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# 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
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%