1. Marking Philosophy Feasibility: could the plan you proposed be used in reality Consistency: are your numbers internally consistent? Optimality: is your plan the best possible, or close to it?

2. Example: Marking of HW1, Q5 You submitted: –The plan: # to catch in years 0 – 30 –The consequence: NPV We plug your plan into a correct model and check: –Feasibility: is fish population always non-negative? –Consistency: does your plan result in the NPV you reported? –Optimality: how does your NPV compare to the best possible NPV?

3. From the Grading Manager Put only numbers in cells for numerical answers –1234 –$1,234 –1 234  Excel interprets this as text, not a number (because of the space) –1234 fish  ditto

4. Reminders HW 2 due Wednesday at 11:59 pm

5. MGTSC 352 Lecture 4: Forecasting Methods that capture Level, Trend, and Seasonality: TES = Triple Exponential Smoothing Intro to SLR w SI = Simple Linear Regression with Seasonality Indices

6. Forecasting: Common Mistakes Computing forecast error when either the data or the forecast is missing MSE: dividing with “n” instead of “n-1” MSE: SSE/n – 1 instead of SSE/(n – 1) Simple methods: forgetting that the forecasts are the same for all future time periods

7. Recap: How Different Models Predict Simple models: –F t+k = F t+1, k = 2, 3, … DES: –F t+k = L t + (k  T t ), k = 1, 2, 3, … –Linear trend TES and SLR w SI (cover today): –F t+k = (L t + k  T t )  (Seasonality Index)

8. What’s a Seasonality Index (SI)? Informal definition: SI = actual / level Example: –Average monthly sales = $100M –July sales = $150M –July SI = 150/100 = 1.5 SI = actual / level means: –Actual = level  SI –Level = actual / SI

9. TES tamed Works in three phases Initialization Learning Prediction Tracks three components Level Trend Seasonality

10. Actual data Level Prediction Initialization Learning Prediction

11. Actual data Level Prediction k periods into future k  trend Forecast = (predicted level)  SI predicted level Time to try it out – Excel

12. TES - Calibration (p = # of seasons) One-step Forecast: F t+1 = (L t + T t ) S t+1-p Always: UPDATED = (S) NEW + (1-S) OLD Pg. 29

13. Level: learning phase L(t) = LS * D(t) / S(t-p) + ( 1 - LS )*( L(t-1) + T(t-1) ) NEW: D(t) / S(t-p) = de-seasonalize data for period t using seasonality of corresponding previous season  level = actual / SI OLD: L(t-1) + T(t-1) = best previous estimate of level for period t

14. Trend: learning phase T(t) = TS * ( L(t) - L(t-1) ) + ( 1 - TS ) * T(t-1) NEW: L(t) - L(t-1) = growth from period t-1 to period t OLD: T(t-1) = best previous estimate for trend for period t

15. Seasonality: learning phase S(t) = SS * D(t) / L(t) + ( 1 - SS ) * S(t-p) NEW: D(t) / L(t) = actual / level  SI = actual / level OLD: S(t-p) = previous SI estimate for corresponding season 25

16. One-step forecasting: the past F(t+1) = [L(t) + T(t)] * S(t+1-p) "To forecast one step into the future, take the previous period’s level, add the previous period’s trend, and multiply the sum with the seasonality index from one cycle ago."

17. k-step forecasting: the future (“real” forecast) F(t+1) = [L(t) + k*T(t)] * S(t+1-p) Active learning: translate the formula into English One minute, in pairs Pg. 30

18. TES vs SLRwSI TES F t+k = (L t + k  T t )  S t+k-p SLRwSI F t+k = (intercept + (t + k)  slope)  SI additive trend multiplicative seasonality

19. TES vs SLRwSI Both estimate Level, Trend, Seasonality Data points are weighted differently –TES: weights decline as data age –SLRwSI: same weight for all points Hence, TES adapts, SLRwSI does not

20. Which Method Would Work Well for This Data?

21. Patterns in the Data? Trend: –Yes, but it is not constant –Zero, then positive, then zero again Seasonality? –Yes, cycle of length four

22. Comparison TES: SE = 24.7 TES trend is adaptive SLRwSI: SE = 32.6 SLR uses constant trend

23. One-minute paper Don’t put on your coat put your books away or whatnot, pull out a piece of paper instead. Review today’s lecture in your mind –What were the two main things you learned? –What did you find most confusing? –Who is going to win the Superbowl? Don’t put your name on the paper. Stay in your seats for 1 minute. Hand in on your way out