ForecastIT 7. Decomposition

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This lesson begins with explaining the decomposition method characteristics, and uses. Decomposition method decomposes the data in to its fundamental pieces and creates a forecast based upon each of the individual pieces. Using an example and the forecasting process, we apply the decomposition method to create a model and forecast based upon it.

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ForecastIT 7. Decomposition

  1. 1. Decomposition<br />Lesson #7<br />Decomposition Method<br />1<br />Copyright 2010 DeepThought, Inc.<br />
  2. 2. Decomposition<br />Model Introduction<br /><ul><li>Assumes that every time series is composed of four components:
  3. 3. Trend, seasonality, cyclical, and random
  4. 4. Method decomposes the time series in to its basic components
  5. 5. Uses the estimated component factors to forecast future values
  6. 6. Method format:
  7. 7. Y = T × S × C</li></ul>2<br />Copyright 2010 DeepThought, Inc.<br />
  8. 8. Decomposition<br />Model Details<br /><ul><li>Method characteristics
  9. 9. Decomposes a time series in to its parts
  10. 10. Estimates each component of the time series individually and then combines then together to generate a forecast for the future.
  11. 11. When to use method
  12. 12. Any time series can be decomposed
  13. 13. When not to use
  14. 14. Not applicable</li></ul>3<br />Copyright 2010 DeepThought, Inc.<br />
  15. 15. Decomposition<br />Forecasting Steps<br />Set an objective<br />Build model<br />Evaluate model<br />Use model<br />4<br />Copyright 2010 DeepThought, Inc.<br />
  16. 16. Decomposition<br />Objective Setting<br /><ul><li>Simpler is better
  17. 17. Decomposition allows to test whether a breaking down of the time series works as a model. Objectives should take that principal under consideration
  18. 18. Example objectives for New One Family Homes Sold (see next slide):
  19. 19. Test if New One Family Homes Sold can be fit to a decomposition model
  20. 20. If One Family Homes Sold exhibits a statistically significant fit, review and interpret results
  21. 21. If model looks good, create a forecast based off model</li></ul>5<br />Copyright 2010 DeepThought, Inc.<br />
  22. 22. Decomposition<br />Example: Houses Sold<br />6<br />Copyright 2010 DeepThought, Inc.<br />
  23. 23. Decomposition<br />Build Model<br /><ul><li>Model breaks down time series in to its appropriate parts, independently estimates each part, and then combines the estimated parts together to forecast future values</li></ul>7<br />Copyright 2010 DeepThought, Inc.<br />
  24. 24. Decomposition<br />Evaluate Model<br /><ul><li>Descriptive Statistics
  25. 25. Mean
  26. 26. Variance & Standard Deviation
  27. 27. Accuracy / Error
  28. 28. SSE
  29. 29. RMSE
  30. 30. MAPE
  31. 31. R2; Adjusted R2
  32. 32. Statistical Significance
  33. 33. F-Test
  34. 34. P-Value F-Test</li></ul>8<br />Copyright 2010 DeepThought, Inc.<br />
  35. 35. Decomposition<br />ExampleDescriptive Statistics<br /><ul><li>Mean
  36. 36. 5.88
  37. 37. Variance
  38. 38. 0.34
  39. 39. Standard Deviation
  40. 40. 0.58 </li></ul>9<br />Copyright 2010 DeepThought, Inc.<br />
  41. 41. Decomposition<br />ExampleAccuracy / Error<br /><ul><li>SSE
  42. 42. 1.97
  43. 43. RMSE
  44. 44. 0.22
  45. 45. MAPE
  46. 46. 2.78%
  47. 47. R2; Adjusted R2
  48. 48. 84.80%
  49. 49. 84.39%</li></ul>10<br />Copyright 2010 DeepThought, Inc.<br />
  50. 50. Decomposition<br />ExampleStatistical Significance<br /><ul><li>F-Test
  51. 51. 55.80
  52. 52. P-Value F-Test
  53. 53. 0.000021</li></ul>11<br />Copyright 2010 DeepThought, Inc.<br />
  54. 54. Decomposition<br />Compare Multiple Models<br /><ul><li>Skip this step until have knowledge of multiple methods
  55. 55. Will use accuracy/error statistics to compare multiple models to find best models</li></ul>12<br />Copyright 2010 DeepThought, Inc.<br />
  56. 56. Decomposition<br />Use Model<br /><ul><li>Understand limitations of model
  57. 57. Answer objectives</li></ul>13<br />Copyright 2010 DeepThought, Inc.<br />
  58. 58. Decomposition<br />Example<br /><ul><li>Forecasts
  59. 59. 4.888234437</li></ul>14<br />Copyright 2010 DeepThought, Inc.<br />

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