Quantitative Techniques These are forecasting techniques that make use of historical quantitative data. A statistical concept is applied to this existing data about the dema- nd for a commodity over the past years in order to generate the predicted demand in the forecast period. So these quantitative techniques are also know as statistical methods.
In this the demand and time data are fitted into a mathematical equation. The most common equations are
Linear trend : Y = a + bx
Quadratic trend : Y = a + bx + cX 2
Cubic trend : Y = a + bX+ cX 2 + dX 3
Exponential trend : Y = ae b/x
Double log trend : Y = aX b
The linear trend is the most widely used mode of time series analysis.
It is represented by
Y = a =bX
Y = demand
X = time period ( no of years )
a,b are constant representing respectively the intercept and slope of line.
The calculation of Y for any value of X requires are to be solved. These are
Є Y = na + b Є X
Є XY = a Є X + b Є X 2
Eg:- The following data relate to the sale of watches of a company over the last five year. Years 1996 1997 1998 1999 2000 No of watches 120 130 150 140 160 Estimate the demand for generators in the year 2005, if the present trend is to Continue. Sol:- Since the present trend is expected to continue, the least square method is employed here to calculate the future demand. Let the base year be 1995. Year X Y X 2 Y 2 XY 1996 1 120 1 14400 120 1997 2 130 4 16900 260 1998 3 150 9 22500 450 1999 4 140 16 19600 560 2000 5 160 25 25600 800 Total 15 700 55 99000 2190
For a linear equation Y = a + bX (1) The set of normal equations are Є Y = na + b Є X (2) Є XY = a Є X + b Є X 2 (3) Substituting the table values in eq. (2) and (3), we get 700 = 5a + 15b (4) 2190 = 15a + 55b (5) Solving the set of simultaneous equations by multiplying equation (4) by 3 and then subtracting it from equation (5), we get 10b = 90 b = 9 Substituting this value of b in equation (4),we have 700 = 5a + 15 x 9 5a = 565 a = 113 Thus, the trend equation is Y = 113 + 9X Since for the year 2005, X will be 10 Y 2005 = 113 + 9 x 10 = 203 watches
It is not necessary that past trends may continue to
hold good in the future as well.
Barometric Techniques:- Forecasting techniques that use the lead and lag relationship between economic variables for predicting the directional changes in the concerned variables are known as Barometric Techniques. These techniques require ascertaining the lead-lag relationship between two series and then keeping a track of the movement of the leading indicator. Thus, there is always some time series which is closely correlated with a given time series. This correlation between two time series can be of three types. Either the second series data and move ahead or move behind or move along with the first series data. Accordingly, when the second series moves ahead of the first series, the second series is known as the leading series while the first series is called the lagging series . The opposite holds true when the second series moves behind the first series. The series are called coincident series if both of them moves along with each other.
Advantages:- 1. It is a simple method. 2. It predicts directional changes quite accurately . Disadvantages:- 1. It does not predict the magnitude of changes very well. 2. The method can be used for short-tern forecasts only.