FORECASTING. FORECASTING TECHNIQUES l QUALITATIVE AND QUANTITATIVE l ECONOMETRIC OR REGRESSION ANALYSIS l SIMULTANEOUS EQUATION SETS l TIME SERIES ANALYSIS.

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Presentation transcript:

FORECASTING

FORECASTING TECHNIQUES l QUALITATIVE AND QUANTITATIVE l ECONOMETRIC OR REGRESSION ANALYSIS l SIMULTANEOUS EQUATION SETS l TIME SERIES ANALYSIS –TIME SERIES DECOMPOSITION –EXPONENTIAL SMOOTHING l BAROMETRIC FORECASTING –FORECASTS OF BUSINESS CYCLE TURNING POINTS –USE OF DIFFUSION INDICES l INPUT / OUTPUT ANALYSIS

QUALITATIVE FORECASTINGQUALITATIVE FORECASTING l lEXPERT OPINION l lSURVEYS l lMARKET EXPERIMENTS l lBOEING SURVEY

FORECASTING WITH REGRESSION EQUATIONS l l SINGLE EQUATION MODELS l l MULTIPLE EQUATION SYSTEMS l l SOLUTION WITH A MATRIX ALGORITHM l l MATRIX OPERATIONS ( INVERSION and MULTIPLICATION ) WITHIN THE QUATTRO SPREADSHEET

TIME SERIES DECOMPOSITION l THE MODEL : Q = T x S x C x I l WHERE: Q = DEPENDENT VARIABLE l l T = TREND VARIABLE l l S = SEASONAL VARIABLE l l C = CYCLICAL VARIABLE l l I = IRREGULAR VARIABLE l l A MULTIPLICATIVE MODEL

EXAMPLE OF THE SOLUTION OF A TIME SERIES DECOMPOSITION PROBLEM TREND VARIABLE IS A REGRESSION OF A DATA SET WITH POINTS MADE UP BY A MOVING AVERAGE CYCLICAL INDEX ( BUSINESS CYCLE ) = 1.04 SEASONAL INDEX = TIME INDEX = 16 CMAT = TIME FORECAST = x x 1.04 = TREND SEASONAL CYCLE = FORECAST FOR , FROM PROBLEM SET, NUMBER 2

SPECIFICATION ERROR IN ECONOMETRIC FORECAST Y X FORECAST OF Y AS A LINEAR FUNCTION OF X EQUATION FORM Y = A + BY DATA RANGE FOR REGRESSION 0 FORECAST RANGE FORECAST ERROR REGRESSION LINE ACTUAL RELATIONSHIP LINEAR

BAROMETRIC FORECASTING l USE OF ECONOMIC “SYMPTOMS” THAT INDICATE CHANGE l l BUSINESS CYCLE INDICATORS –LEADING –COINCIDENT –LAGGING l DIFFUSION INDEX OF INDICATORS

BUSINESS CYCLE TURNING POINTS (BAROMETRIC) GDP TIME TREND PEAK TROUGH (LR AVERAGE RATE OF INCREASE) LEADING INDICATOR TIME 6 TO 9 MONTHS PEAK

EXAMPLE OF THE SOLUTION OF A SIMULTANEOUS EQUATION SYSTEM 2.) C = Y 3.) I = Y *1.) Y = C + I + G 4.) G = 10 * = DEFINITIONAL Y = Y Y + 10 Y = Y Y =

MATRIX SOLUTION OF SIMULTANEOUS EQUATIONS Y = C + I + G C + I + G - Y = 0 C = Y C -.6Y = 40 I = 8 +.1Y I -.1Y = 8 G = 10 MATRIX OF COEFFICIENTS: Y C I G RHS A MATRIXB IN QUATTRO, INVERT THE A AND MULTIPLY BY THE B VECTOR TO SOLVE ALL UNKNOWNS A B = X

INPUT / OUTPUT ANALYSIS l PURPOSE AND APPLICATION l STRUCTURE l SOLUTION l INTERPRETATION OF RESULTS

EXAMPLE: INPUT / OUTPUT PROBLEM FLOW MATRIX MATRIX OF DIRECT COEFFICIENTS STEPS : SEE HANDOUT FOR NUMERICAL OPERATIONS LEONTIEF MATRIX MATRIX OF TOTAL COEFFICIENTS ORDER OF MATRIX DEVELOPMENT:

INPUT / OUTPUT CONTINUED INTERPRETATION OF INPUT / OUTPUT ANALYSIS: FOR A SYSTEM OF RELATED INPUTS AND OUTPUTS, THE MATRIX OF TOTAL COEFFICIENTS SHOWS HOW A CHANGE IN FINAL DEMAND CAUSES ALL INPUTS TO CHANGE, AND BY HOW MUCH

CRITERION FOR EVALUATION OF FORECASTS l CHOICE OF THE “BEST” MODEL l MUST BE “AFTER THE FACT” BECAUSE ACTUAL AND FORECAST DATA ARE REQUIRED l STATISTICAL MEASUREMENT IS THE “ROOT MEAN SQUARED ERROR”