assification of Forecasts Sales force composites; .Customer surveys Subjective-based on human Jury of executive opinion; judgment .The Delphi method; Causal Models-the forecast for a phenomenon is some function Objective-derived of some variables from analysis of .Time Series Methods- data forecast of future values of some economic or physical phenomenon is derived from a collection of their past observations
Classification of Forecasts Subjective-based on human judgment Objective-derived from analysis of data •Sales force composites; •Customer surveys •Jury of executive opinion; •The Delphi method; •Causal Models-the forecast for a phenomenon is some function of some variables •Time Series Methodsforecast of future values of some economic or physical phenomenon is derived from a collection of their past observations
Objective Forecasting Methods Causal Model Let Y-the phenomenon needed to be forecasted;numbers of house sales) X1,X2,...,X (interest rate of mortgage )are variables supposed to be related to Y .Then,the general casual model is as follows: Y=fX1,X2,…,Xn). .Econometric models are lineal casual models: Y=0+01X1+02X2+..+0nXn2 where a;(i=1~n)are constants. .The method of least squares is most commonly used for finding estimators of these constants
Objective Forecasting Methods Causal Model •Let Y-the phenomenon needed to be forecasted;( numbers of house sales) X1 , X2 , …, Xn (interest rate of mortgage )are variables supposed to be related to Y •Then, the general casual model is as follows: Y=f(X1 , X2 , …, Xn ). •Econometric models are lineal casual models: Y=0+ 1X1+ 2X2+…+ nXn,, where i (i=1~n) are constants. •The method of least squares is most commonly used for finding estimators of these constants
Objective Forecasting Methods Causal Model Assume we have the past data (xi,yi),i=1~n;and the the causal model is simply as Y=a+bX.Define g(a,b)=∑y-(a+bx,J i=1 as the sum of the squares of the distances from line a+bX to data points yi.We may choose a and b to minimize g,by letting 0g 22[y-(a+bx)]=0→a=2[y-x]=-b饭 =0 i ba xy-∑x 0 →∑[y-(a+bx)](-x)=0→b= i=l ab ∑x-x∑x i=l i=l
Objective Forecasting Methods Causal Model Assume we have the past data (xi , yi ), i=1~n; and the the causal model is simply as Y=a+bX. Define 2 1 ( , ) [ ( )] n i i i g a b y a bx as the sum of the squares of the distances from line a+bX to data points yi . We may choose a and b to minimize g, by letting 0 g a 1 1 1 2 0 n n i i i i i i y a bx a y bx y bx n 1 1 1 2 1 1 0 n n n i i i i i i i i n n i i i i i x y y x y a bx x b x x x 0 g b
Objective Forecasting Methods Causal Model g(a,b)=∑y-(a+bx)]P i=1 o =0 a=y-bx Ba =0 ab ∑xy-∑xn∑xy-∑x S b=i= 1= 1= i=l -x22-版2x i=1 i=1 i=l i=l xy 2xy-立x2:S。=n2x-∑x) =1 X= n
Objective Forecasting Methods Causal Model 2 1 ( , ) [ ( )] n i i i g a b y a bx 0 g a a y bx 1 1 1 1 2 2 1 1 1 1 n n n n i i i i i i i i i i xy n n n n xx i i i i i i i i x y y x n x y ny x S b S x x x n x nx x 0 g b 2 2 ; ( ) n n n n n xy i i i i xx i i i i i i i S n x y x y S n x x 1 1 ; ; n n i i i i x x y y n n
Objective Forecasting Methods Time Series Methods- .The idea is that information can be inferred from the pattern of past observations and can be used to forecast future values of the series. .Try to isolate the following patterns that arise most often. -Trend-the tendency of a time series,usually a stable growth or decline,either linear (a line)or nonlinear (described as nonlinear function,e.g.a quadratic or exponential curve) -Seasonality-Variation of a series related to seasonal changes and repeated every season. -Cycles-Cyclic variation similar to seasonality,except that the length and the magnitude may change,usually associated with economic variation. Randomness-No recognizable pattern to the data
Objective Forecasting Methods Time Series Methods- •The idea is that information can be inferred from the pattern of past observations and can be used to forecast future values of the series. •Try to isolate the following patterns that arise most often. Trend-the tendency of a time series, usually a stable growth or decline, either linear (a line) or nonlinear (described as nonlinear function, e. g. a quadratic or exponential curve) Seasonality-Variation of a series related to seasonal changes and repeated every season. Cycles-Cyclic variation similar to seasonality, except that the length and the magnitude may change, usually associated with economic variation. Randomness-No recognizable pattern to the data