1. HW1 Q5: One Possible Approach First, let the population grow At some point, start harvesting the growth –Annual catch = annual growth In year 30, catch all but 1,000 fish –Maybe not be a good idea in reality Remaining question: how far should we let the population grow?

2. MGTSC 352 Lecture 3: Forecasting “Simple” time series forecasting methods Including SES = Simple Exponential Smoothing Performance measures “Tuning” a forecasting method to optimize a performance measure Components of a time series DES = Double Exponential Smoothing

3. Today’s active learning Groups of two again Recorder: person who got up earlier this morning

4. SES is really a WMA (pg. 19) F t+1 = LS  D t + (1–LS)  F t t = 6: F 7 = LS  D 6 + (1–LS)  F 6 t = 5: F 6 = LS  D 5 + (1–LS)  F 5 t = 4: F 5 = LS  D 4 + (1–LS)  F 4 t = 3: F 4 = LS  D 3 + (1–LS)  F 3 t = 2: F 3 = LS  D 2 + (1–LS)  F 2 t = 1: F 2 = D 1 Plug t = 5 equation into t = 6 equation: F 7 = LS  D 6 + (1–LS)  (LS  D 5 + (1–LS)  F 5 ) Active learning: Multiply out F 7 = LS  D 6 + LS  (1–LS)  D 5 + (1–LS) 2  F 5 Repeat for t = 4, 3, 2, 1 Final result: F 7 = [LS  D 6 ] + [LS  (1–LS)  D 5 ] + [LS  (1–LS) 2  D 4 ] + [LS  (1–LS) 3  D 3 ] + LS  (1–LS) 4  D 2 ] + (1–LS) 5  D 1

5. The Weights LS = 0.5 LS = 0.3 LS = 0.1

6. Weights get smaller and smaller for demand that is further and further in the past – except: –Oldest data point may have more weight than second oldest data point. –Only matters for small data sets and small LS

7. Simple Models Recap LP, AVG, SMA, WMA, SES Three phases: –Initialization –Learning –Prediction Prediction: so far, we’ve only done one-period- into-the-future k periods-into-the-future: F t+k = F t+1, k = 2, 3, … Active learning: translate formula into English

8. Performance Measures BIAS = Bias MAD = Mean Absolute Deviation SE = Standard Error MSE = Mean Squared Error MAPE = Mean Absolute Percent Error (formulas in course pack, p. 21) Excel

9. Components of a Time Series –level –trend –seasonality –cyclic (we will ignore this) –random (unpredictable by definition) (Simple) Exponential Smoothing incorporates... –Level only –Will lag trend –Miss seasonality Pg. 23

10. Level, Trend, Seasonality Level + random Level + trend + random Level + trend + seasonality + random

11. Level, Trend, Seasonality Additive trend, multiplicative seasonality (Level + Trend)  seasonality index Example: –Level: 1000 –Trend: 10 –Seasonality index: 1.1 –Forecast: (1000 + 10)  1.1 = 1111

12. Models Double Exponential Smoothing –Level, Trend –Today Triple Exponential Smoothing –Next week Simple Linear Regression with Seas. Indices –Next week

13. Double Exponential Smoothing Initialization –Level, Trend Learning Prediction Formulas in course pack Work on an example Excel Pg. 25

14. Learning In general: UPDATED = S  NEW + (1 – S)  OLD