2. Time-Series Forecasting

3. Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data Series 5.Forecast Using Smoothing Methods, & Trend 6.Use MAD to Measure Forecast Error

4. What Is Forecasting? 1.Process of Predicting a Future Event 2.Underlying Basis of All Business Planning Production Inventory Personnel Facilities Sales will be $200 Million!

5. Forecasting Methods 1.Qualitative Methods Expert Opinion Delphi Method Surveys 2.Quantitative Methods Time Series Causal Regression

6. Quantitative Forecasting Steps 1.Select Several Forecasting Methods 2.‘Forecast’ the Past 3.Evaluate Forecasts 4.Select Best Method 5.Forecast the Future 6.Monitor Continuously Forecast Accuracy

7. What’s a Time Series? 1.Set of Numerical Data 2.Obtained by Observing Response Variable at Regular Time Periods 3.Assumes that Factors Influencing Past & Present Will Continue 4.Example Year:19901991199219931994 Sales:78.763.589.793.292.1

8. Time Series Components Trend Seasonal Cyclical Irregular

9. Trend Component 1. Persistent, Overall Upward or Downward Pattern 2. Due to Population, Technology, etc. 3. 15 to 20 Years Duration Mo., Qtr., Yr. Response

10. Linear Increasing Trend Linear Decreasing Trend Nonlinear TrendNo Trend Examples of Some Time Series Trend Patterns

11. Toaster Sales in Hundreds, By Quarter, 1990-1998 TIME QUARTER1 QUARTER2 QUARTER3 QUARTER4 ------------------------------------------- 1990 187 243 209 291 1991 198 263 270 297 1992 274 363 294 336 1993 232 273 241 289 1994 206 295 239 317 1995 237 366 300 429 1996 282 424 383 478 1997 375 429 393 560 1998 373 423 387 433

12. Long-Term Trend in Toaster Sales

13. Cyclical Component 1. Repeating Up & Down Movements 2. Due to Interactions of Factors Influencing Economy 3. Usually 2-15 Years Duration Mo., Qtr., Yr. Response Cycle Prosperity Recession Depression Recovery

14. Cycles in Toaster Sales

15. Seasonal Component 1. Regular Pattern of Up & Down Fluctuations 2. Due to Weather, Customs,etc. 3. Occurs Within 1 Year Mo., Qtr. Response Summer

16. The Seasonal Pattern of Toaster Sales

17. Irregular Component l 1.Erratic, Unsystematic, ‘Residual’ Fluctuations l 2.Due to Random Variation or Unforeseen Events n Union Strike n Tornado l 3.Short Duration & Nonrepeating

18. Irregular Fluctuations in Toaster Sales Quarters

19. Multiplicative Time-Series Model l 1.Any Observed Value in a Time Series Is the Product of Time Series Components l 2.If Annual Data n Y = T x C x I l 3.If Quarterly or Monthly Data n Y i = T x S x C x I

20. Time Series Forecasting Linear Time Series Forecasting Trend? Smoothing Methods Trend Models YesNo Exponential Smoothing QuadraticExponential Holt- Winters Auto- Regressive Moving Average

21. Moving Average Method 1.Series of Arithmetic Means 2.Used Only for Smoothing Provides Overall Impression of Data Over Time 3.Equation L = Averaging Period (Odd # Years) MA (L) Y L i it    (L-1)/2 T=(1-L)/2

22. Time Response Y i Moving Total ( L =3) Moving Avg ( L =3) 19914NA 199264 + 6 + 5 = 1515/3 = 5.0 199356 + 5 + 3 = 1414/3 = 4.7 199435 + 3 + 7 = 1515/3 = 5.0 199573 + 7 + 6 = 1616/3 = 5.3 19966NA Moving Average Calculation

23. Moving Average Graph Year Sales 0 2 4 6 8 919293949596

24. Moving Average with Even Number of Periods

25. Time Series Forecasting Linear Time Series Forecasting Trend? Smoothing Methods Trend Models YesNo Exponential Smoothing QuadraticExponential Holt- Winters Auto- Regressive Moving Average

26. Exponential Smoothing Method l 1.Form of Weighted Moving Average n Weights Decline Exponentially n Most Recent Data Weighted Most l 2.Used for Smoothing & Forecasting n Assumes No Trend l 3.Requires Smoothing Coefficient (W) n Subjectively Chosen n Ranges from 0 to 1

27. Exponential Smoothing Equations l 1.Smoothing Equations E i = W·Y i + (1 - W)·E i-1 l 2.Forecasting Equation Y i+1 = E i E i = Smoothed Value Y i = Actual Value W = Smoothing Coefficient

28. Time Y i Smoothed Value, E i ( W =.2) Forecast Y i +1 199144.0NA 19926(.2)(6) + (1-.2)(4.0) = 4.44.0 19935(.2)(5) + (1-.2)(4.4) = 4.54.4 19943(.2)(3) + (1-.2)(4.5) = 4.24.5 19957(.2)(7) + (1-.2)(4.2) = 4.84.2 1996NA 4.8 Exponential Smoothing Calculation ^ E i = W·Y i + (1 - W)·E i-1

29. Exponential Smoothing Graph Year Sales 0 2 4 6 8 9192939495

30. Exponential Smoothing Thinking Challenge l You’re an economist for GM. You want to get a feel for the long-term trend in car sales. You want to smooth cyclical & random fluctuations using exponential smoothing with W =.25. Yearly sales (million units) are 2, 4, 1, 3.

31. To obtain starting values: 1.E 1 = Y 1 = 2 l 2.E 2 = W·Y 2 + (1 - W)·E 1 = (.25)(4) + (1.00 -.25)(2) = 2.5 l 3.E 3 = W·Y 3 + (1 - W)·E 2 = (.25)(1) + (1.00 -.25)(2.5) = 2.125 l 4.E 4 = W·Y 4 + (1 - W)·E 3 l = (.25)(3)+(1.00 -.25)(2.125)=2.34 Exponential Smoothing Solution*

32. Selecting Smoothing Coefficient (W) l 1.Subjectively Chosen n Computer Search Routines Available l 2.To Smooth Cyclical & Irregular, Small W n Reveals Long-Term Pattern l 3.To Forecast, Large W n Forecast Will Reflect Prior Period Data Most l 4.Recent Data Weighted Most for All W