v₂ = y₂ y₃ y₄ y₅/4 against t₂.

Third moving average v₃ = y₃ y₄ y₅ y₆ /4 against t_2.