This lesson begins with explaining the Winters’ exponential smoothing method characteristics, and uses. Winters’ exponential smoothing method attempts to best fit a smoothing constant, trend constant, and seasonal constants to past data. Using an example and the forecasting process, we apply the winters’ exponential smoothing method to create a model and forecast based upon it.

1. Winters’ Exponential Smoothing Lesson #5 Winters’ Exponential Smoothing Method 1 Copyright 2010 DeepThought, Inc.

3. Estimates a smoothing equation

4. Uses the estimated smoothing equation to forecast future values

5. Method format:

6. F(t) = a × X(t)/S(t-p) + (1-a) × [F(t-1) + T(t-1)]

7. S(t) = b × X(t)/F(t) + (1-b) × S(t-p)

8. T(t) = g × [F(t)-F(t-1)] + (1-g) × T (t-1)

9. W(t+m) = [F(t) + m × T (t)] × S(t+m-p) 2 Copyright 2010 DeepThought, Inc.

11. Fits a smoothing equation to data

12. Estimating a smoothing equation which minimizes the errors between actual data points and model estimates

13. When to use method

14. Data has trend and seasonality

15. When not to use

16. Data does not exhibits trend or seasonality3 Copyright 2010 DeepThought, Inc.

17. Winters’ Exponential Smoothing Forecasting Steps Set an objective Build model Evaluate model Use model 4 Copyright 2010 DeepThought, Inc.

19. Winters’ exponential smoothing allows to test whether a smoothing technique with a trend and seasonality works as a model.Objectives should take that principal under consideration

20. Example objectives for E-Commerce Retail Sales (see next slide):

21. Test if E-Commerce Retail Sales can be fit to a trend and seasonality exponential smoothing model

22. If E-Commerce Retail Sales exhibits a statistically significant fit, review and interpret results

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

24. Winters’ Exponential Smoothing Example: E-Commerce Retail Sales 6 Copyright 2010 DeepThought, Inc.

27. Mean

28. Variance & Standard Deviation

29. Accuracy / Error

30. SSE

31. RMSE

32. MAPE

33. R2; Adjusted R2

34. Statistical Significance

35. F-Test

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

38. 19673.68

39. Variance

40. 99993090.28

41. Standard Deviation

42. 9999.65 9 Copyright 2010 DeepThought, Inc.

44. 82863394.84

45. RMSE

46. 1439.30

47. MAPE

48. 5%

49. R2; Adjusted R2

50. 97.9%

51. 97.8%10 Copyright 2010 DeepThought, Inc.

53. 1704.30

54. P-Value F-Test

55. 0.0011 Copyright 2010 DeepThought, Inc.

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

59. Answer objectives13 Copyright 2010 DeepThought, Inc.