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# Forecasting

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• 1. 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.
• 2.
• 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
• Graphical method
• Algebric Method
• 3. 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.
• 4.
• 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 + 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
• 5. 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
• 6. 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
• 7.