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.

1. Decomposition Lesson #7 Decomposition Method 1 Copyright 2010 DeepThought, Inc.

3. Trend, seasonality, cyclical, and random

4. Method decomposes the time series in to its basic components

5. Uses the estimated component factors to forecast future values

6. Method format:

7. Y = T × S × C2 Copyright 2010 DeepThought, Inc.

9. Decomposes a time series in to its parts

10. Estimates each component of the time series individually and then combines then together to generate a forecast for the future.

11. When to use method

12. Any time series can be decomposed

13. When not to use

14. Not applicable3 Copyright 2010 DeepThought, Inc.

15. Decomposition Forecasting Steps Set an objective Build model Evaluate model Use model 4 Copyright 2010 DeepThought, Inc.

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. Example objectives for New One Family Homes Sold (see next slide):

19. Test if New One Family Homes Sold can be fit to a decomposition model

20. If One Family Homes Sold exhibits a statistically significant fit, review and interpret results

21. If model looks good, create a forecast based off model5 Copyright 2010 DeepThought, Inc.

22. Decomposition Example: Houses Sold 6 Copyright 2010 DeepThought, Inc.

25. Mean

26. Variance & Standard Deviation

27. Accuracy / Error

28. SSE

29. RMSE

30. MAPE

31. R2; Adjusted R2

32. Statistical Significance

33. F-Test

34. P-Value F-Test8 Copyright 2010 DeepThought, Inc.

36. 5.88

37. Variance

38. 0.34

39. Standard Deviation

40. 0.58 9 Copyright 2010 DeepThought, Inc.

42. 1.97

43. RMSE

44. 0.22

45. MAPE

46. 2.78%

47. R2; Adjusted R2

48. 84.80%

49. 84.39%10 Copyright 2010 DeepThought, Inc.

51. 55.80

52. P-Value F-Test

53. 0.00002111 Copyright 2010 DeepThought, Inc.

55. Will use accuracy/error statistics to compare multiple models to find best models12 Copyright 2010 DeepThought, Inc.

57. Answer objectives13 Copyright 2010 DeepThought, Inc.

59. 4.88823443714 Copyright 2010 DeepThought, Inc.