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Unformatted text preview: Operations Management DS 412 Forecasting Part II Recap: Methods for forecasting time series with level pattern Moving averages Must determine n Larger n smoothes out more the randomness Get nave forecast when n=1 Weighted moving averages Must determine n and the weights Typically, larger weights are given to more recent data Sum of weights must equal 1 Exponential smoothing Must choose alpha the smoothing constant Smaller alpha smoothes more, larger alpha gives forecasts that react more closely to changes in data. Outline of Forecasting Part II 1. Discuss error measurements. 2. Learn methods to forecast time series with trend pattern and show how it can be done in Excel. 3. Learn methods to forecast time series with seasonality and show how it can be done in Excel. 4. Learn how to monitor the forecasts (optional). Accuracy of Forecasts and Model Validation Forecast error in period t is the difference between the actual observation and the forecast: Et = At Ft ( or Et = Yt Ft ) We use the notation At or Yt to refer to actual data in period t Error measurements tell us: if forecasts are over/understated? how far off are forecasts from actual? Smaller errors imply better accuracy What criteria can we use to measure errors? Error Measurements BIAS = Average error Mean Absolute Deviation ( MAD ) Average distance Mean squared error ( MSE ) Similar to average of squared error SE = n F A MAD t t  = n A t F t A MAPE t  = ( 29 1 2 = n F A MSE t t ( 29 n F A BIAS t t  = MSE In the forecasting context, it is common to compute MSE dividing by n instead of by n1 Error Measurements for MA(n=3) Month Actual MA n=3 Error AbsErr (Err)^2 %AbsErr 1 70 2 45 3 72 4 54 62.338.33 8.33 69.44 0.15 5 80 57.00 23.00 23.00 529.00 0.29 6 66 68.672.67 2.67 7.11 0.04 7 35 66.67 31.67 31.67 1002.78 0.90 8 82 60.33 21.67 21.67 469.44 0.26 9 56 61.005.00 5.00 25.00 0.09 10 74 57.67 16.33 16.33 266.78 0.22 11 37 70.67 33.67 33.67 1133.44 0.91 12 63 55.67 7.33 7.33 53.78 0.12 58.001.44 16.63 395.20 0.33 BIAS MAD MSE MAPE For this example there are 9 errors Compare Error Measurements Error measurements for all four methods BIAS MAD MSE MAPE MA(n=3) 1.44 16.63 395.20 0.33 MA(n=5) 3.23 14.31 298.11 0.31 ExpSm(alpha=0.25) 3.83 15.60 337.40 0.31 ExpSm(alpha=0.5) 2.24 18.43 430.27 0.36 MA(n=5) has lower error measurements on MAD, MSE, and MAPE than the other three approaches. Which forecasting method to choose? Each forecasting method yields its own errors and hence different error measurement criteria. Try different methods and choose the one that has best performance on error criteria....
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 Fall '07
 Eng

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