MathematicalForecasting_Box-Jenkins.doc

MathematicalForecasting_Box-Jenkins.doc - MATHEMATICAL...

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MATHEMATICAL FORECASTING USING THE BOX-JENKINS METHODOLOGY TECHNICAL BRIEFING JOSEPH GEORGE CALDWELL, PHD © 2007 JOSEPH GEORGE CALDWELL. ALL RIGHTS RESERVED. POSTED AT INTERNET WEBSITES AND . MAY BE COPIED OR REPOSTED FOR NONCOMMERCIAL USE, WITH ATTRIBUTION. Note: The document The Box-Jenkins Forecasting Technique , posted at , presents a nontechnical description of the Box-Jenkins methodology. For a technical description of the Box-Jenkins approach, see the document, TIMES Box-Jenkins Forecasting System , posted at . A computer program that can be used to develop a broad class of Box-Jenkins models is posted at the Foundation website, (6 February 2009). 1
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BRIEFING ROAD MAP 1. MATHEMATICAL FORECASTING CONCEPTS (20-30 MINUTES) 2. TECHNICAL INTRODUCTION TO THE BOX-JENKINS METHODOLOGY (20-30) 3. FORECASTING ACCURACY COMPARISONS (5-10) 4. MODEL BUILDING WITH THE BOX-JENKINS METHODOLOGY (40-60) 5. APPLICATION TO ECONOMETRIC AND CONTROL PROBLEMS (10-15) 2
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1. MATHEMATICAL FORECASTING CONCEPTS 3
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MATHEMATICAL FORECASTING METHODOLOGY (“FORECASTER”) BASED ON A MATHEMATICAL MODEL OF THE PROCESS TWO APPROACHES MODEL FITTING (INTUITIVE, HEURISTIC) MODEL BUILDING (THEORETICAL FOUNDATION) 4
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HEURISTIC FORECASTERS A PARTICULAR MODEL IS FITTED TO DATA EXAMPLES: MOVING AVERAGE EXPONENTIAL SMOOTHING TRENDS, CURVES, HARMONICS, PATTERNS GOOD FIT → GOOD FORECAST? GOOD MODEL → GOOD FORECAST NEED TO BUILD A GOOD MODEL 5
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MODEL BUILDING CHOOSE A COMPREHENSIVE CLASS OF MODELS IDENTIFICATION FITTING DIAGNOSTIC CHECKING REPEAT UNTIL ADEQUATE MODEL CONSTRUCTED 6
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CLASSES OF MODELS (FOR PREDICTION AND CONTROL) ECONOMETRIC MODELS DYNAMIC CAUSAL MODEL (MANY VARIABLES) ECONOMIC THEORY EXAMPLE: MODEL OF THE ECONOMY USUAL METHODOLOGY: ECONOMETRICS (E.G., MULTIPLE REGRESSION ANALYSIS, TWO-STAGE LEAST SQUARES) PHYSICAL MODELS DYNAMIC CAUSAL MODEL (EQUATIONS OF MOTION) PHYSICS EXAMPLE: RADAR TRACKING OF A MISSILE USUAL METHODOLOGY: KALMAN FILTERING PURELY STOCHASTIC MODELS (UNIVARIATE, NO EXOGENOUS VARIABLES) DESCRIBE STOCHASTIC BEHAVIOR TIME SERIES ANALYSIS (EMPIRICAL: NO UNDERLYING ECONOMIC OR PHYSICAL MODEL) EXAMPLE: FORECASTING PRODUCT DEMAND USUAL METHODOLOGY: BOX-JENKINS (ARIMA) METHODOLOGY COMBINATION DYNAMIC-STOCHASTIC MODELS FEW VARIABLES (BUT MORE THAN ONE) SIMPLE (EMPIRICAL) MODEL OF RELATIONSHIP EXAMPLES: TRANSFER-FUNCTION MODEL, FUEL-MIXTURE CONTROL USUAL METHODOLOGY: BOX-JENKINS; KALMAN FILTERING, “STATE-SPACE” MODELS 7
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FORECASTING ACCURACY STOCHASTIC VS. HEURISTIC FORECAST ERROR VARIANCE LEAD TIME 1 2 3 4 5 6 7 8 9 10 MSE (BROWN) 102 158 218 256 363 452 554 669 799 944 MSE(B-J) 42 91 136 180 222 266 317 371 427 483 ECONOMETRIC VS. STOCHASTIC THEIL COEFFICIENT MODEL PRICE QUANTITY ECONOMETRIC 0.80 0.65 BOX-JENKINS 1.00 0.70 RANDOM WALK 1.00 1.00 MEAN 18.23 0.96 8
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FORECASTING DIFFICULTY STOCHASTIC MODEL
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