Mostly trend is used forecasting in practice. There are many methods to determine trend. Some of the methods are: (a) Graphical method, (b) Least square method, (c) Moving average method.
(a) Graphical Method : In this method the period is taken on x- axis and the corresponding sales values on y-axis and the points are plotted for given data on graph paper. Then a free hand curve passing through most of the plotted points is drawn. This curve can be used to forecast the values of future.
It is an approximate method as the shape of the curve mainly depends on the choice of scale for the graph and the individual who draws the free hand curve.
(b) Least Squares Method : This is one of the best methods to determine trend. In most cases, we try to fit a straight line to the given data. The line is known as “Line of best fit” as we try to machine the sum of the squares of deviation between the observed and the fitted values of the data.
The basic assumption here is that the relationship between the various factors remains unchanged in future period also.
Let y denote the demands and x the period for a certain commodity. Then the linear relationship between y and x is given by y = a + ox; the nature of the relationship is determined by the values of a and o. The values of a and o can be estimated with the help of the past information about y and x. If x and y denote the deviations x and y from their respective means, then the least squares estimates of a and o are given by
â=∑y/n
ô=∑xy/∑x² where n is the number of observation. The calculation of ∑y, ∑xy and ∑x² can be done with the help of given data on y and x and using the statistical steps.
Advantages of least squares method
(i) There is no need to conduct any sample survey as only past information about sales is required.
(ii) This method is simple and easy to understand.
(iii) Under normal situations the method is likely to give reliable and accurate results.
Disadvantages of least squares method
(i) the method is based on some mathematical formulae which may not be understood by common man.
(ii) the assumption that other things remaining constant may not hold good in practice.
(c) Method of Moving Averages : This method can be used to determine the trend values for given data without going into complex mathematical calculations. The calculations are based on some predetermined period in weeks, months, years etc. The period depends on the nature of characteristics in the time series and can be determined by plotting the observations on graph paper.
A moving average of some fixed or predetermined number of observations (given by the period) which moves through the series by dropping the top item of the previous averaged group and adding the next item below in each successive average. The calculation depends upon the period to be old or even. In the case of odd order periods (3,5,7,…) the average of the observations is calculated for the given period and the calculated value is written in front of central value of the period, e.g. for a period of 5 years, the average of the values of five years is calculated and is recorded against the third year. Thus in case of five yearly moving averages, first two years and last two year of the data will not have any average value.
If period of observations is even e.g. four years, then the average of the four yearly observations is written between second and 3rd year values. After this centring is done by finding the average of the period values. The even order periods creates the problem of centring between the periods. Due to this generally odd order periods are preferred.
Merits of moving average method
(i) The method is simple easy to apply in practice,
(ii) It is based on mathematical calculations.
(iii) More accurate than graphical method.
Demerits of moving average method
(i) Choice of period of moving average is difficult.
(ii) cannot be applied if some observations are missing.
(iii) Some trend values for the periods in the beginning as well as in the end cannot be determined.
(iv) When the period of the moving average coincides with the periodicity in the data, if any, then the trend values may not be representative.
4. Association with other events : The sale of any commodity does not depend on time only but there are some other economic factors viz. change in population, income, size of the families tastes of the consumer, environment etc. which can affect the demand of a product. The nature of relationship between these factors and the sales can be used to forecast future sales. Assuming the relationship to be linear, the regression of Y on X can be defined as a + bX, a and b can be estimated by least square methods or regression method.
The following are the various steps in the method
(i) Verify whether there exists any relation between the demand of the product and the corresponding economic indicator or not.
(ii) if the relationship exists, then assuming the relationship to be linear, estimate the equation Y = a+bX by least square method or find the regression equation of Yon X.
(iii) It is not necessary that the same relationship as in past may hold good in future also. Thus there is a need of proper judgement and consideration of new factors as well.
The technique appears to be easy and simple to apply in practice. But it is difficult to select the appropriate economic indicator which can affect the sales. The method requires specialized skill and in some situation there may be a necessity of change the economic indicator of past data due to changes in fashion, nature and customs.
