Quantitative TechniquesThese are forecasting techniques that make use of historical quantitativedata. 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 predicteddemand in the forecast period.So these quantitative techniques are also know as statistical methods.

Trends Projection Methods:-

This technique assumes that whatever has been the pattern of demand in the past, will continue to hold good in the future as well. Historical Data can thus be used to predict the demand for a commodity in he future. Future demand through the trend method can be found by either of the two methods

1. Graphical method2. Algebric Method

Graphical method

In this method the past data will be plotted on a graph and the identified trend will be extended further in the same pattern to ascertain the demand in the forecast period.

Algebraic Method

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 + cX2

• Cubic trend : Y = a + bX+ cX2 + dX3

• Exponential trend : Y = aeb/x

• Double log trend : Y = aXb

The linear trend is the most widely used mode of time series analysis.It is represented by

Y = a =bXY = demandX = 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 ЄY = na + bЄX ЄXY = aЄX + bЄX2

Eg:- The following data relate to the sale of watches of a company over the last five year.Years 1996 1997 1998 1999 2000No 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 methodis employed here to calculate the future demand.

Let the base year be 1995.

Year X Y X2 Y2 XY1996 1 120 1 14400 1201997 2 130 4 16900 2601998 3 150 9 22500 4501999 4 140 16 19600 5602000 5 160 25 25600 800Total 15 700 55 99000 2190

For a linear equation Y = a + bX (1)

The set of normal equations are ЄY = na + bЄX (2)

ЄXY = aЄX + bЄX2 (3)

Substituting the table values in eq. (2) and (3), we get700 = 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 have700 = 5a + 15x95a = 565a = 113

Thus, the trend equation is Y = 113 + 9X

Since for the year 2005, X will be 10Y2005 = 113 + 9 x 10 = 203 watches

Advantages :-• It is a very simple method.• It is quick and inexpensive.

Disadvantages :-• It can be used only if past data is available• 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 relationshipbetween economic variables for predicting the directional changes in the concerned variables are known as Barometric Techniques. Thesetechniques require ascertaining the lead-lag relationship between two seriesand then keeping a track of the movement of the leading indicator.

Thus, there is always some time series which is closely correlated witha 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 alongwith 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 secondseries moves behind the first series. The series are called coincident series ifboth 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.