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FORECASTING

FORECASTING. FORECASTING TECHNIQUES. QUALITATIVE AND QUANTITATIVE ECONOMETRIC OR REGRESSION ANALYSIS SIMULTANEOUS EQUATION SETS TIME SERIES ANALYSIS TIME SERIES DECOMPOSITION EXPONENTIAL SMOOTHING BAROMETRIC FORECASTING FORECASTS OF BUSINESS CYCLE TURNING POINTS

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FORECASTING

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  1. FORECASTING

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

  3. QUALITATIVE FORECASTING • EXPERT OPINION • SURVEYS • MARKET EXPERIMENTS • BOEING SURVEY

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

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

  6. 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 CMAT = 8.7 + .454 TIME TIME INDEX = 16 SEASONAL INDEX = 1.234 CYCLICAL INDEX ( BUSINESS CYCLE ) = 1.04 FORECAST = 15.964 x 1.234 x 1.04 = 20.49 TREND SEASONAL CYCLE = FORECAST FOR 1990.1, FROM PROBLEM SET, NUMBER 2

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

  8. BAROMETRIC FORECASTING • USE OF ECONOMIC “SYMPTOMS” THAT INDICATE CHANGE • BUSINESS CYCLE INDICATORS • LEADING • COINCIDENT • LAGGING • DIFFUSION INDEX OF INDICATORS

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

  10. EXAMPLE OF THE SOLUTION OF A SIMULTANEOUS EQUATION SYSTEM *1.) Y = C + I + G * = DEFINITIONAL 2.) C = 40 + .6 Y 3.) I = 8 + .1 Y 4.) G = 10 Y = 40 + .6Y + 8 + .1Y + 10 Y = 58 + .7Y Y = 193.333

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

  12. INPUT / OUTPUT ANALYSIS • PURPOSE AND APPLICATION • STRUCTURE • SOLUTION • INTERPRETATION OF RESULTS

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

  14. 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

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

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