FREEHAND OR GRAPHIC METHOD This is the simplest method of studying trend.

Steps for obtaining a straight line trend by this method are:

1. Plot the given time series on a graph paper.2. Examine the direction on the trend on the basis of

plotted points.3. Draw a straight line which well best fit to the data

according to personal judgement. This line given the direction of trend.

Following care should be taken in to consideration while fitting a trend line by free hand method.

1. Smoothing. It should be smooth to remove all the irregularities. It should be either a straight line or a combination of long gradual curves.

2. The sum of the vertical deviations from the trend of the annual observations above the trend should be equal to the sum of the vertical deviations from the annual trend of observations below the trend.

3. The sum of the squares of the vertical deviations of the observations from the trend should be as least as possible.

4. The trend should cut the cycles into halves in such a way that the areas above the trend equal those below the trend. This condition may not be always fulfilled but attempt should be made to meet this condition as much as possible.

Merits and Demerits of Free Hand Method Merits :1. It is the simplest method of measuring trend.2. It is very flexible.3. An experienced statistician who is familiar with the institutional

setting or economic history of the concern may well be able manually to fit a trend than the one which is set by using mathematical model.

Demerits:1. It is based on the personal judgement of the investigator.

Different persons may have different personal judgement and we may have different trend lines for the same set of the data.

2. Since it is highly subjective, it cannot be left to unexperirnced and untrained people.

3. It is a time consuming process.4. It cannot be used for future predications as it is based on

personal judgement.

METHOD OF SEMI AVERAGES

• In this method the given data is divided into two groups preferably with same number of year. After that, an arithmetic mean of each part is obtained. We then get two points are plotted at the midpoint of the class interval covered by their respective parts. Then the two points jointed by a straight line which gives us the required trend line.

Merits:1. It is simple to understand than the other models such as moving

averages method, method of least squares.2. It is an objective method. Everyone will get the same answer by

this method. Demerits:1. It always assumes the straight line relationship between the

plotted regardless of the fact whether that relationship exist or not.2. Since it is based on the arithmetic mean, limitations of the

arithmetic mean shall automatically apply.

MOVING AVERAGE METHOD

This method is used when seasonal variations and irregular variation are involved this method is generally used when length of the period is large. While applying this method a period of moving average is selected such as 3 yearly moving average 5 yearly moving average 4 yearly moving average etc.

Merits and Demerits of Moving Average Method Merits:• It is simple to understand and easy to compute.• It is a flexible method.• It is effective if the trend of the serious is irregular.• Cyclic fluctuations are automatically if the period of moving average

coincides with the period of cyclic fluctuations. Demerits : • Trend values cannot be computed for all the year. For example, in

5-year moving average, the trend values cannot be obtained for the first two and last two year.

• There is no fixed rule for selecting the period of moving average.• This method cannt be used in forecasting as it does not involve any

mathematical function.

METHOD OF LEAST SQUARES

This is a mathematical model to determine the trend. It is based on the following two conditions:

1. The sum of deviations of the actual vales of y