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# lect4 - Demand Forecasting II Causal Analysis Chris Caplice...

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Demand Forecasting II Causal Analysis Chris Caplice ESD.260/15.770/1.260 Logistics Systems Sept 2006

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© Chris Caplice, MIT 2 MIT Center for Transportation & Logistics – ESD.260 Agenda Forecasting Evaluation Use of Causal Models in Forecasting Approach and Methods ± Ordinary Least Squares (OLS) Regression ± Other Approaches Closing Comments on Forecasting
© Chris Caplice, MIT 3 MIT Center for Transportation & Logistics – ESD.260 Forecast Evaluation How do we determine what is a good forecast? ± Accuracy - Closeness to actual observations ± Bias - Persistent tendency to over or under predict ± Fit versus Forecast – Tradeoff between accuracy to past forecast to usefulness of predictability ± Forecast Optimality – Error is equal to the random noise distribution Combination of art and science ± Statistically – find a valid model ± Art – find a model that makes sense

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© Chris Caplice, MIT 4 MIT Center for Transportation & Logistics – ESD.260 Accuracy and Bias Measures 1. Forecast Error: e t = x t - ̂ x t 2. Mean Deviation: 3. Mean Absolute Deviation 4. Mean Squared Error: 5. Root Mean Squared Error: 6. Mean Percent Error: 7. Mean Absolute Percent Error: 1 n t t e MD n = = 1 n t t e MAD n = = 1 n t t t e D MPE n = = 2 1 n t t e MSE n = = 1 n t t t e D MAPE n = = 2 1 n t t e RMSE n = =
© Chris Caplice, MIT 5 MIT Center for Transportation & Logistics – ESD.260 108.00 109.00 110.00 111.00 112.00 113.00 114.00 115.00 116.00 - 20.00 40.00 60.00 80.00 100.00 120.00 MA3 MA10 MA20 ActDemand M A 3M A 1 0M A 2 0 MD 0.05 0.21 0.35 MAD 0.56 1.07 1.41 MSE 0.47 1.67 2.71 RMSE 0.68 1.29 1.65 MAPE 0.50% 0.96% 1.27% Moving Average Forecasts

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© Chris Caplice, MIT 6 MIT Center for Transportation & Logistics – ESD.260 Analysis of the Forecast Are the forecast errors ~N(0,Var(e))? ± For Moving Averages: ² What is the expected value of the errors? ² What is the variance of the errors? ± From actual observations, ² Are the observed errors ~N(0,Var(e))? ² For the MA3 data ± μ e = 0.05 ± σ e = 0.69 ± σ D = 1.478 ² Testing for Normalcy – Chi-Square, Kolmogorov-Smirnov, or other tests 0 5 10 15 20 25 ( 1. 4 0) 1 .1 (0. 7 9) 0 .4 0. 12 42 0.72 1.03 1.33 M o re error Frequency Errors (2.00) (1.50) (1.00) (0.50) - 0.50 1.00 1.50 2.00 - 2 04 06 08 01 0 0 1 2 0
© Chris Caplice, MIT 7 MIT Center for Transportation & Logistics – ESD.260 Corrective Actions to Forecasts Measures of Bias ± Cumulative Sum of Errors (C t ) ² Normalize by dividing by RMSE (U t ) ² U t should ~0 if unbiased ± Smoothed Error Tracking Signal (T t ) ² T t =z t /MAD t ² Where z t = ω e t + (1- ω )z t-1 (smoothing constant) ± Autocorrelation of forecast Errors ² Correlation between successive observations Corrective Actions ±

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lect4 - Demand Forecasting II Causal Analysis Chris Caplice...

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