Trend Based + Reg And Holtns

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Trend Based + Reg And Holtns

  1. 1. Forecasting Trend Based Methods
  2. 2. Regression Analysis
  3. 3. Regression line
  4. 4. Forecasting <ul><li>Y: demand D </li></ul><ul><li>x : time period </li></ul><ul><li>(1, D 1 ), (2, D 2 ), …, (n, D n ) </li></ul>
  5. 5. Regression Analysis <ul><li>The optimal value of a and b are given by: </li></ul>
  6. 9. Trend-Based Methods Double Exponential Smoothing
  7. 10. Holt’s method <ul><li>Method requires </li></ul><ul><ul><li>two smoothing constants α and β </li></ul></ul><ul><ul><li>Uses two equations </li></ul></ul><ul><ul><li>Value of the intercept at time t </li></ul></ul><ul><ul><li>Value of the slope at time t </li></ul></ul>
  8. 11. S t : intercept at time t G t : slope at time t First Equation : similar to simple exponential smoothing Average of current demand & prior forecast of the currebt demand 2nd Equation : New intercept  revise estimate of slope to S t – S t-1 This value is averaged with previous value of the slope
  9. 12. Double Exponential Smoothing <ul><li>Intercept at time t </li></ul><ul><li>and slope at time t </li></ul>
  10. 13. The τ -step-ahead forecast made in period t
  11. 14. S 1 =(0.1)( 200 )+(.9)(200+ 10 )=209.0 190 8 305 7 285 6 225 5 186 4 175 3 250 2 200 1 |error| F t D t
  12. 15. S 1 =(0.1)( 200 )+(.9)(200+ 10 )=209.0 G 1 =(0.1)( 209-200 )+(.9)( 10 )=9.9 190 8 305 7 285 6 225 5 186 4 175 3 250 2 200 1 |error| F t D t
  13. 16. S 2 =(0.1)(250)+(.9)(209+ 9.9 )=222.0 G 2 =(0.1)( 222-209 )+(.9)( 9.9 )=10.2 S 1 =(0.1)( 200 )+(.9)(200+ 10 )=209.0 G 1 =(0.1)( 209-200 )+(.9)( 10 )=9.9 190 8 305 7 285 6 225 5 186 4 175 3 250 2 200 1 |error| F t D t
  14. 17. S 3 =(0.1)(175)+(.9)(222+ 10.2 )=226.5 G 3 =(0.1)( 226.5-222 )+(.9)( 10.2 )=9.6 S 2 =(0.1)(250)+(.9)(209+ 9.9 )=222.0 G 2 =(0.1)( 222-209 )+(.9)( 9.9 )=10.2 S 1 =(0.1)( 200 )+(.9)(200+ 10 )=209.0 G 1 =(0.1)( 209-200 )+(.9)( 10 )=9.9 190 8 305 7 285 6 225 5 186 4 175 3 250 2 200 1 |error| F t D t
  15. 18. MAD=46.4 S 3 =(0.1)(175)+(.9)(222+ 10.2 )=226.5 G 3 =(0.1)( 226.5-222 )+(.9)( 10.2 )=9.6 S 2 =(0.1)(250)+(.9)(209+ 9.9 )=222.0 G 2 =(0.1)( 222-209 )+(.9)( 9.9 )=10.2 S 1 =(0.1)( 200 )+(.9)(200+ 10 )=209.0 G 1 =(0.1)( 209-200 )+(.9)( 10 )=9.9 85.0 275 190 8 44.2 260.8 305 7 37.3 247.7 285 6 15.3 240.3 225 5 50.1 236.1 186 4 175 3 250 2 200 1 |error| F t D t
  16. 19. MAD=46.4 3-step-ahead forecast: F 2,5 = S 3 =(0.1)(175)+(.9)(222+ 10.2 )=226.5 G 3 =(0.1)( 226.5-222 )+(.9)( 10.2 )=9.6 S 2 =(0.1)(250)+(.9)(209+ 9.9 )=222.0 G 2 =(0.1)( 222-209 )+(.9)( 9.9 )=10.2 S 1 =(0.1)( 200 )+(.9)(200+ 10 )=209.0 G 1 =(0.1)( 209-200 )+(.9)( 10 )=9.9 85.0 275 190 8 44.2 260.8 305 7 37.3 247.7 285 6 15.3 240.3 225 5 50.1 236.1 186 4 175 3 250 2 200 1 |error| F t D t
  17. 20. MAD=46.4 3-step-ahead forecast: F 2,5 = S 2 +(3) G 2 = 222 + (3) 10.2=252.6 S 3 =(0.1)(175)+(.9)(222+ 10.2 )=226.5 G 3 =(0.1)( 226.5-222 )+(.9)( 10.2 )=9.6 S 2 =(0.1)(250)+(.9)(209+ 9.9 )=222.0 G 2 =(0.1)( 222-209 )+(.9)( 9.9 )=10.2 S 1 =(0.1)( 200 )+(.9)(200+ 10 )=209.0 G 1 =(0.1)( 209-200 )+(.9)( 10 )=9.9 85.0 275 190 8 44.2 260.8 305 7 37.3 247.7 285 6 15.3 240.3 225 5 50.1 236.1 186 4 175 3 250 2 200 1 |error| F t D t
  18. 21. Trend Based Methods <ul><li>Regression Analysis </li></ul><ul><li>Double Exponential Smoothing </li></ul>

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