@ Chapter 2 Forecasting Contents 1.Introduction 2.The Time Horizon in Forecasting 3.Classification of Forecasts 4.Evaluating Forecast 5.Notation Conventions 6.Methods for Forecasting Stationary Series 7.Trend-Based Methods 8.Methods for Seasonal Series
Chapter 2 Forecasting Contents 1. Introduction 2. The Time Horizon in Forecasting 3. Classification of Forecasts 4. Evaluating Forecast 5. Notation Conventions 6. Methods for Forecasting Stationary Series 7. Trend-Based Methods 8. Methods for Seasonal Series
2.3.Classification 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 -forecast data of future values of some economic or physical phenomenon is derived from a collection of their past observations
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 Methods -forecast of future values of some economic or physical phenomenon is derived from a collection of their past observations 2.3. Classification of Forecasts
2.3.Classification of Forecasts -Objective 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=f(X1,X2...,X). Econometric models are lineal casual models: Y=0+01X+02X2+..+0nXn, where a;(i=1~n)are constants
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. 2.3. Classification of Forecasts - Objective
2.3.Classification of Forecasts -Objective Causal Model The method of least squares is most commonly used for finding estimators of these constants. Assume we have the past data (xi,y),i=1~n;and the causal model is simplified as Y=a+bX.Define g(a,b)=∑y-(a+bx,)P i=l as the sum of the squares of the distances from line a+bX to data points yi
Causal Model The method of least squares is most commonly used for finding estimators of these constants. Assume we have the past data (xi, yi), i=1~n; and the causal model is simplified 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. 2.3. Classification of Forecasts - Objective
2.3.Classification of Forecasts -Objective Causal Model We may choose a and b to minimize(y(+ by letting 0g =0 Ba →22[y-(a+bx】-0a=2y-bx]=-饭 n i=1 .- 6 =0 →2[y-a+x小()-0 →b=L i=1 x-x∑x i=1 i=1
Causal Model 2 1 ( , ) [ ( )] n i i i g a b y a bx We may choose a and b to minimize by letting 0 g a 1 2 0 n i i i y a bx 1 0 n i ii i 0 y a bx x gb 2.3. Classification of Forecasts - Objective 1 1 2 1 1 n n ii i i i n n i i i i x yyx b x x x 1 1 n i i i a y bx y bx n