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

2. Agenda I.Why is forecasting important? II.Use a project to teach Time Series Seasonal Forecasting. III.Phases (milestones) of the project and Rubric(handout). IV.Use the Method of “Ratio-to-Moving- Averages” to obtain a Forecast. V.Forecasting errors. VI.Other methods typically used and References. VII.Conclusions and recommendations. 11/10/20152

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” 11/10/20153

4. II. 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. 11/10/20154

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 11/10/20155

6. IV. Time Series Components Components Trend (Linear or Power Model) Seasonal Cyclical Random error Prediction Horizon Short term Mid term Long term 11/10/20156

7. IV. Quarterly Data Electric Power USA in Million Kilowatt hour per day QtrIndex Dt= Total 10E6 KWhr per day Roll.Avg.Dt 2004 Q11 9,588.0 Q22 9,337.0 Q33 10,580.09,708.5 Q44 9,260.09,735.9 2005 Q15 9,726.09,848.8 Q26 9,418.09,989.0 Q37 11,402.010,027.3 Q48 9,560.010,055.8 2006 Q19 9,732.010,082.6 Q210 9,640.010,066.8 Q311 11,395.010,096.5 Q412 9,440.010,160.4 2007 Q113 10,090.010,200.1 Q214 9,793.010,266.0 Q315 11,560.010,317.8 Q416 9,802.010,324.5 2008 Q117 10,142.010,281.9 Q218 9,795.010,203.1 Q319 11,217.0 Q420 9,515.0 Refer to Part B, Handout #1 11/10/20157

8. IV. Four-Quarters Rolling Average, and the Seasonality Index Dt= Total 10E6 KWhr per day Roll.Avg.Dt Roll.Seas. Index Typical.Seas. Index 9,588.0 0.9821 9,337.0 0.9536 10,580.09,708.51.08981.1190 9,260.09,735.90.95110.9451 9,726.09,848.80.98750.9821 9,418.09,989.00.94280.9536 11,402.010,027.31.13711.1190 9,560.010,055.80.95070.9451 9,732.010,082.60.96520.9821 9,640.010,066.80.95760.9536 11,395.010,096.51.12861.1190 9,440.010,160.40.92910.9451 10,090.010,200.10.98920.9821 9,793.010,266.00.95390.9536 11,560.010,317.81.12041.1190 9,802.010,324.50.94940.9451 10,142.010,281.90.98640.9821 9,795.010,203.10.96000.9536 11,217.0 1.1190 9,515.0 0.9451 Q1 Seas.Factor Q2 Seas.Factor Q3 Seas.Factor Q4 Seas.Factor 0.98750.94281.08980.9511 0.96520.95761.13710.9507 0.98920.95391.12860.9291 0.98640.96001.12040.9494 0.98210.95361.11900.9451 Refer to Part C, Handout #1 11/10/20158

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) 11/10/20159 Refer to Part A, Handout #2

10. IV. De- Seasonalized Data indicates the Trend, while Seasonalized Data contains Forecasted values YearQtrIndex # Dt= Total 10E6 KWhr per day Deseasonali zed Dt LS.Roll Avg Dt Ft=Seasonal ized Dt et=Dt-Ft error residual 2004Q119,588.09,762.99,766.89,591.9-3.9 Q229,337.09,791.49,796.79,342.1-5.1 Q3310,580.09,455.19,826.610,995.7-415.7 Q449,260.09,798.19,856.69,315.2-55.2 2005Q159,726.09,903.49,886.59,709.416.6 Q269,418.09,876.39,916.49,456.2-38.2 Q3711,402.010,189.79,946.311,129.6272.4 Q489,560.010,115.69,976.29,428.3131.7 2006Q199,732.09,909.510,006.19,826.9-94.9 Q2109,640.010,109.110,036.09,570.369.7 Q31111,395.010,183.510,066.011,263.5131.5 Q4129,440.09,988.610,095.99,541.4-101.4 2007Q11310,090.010,274.010,125.89,944.4145.6 Q2149,793.010,269.610,155.79,684.4108.6 Q31511,560.010,330.910,185.611,397.4162.6 Q4169,802.010,371.610,215.59,654.5147.5 2008Q11710,142.010,327.010,245.410,061.980.1 Q2189,795.010,271.710,275.49,798.5-3.5 Q31911,217.010,024.410,305.311,531.3-314.3 Q4209,515.010,067.910,335.29,767.6-252.6 "Future" 2009Q12110,365.110,179.5 Q222 10,395.09,912.6 Refer to Part B, Handout #2 11/10/201510

11. IV. IV. Data Dt, and its Forecast Ft Forecasted values Ft, are used to estimate the probable forecast error 11/10/201511 Refer to Part A, Handout #3

12. IV. 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. 11/10/201512 Refer to Part B, Handout #3

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” 11/10/201513

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. 11/10/201514

15. VI. References EIA data set downloaded July 17, 2009: http://tonto.eia.doe.gov/cfapps/STEO_Query/s teotables.cfm?tableNumber=8 http://tonto.eia.doe.gov/cfapps/STEO_Query/s teotables.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_p c.html http://www.census.gov/srd/www/x12a/x12down_p c.html Ellis,Wade. Inquiry-base Software MicroWorlds: Promoting Understanding and Retention of Concepts. International Merlot Conference 2009 11/10/201515 Refer to Part C, Handout #3

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). “ 11/10/201516

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. 11/10/201517