By: W Jorge Sitkewich, Mathematics and Statistics Adjunct Instructor

1. By: W Jorge Sitkewich, Mathematics and Statistics Adjunct Instructor San Jose City College. jsitke@ieee.org Teaching Seasonal Forecasting to Students of Statistics

2. Agenda • Why is forecasting important? • Use a project to teach Time Series Seasonal Forecasting. • Phases (milestones) of the project and Rubric(handout). • Use the Method of “Ratio-to-Moving-Averages” to obtain a Forecast. • Forecasting errors. • Other methods typically used and References. • Conclusions and recommendations. 9/25/2014 2

3. I. Why is forecasting important? • Forecasting is a necessary tool in any business to align the resources to the estimated demand. • Several Forecasting methods are in use in Statistics and most use Regression and Modeling. • One of the Projects assigned to students of Statistics consists of Seasonal Forecasting a Time Series by the Ratio-to-Moving-Average Method. • The example we will demonstrate is about predicting the Electric Power consumption of the USA using data available from EIA government documents. See references. Table 7b. “U.S. Regional Electricity Retail Sales” 9/25/2014 3

4. II. Use a project to teach Forecasting • Students form Teams, Select the Problem, and learn the basics of Project Management. • In most Statistics Courses there are usually two or three key application concepts that are left for the end of the course, and not taught in detail. • The Project of Seasonal Forecasting provides the learning environment and engages the students in team work to learn one the key applications in forecasting a time series. 9/25/2014 4

5. III. Phases of the Project and Rubric Phase 1. Select the specific project and justify it as a valid team activity for this course. Phase 2. Estimate the Schedule and adjust the Project Scope for a duration of four calendar weeks. Phase 3. Execute the Method using available Technology. Generate spread sheets and Charts. Phase 4. Estimate errors of the Model and provide Conclusions and References. Phase 5. Create PowerPoint Summary Presentation. Each team presents their summary as a 10 minute presentation to conclude the Project. Refer to the Rubric provided in Part A handout #1 9/25/2014 5

6. IV. Time Series Components Components • Trend (Linear or Power Model) • Seasonal • Cyclical • Random error Prediction Horizon • Short term • Mid term • Long term 9/25/2014 6

7. IV. Quarterly Data Electric Power USAin Million Kilowatt hour per day Refer to Part B, Handout #1 9/25/2014 7

8. IV. Four-Quarters Rolling Average, and the Seasonality Index Refer to Part C, Handout #1 9/25/2014 8

9. IV. Data, De-Seasonalized Data, and Trend • De-Seasonalized data is used to create a linear trend that we extrapolate into the future. • Ft = (linear trend)* (typical seasonal index) Refer to Part A, Handout #2 9/25/2014 9

10. IV. De-Seasonalized Data indicates the Trend, while Seasonalized Data contains Forecasted values Refer to Part B, Handout #2 9/25/2014 10

11. IV. Data Dt, and its Forecast Ft • Forecasted values Ft, are used to estimate the probable forecast error Refer to Part A, Handout #3 9/25/2014 11

12. IV. Error terms in Forecasting • Error terms indicate a small forecast error. • A cyclical component with a period of about four years is also noticed. Refer to Part B, Handout #3 9/25/2014 12

13. V. Discussion of Forecasting Errors • MAD or “mean absolute deviation” • MAPE or “mean absolute percent deviation” • Std deviation of forecasting error • MSE or “mean squared error” 9/25/2014 13

14. V. Other Methods Typically Used • Single exponential smoothing, and double exponential smoothing. • ARMA and ARIMA (Box-Jenkins methods). Even though the more advanced methods may provide smaller forecasting error, they are harder to visualize and to perform with simple laptop tools. 9/25/2014 14

15. VI. References EIA data set downloaded July 17, 2009: http://tonto.eia.doe.gov/cfapps/STEO_Query/steotables.cfm?tableNumber=8 Mason,R., Lind,D. Statistical Techniques in Business and Economics. R.D.Irwin 1993 X-12, ARIMA Reference manual, (July 17, 2009), http://www.census.gov/srd/www/x12a/x12down_pc.html Ellis,Wade. Inquiry-base Software MicroWorlds: Promoting Understanding and Retention of Concepts. International Merlot Conference 2009 Refer to Part C, Handout #3 9/25/2014 15

16. VI. Value of Problem Solving Projects Quote from Ellis Wade’s paper: “…research indicates that students retain a concept only if the concept is learned to the level of problem-solving (level 4) or at least application of the concept (level 3 of the Bloom taxonomy). “ 9/25/2014 16

17. VII. Conclusions and Recommendations • Students perform their assigned projects in Five Phases, each one is graded and feedback is given to each student. • The final phase is the PowerPoint Summary given on the last day, and each group presents their PowerPoint Summary for 5 to 10 minutes each. • Lessons-learned are discussed at the end of the final presentation by all students. • The Instructor provides the pizza and refreshments. 9/25/2014 17