**Demerits:** The demerits of the free-hand method are as follows:

1. The main demerit of this method is that it is highly subjective. The results will depend very much on the judgment of the drawer of the line, hence subject to personal bias, mistakes, etc

2 Free-hand method of curve fitting, being subjective, has little value as a bias of projection for the future.

**Semi-Average Method – **In this method, the original data is divided into two equal parts, and averages are calculated for both parts. These averages are called semi-averages. For example, we can divide the 10 years, 1983 to 1992 into two equal parts; from 1983 to 1987 and from 1988 to 1992. If the period is an odd number of years, the value of the middle year is omitted. Say from 1983 to 1993 we omit the year 1988. We can draw the line as a straight line joining the two points of average. By extending the line downward or upward, we can get the intermediate values or we can predict the future values.

**Merits:** The merits of the semi-average method are as follows:

- It is simple and easier to understand the moving average and least square method.
- As the line can be extended both ways, we can get the intermediate values and predict the future values.

**Demerits:** The demerits of the semi-average method are as follows:

- Under this method, it has an assumption of a linear trend whether such a relationship exists or not.
- It is affected by the limitation of the arithmetic mean.

**Moving-Average Method**

The moving-average method is a simple method of reducing fluctuations and obtaining trend values with a fair degree of accuracy. In this method, the average value of a number of years (months, weeks, or days) is taken as the trend value for the middle point of the period of moving average. The process of averaging smoothens the prevailing fluctuations.

The first thing to be decided in this method is the period of the moving average. What it means is to make a decision about the number of consecutive items whose average would be calculated each time. Suppose it has been decided that the period of the moving average would be five years, months, weeks, or days (as the case may be) then the arithmetic average of the first 5 items (numbers 1, 2, 3, 4, and 5) would be placed against item number 3 and then the arithmetic average of item numbers 2, 3, 4, 5 and 6 would be placed against item number 4. This process would be repeated till the arithmetic average of the last 5 items has been calculated.

**Time Series Analysis MBA 1st Year Semester Long Question Answer Study Notes**

**Merits:** The merits of the moving average method are as follows:

- This method is used to measure trends, seasonal, cyclical, and irregular fluctuations.
- Moving average method is easy to apply as this method does not involve any difficult calculation.
- The choice of the period of moving average is made by observing the oscillatory movements in the data and not by the personal judgment of the statistician.

**Demerits:** The demerits of the moving average method are as follows:

- Some trend values present at the beginning and at the end of the series cannot be determined.
- This method cannot be used to forecast future trend values as the moving averages do not obey any law.
- This method may generate cycles or other movements, which were not present in the original data.

**1. Methods of Least Squares**

The method of least square is the most objective and widely used method in determining the trend in time series data. When the data are plotted on the graph paper, it will be seen that all the points will not lie on a curve and quite a large number of curves can be drawn, by inspection between the points. In order to find the best fitting curve to the data, the method of least square is followed. This method consists in finding the best fitting curve to the time series data as that curve, from all possible curves, is as follows:

- The sum of the vertical deviations of the actual (observed) values from the fitted curve is zero and,
- The sum of the squared vertical deviations is minimum, that is, no other curve would have a smaller sum of squared deviations. A graphical representation of the data is required to enable a decision to be made as the particular curve to be fitted.

**Merits:** The merits of the least-squares method are as follows:

- This method is completely objective in character and its subjectivity associated with the free-hand curve method is not found in it. There is no personal bias in its calculation.
- The equation of a straight line establishes a functional relationship between the X and Y series and as such can be used to forecast future values. This is not possible in the case of the moving average method.