TM 745 Forecasting for Business & Technology Paula Jensen

1. TM 745 Forecasting for Business & TechnologyPaula Jensen 7th Session 3/14/10: Chapter 6 Time-Series Decomposition South Dakota School of Mines and Technology, Rapid City

2. Time-Series Decomposition • Trend, seasonal, cyclical, random • Oldest, but popular • 1. They make good forecasts • 2. Easy to understand & explain • 3. How managers look at data (in the other books, courses) • Ratio to moving average • Classical time-series decomposition

3. The Basic Time-Series Decomposition Model • Y = T x S x C x I • T: long term trend in the data • S: seasonal adjustment factor • C: cyclic adjustment factor • I: irregular or random variations in the series

4. The Basic Time-Series Decomposition Model Identify?

5. Deseasonalizing the Data and Finding Seasonal Indexes • The process verbally • 1. Find the MA’s (moving averages) • 2. From the MA’s compute the CMA’s • 3. Find the SF (seasonal factors) by dividing the data by the CMA’s • 4. Average the SF to find the SI’sSI: seasonal index • Two products CMA’s & SI’s • Use CMA’s & SI’s How?

6. Deseasonalizing the Data and Finding Seasonal Indexes • 1. Find the MA’s (moving averages)

7. Deseasonalizing the Data and Finding Seasonal Indexes • 1. Find the MA’s (moving averages) swimwear example

8. Deseasonalizing the Data and Finding Seasonal Indexes • 1. Find the MA’s (moving averages) swimwear exampleCheck arrows on previous slide

9. Deseasonalizing the Data and Finding Seasonal Indexes • 2. From the MA’s compute the CMA’s check arrows again

10. Deseasonalizing the Data and Finding Seasonal Indexes • 3. Find the SF (seasonal factors) by dividing the data by the CMA’sSF>1 means? SF<1 means?

11. Deseasonalizing the Data and Finding Seasonal Indexes 4th ed

12. Deseasonalizing the Data and Finding Seasonal Indexes 4th ed

13. Deseasonalizing the Data and Finding Seasonal Indexes

14. Deseasonalizing the Data and Finding Seasonal Indexes 4th ed

15. Deseasonalizing the Data and Finding Seasonal Indexes 5th ed.

16. Finding the Long-Term Trend • Usually linear, but can be other. • Gap data was fit to exponential • CMA = f (TIME) = a + b (TIME) • Linear fit to PHSCMA givesPHSCAT = 134.8 - 0.04(TIME)a slightly downward trend

18. Measuring the Cyclical Component • CF = CMA/CMAT • CF: cycle factor • CMA: centered moving average • CMAT: centered moving average trend • Most difficult to analyze • Can hint at future by noting characteristics of the cycle

19. Overview of Business Cycles • Expansion phase • Contraction phase (recession) • Business Cycles • amplitude is not constant • period is not constant • Official definitions of beginning & end of recession (3 month rule)

20. Overview of Business Cycles

21. Business Cycle Indicators • Can be used a independent variables (predictors) in regression analysis • Major indexes or components useful • Major indexes see table 6.4 page 300 • I. of leading economic indicators • I. of coincident economic indicators • I. of lagging economic indicators • Figure 6-5 follows

23. Cycle Factor for PHS • Note period and troughs figure 6-6 • CF = PHMCMA/PHCMATJune - 03: CF = 153.10/120.42 = 1.27

24. Cycle Factor for PHS

26. The Time-Series Decomposition Forecast • Y = T x S x C x I • T: Long-term trend • based on the deseasonalized data • centered moving average trend (CMAT) • S: Seasonal indexes (SI) • Normalized avgs of seasonal factors • Ratio of each period's actual value (Y) to the deseasonalized value (CMA)

27. The Time-Series Decomposition Forecast • Y = T x S x C x I • C: Cycle component. • Cycle factor (CF = CMA/ CMAT) • gradual wavelike series about the trend line • I: Irregular component. (random) • Assumed equal to 1, usually • If a shock occurred, not 1 • When doing simulation, random

28. The Time-Series Decomposition Forecast: PHS • FY = (CMAT)(SI)(CF)(I) • PHSFTSD = (PHSCMAT)(SI)(CF)(1) • Historical RMSE = 9.16 • Holdout RMSE = 12.29 see fig 6-8 • Light on Math and Statistics • Easy for end user to understand • So, user has more confidence

30. Forecasting Shoe Store Sales: Time-Series Decomposition

31. Forecasting Shoe Store Sales: Time-Series Decomposition

32. Forecasting Total Houses Sold: Time-Series Decomposition

33. Forecasting Total Houses Sold: Time-Series Decomposition

34. Forecasting at Vermont Gas Systems Winter Daily Forecast • 26,000 customers in NW Vermont • Closest big city for customers? • Gas suppliers in western Canada • Storage along Trans-Canada pipeline • Quantities must be specifiedat least 24 hours in advance • Only 1 hour’s capacity in a storage buffer Yikes!

35. Integrative Case: The Gap 4th

36. Integrative Case: The Gap 4th

38. Integrative Case: The Gap 4th

40. Appendix Components of the Composite Indexes Leading • Average weekly hours, manufacturing • Average weekly initial claims for unemployment insurance • Manufacturers' new orders, consumer goods & materials • Vendor performance, slower deliveries diffusion index

41. Appendix Components of the Composite Indexes Leading • Manufacturers' new orders, nondefense capital goods • Building permits, new private housing units • Stock prices, 500 common stocks • Money supply M2 (inflation adjusted) • demand deposits, checkable deposits,savings deposits, balances in money market funds (money like stuff)

42. Appendix Components of the Composite Indexes Leading • Interest-rate spread, 10-year Treasury bonds less federal funds • Difference between long & short rates • Called the yield curve • negative recession, • Index of consumer expectations • U. of Michigan’s Survey Research Center • Measures consumer attitude

43. Appendix Components of the Composite Indexes Coincident • Employees on nonagricultural payrolls • U.S. Bureau of Labor Statistics • Payroll employment • Personal income less transfer payments • Industrial production • Numerous sources • Valued added concept • Manufacturing and trade sales • Aggregate sales > GDP

44. Appendix Components of the Composite Indexes Coincident • Average duration of unemployment • Inventories to sales ratio, manufacturing and trade • Labor cost per unit of output, manufacturing • Average prime rate

45. Appendix Components of the Composite Indexes Lagging • Commercial and industrial loans • Consumer installment credit to personal income ratio • Consumer price index for services