FORECASTING

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FORECASTING
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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

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QUALITATIVE FORECASTING

• EXPERT OPINION
• SURVEYS
• MARKET EXPERIMENTS
• BOEING SURVEY

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FORECASTING WITH REGRESSION EQUATIONS

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

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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

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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
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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
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BAROMETRIC FORECASTING

• USE OF ECONOMIC SYMPTOMS THAT INDICATE
  CHANGE
• BUSINESS CYCLE INDICATORS
• LEADING
• COINCIDENT
• LAGGING
• DIFFUSION INDEX OF INDICATORS

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

• PURPOSE AND APPLICATION
• STRUCTURE
• SOLUTION
• INTERPRETATION OF RESULTS

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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
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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
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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