1. Financial Analysis, Planning and Forecasting Theory and Application
Chapter 25
Time-Series: Analysis, Model, and Forecasting By
Cheng F. Lee
Rutgers University, USA
John Lee
Center for PBBEF Research, USA

2. Outline
25.1 Introduction
25.2 The Classical Time-Series Component Model
25.3 Moving Average and Seasonally Adjusted Time-Series
25.4 Linear and Log-Linear Time Trend Regressions
25.5 Exponential Smoothing and Forecasting
25.6 Autoregressive Forecasting Model
25.7 Summary
Appendix 25A. The X-11 Model for Decomposing Time-Series Components
Appendix 25B. The Holt-Winters Forecasting Model for Seasonal Series

3. 25.2 The Classical Time-Series Component Model
Table 25.1 Earnings per share of JNJ
Year
EPS
2001
$1.87
2002
2.2
2003
2.42
2004
2.87
2005
3.5
2006
3.76
2007
3.67
2008
4.62
2009
4.45
2010
4.85

4. 25.2 The Classical Time-Series Component Model
Figure Earnings per share of Johnson & Johnson

5. 25.2 The Classical Time-Series Component Model

6. 25.2 The Classical Time-Series Component Model

7. 25.2 The Classical Time-Series Component Model

8. 25.2 The Classical Time-Series Component Model

9. 25.2 The Classical Time-Series Component Model
（25.1）
（25.2）
where
Tt = trend component
Ct = cyclical component
St = seasonal component
It = irregular component

10. 25.2 The Classical Time-Series Component Model
Figure 25.5
Time-Series Decomposition

11. 25.3 Moving Average and Seasonally Adjusted Time-Series
（25.3）
（25.4）
（25.5）

12. 25.3 Moving Average and Seasonally Adjusted Time-Series
Table Weighted average

13. 24.3 Moving Average and Seasonally Adjusted Time-Series
（25.6）

14. 25.3 Moving Average and Seasonally Adjusted Time-Series

15. 25.3 Moving Average and Seasonally Adjusted Time-Series

16. 25.3 Moving Average and Seasonally Adjusted Time-Series
（25.7）
（25.7a）
（25.8）

17. 25.3 Moving Average and Seasonally Adjusted Time-Series
（25.9）

18. 25.3 Moving Average and Seasonally Adjusted Time-Series

19. 25.3 Moving Average and Seasonally Adjusted Time-Series

20. 25.3 Moving Average and Seasonally Adjusted Time-Series
Figure 25.7 Trend of Ratio for Johnson & Johnson

21. 25.3 Moving Average and Seasonally Adjusted Time-Series
（25.10）

22. 25.3 Moving Average and Seasonally Adjusted Time-Series
Figure Adjusted Earnings per Share (EPS) of Johnson & Johnson

23. 25.4 Linear and Log-Linear Time Trend Regressions
（25.11）
（25.12）
（25.13）

24. 25.4 Linear and Log-Linear Time Trend Regressions

25. 25.4 Linear and Log-Linear Time Trend Regressions

26. 25.4 Linear and Log-Linear Time Trend Regressions

27. 25.4 Linear and Log-Linear Time Trend Regressions

28. 25.4 Linear and Log-Linear Time Trend Regressions

29. 25.5 Exponential Smoothing and Forecasting
（25.14）

30. 25.5 Exponential Smoothing and Forecasting
（25.15）
（25.16）

31. 25.5 Exponential Smoothing and Forecasting

32. 25.5 Exponential Smoothing and Forecasting

33. 25.5 Exponential Smoothing and Forecasting

34. 25.5 Exponential Smoothing and Forecasting

35. 25.5 Exponential Smoothing and Forecasting
（25.18）
（25.19a）
（25.19b）

36. 25.5 Exponential Smoothing and Forecasting

37. 25.5 Exponential Smoothing and Forecasting
（25.20）

38. 25.5 Exponential Smoothing and Forecasting

39. 25.5 Exponential Smoothing and Forecasting

40. 25.6 Autoregressive Forecasting Model
（25.21）
（25.22）
（25.23）

41. 25.6 Autoregressive Forecasting Model
（25.24）
（25.25）
（25.26）

42. 25.6 Autoregressive Forecasting Model

43. 25.6 Autoregressive Forecasting Model

44. 25.6 Autoregressive Forecasting Model

45. 25.6 Autoregressive Forecasting Model
(25.27)

46. 25.7 Summary
In this chapter, we examined time-series component analysis and several methods of forecasting. The major components of a time series are the trend, cyclical, seasonal, and irregular components. To analyze these time-series components, we used the moving-average method to obtain seasonally adjusted time series. After investigating the analysis of time-series components, we discussed several forecasting models in detail. These forecasting models are linear time trend regression, simple exponential smoothing, the Holt-Winters forecasting model without seasonality, the Holt-Winters forecasting model with seasonality, and autoregressive forecasting.
Many factors determine the power of any forecasting model. They include the time horizon of the forecast, the stability of variance of data, and the presence of a trend, seasonal, or cyclical component.

47. Appendix 25A. The X-11 Model for Decomposing Time- Series Components
Table 25A.1

48. Appendix 25A. The X-11 Model for Decomposing Time- Series Components
Figure 25A.1
Original Sales and the X-11
Final Component Series
of Caterpillar,
Source: J. A. Gentry and C. F. Lee, “Measuring and Interpreting Time, Firm and Ledger Effect,” in Cheng F. Lee(1983), Financial Analysis and Planning: Theory and Application, A book of Readings

49. Appendix 25A. The X-11 Model for Decomposing Time- Series Components
Table 25A.2

50. Appendix 25A. The X-11 Model for Decomposing Time- Series Components

51. Appendix 25A. The X-11 Model for Decomposing Time- Series Components
Table 25A.3 Relative Contributions of Components to Changes in Caterpillar Sales for 1-, 2-, 3-, and Quarter Time Spans
Relative Contribution (in percent)
Span in Quarters
Trend-Cycle
Seasonal
Irregular
Total 1
17.86
29.27
52.88
100 2
46.94
28.44
24.62 3
68.50
13.08
18.42 4
82.58
0.15
17.27

52. Appendix 25B. The Holt-Winters Forecasting Model for Seasonal Series

53. Appendix 25B. The Holt-Winters Forecasting Model for Seasonal Series

54. Appendix 25B. The Holt-Winters Forecasting Model for Seasonal Series

55. Appendix 25B. The Holt-Winters Forecasting Model for Seasonal Series

56. Appendix 25B. The Holt-Winters Forecasting Model for Seasonal Series

57. Appendix 25B. The Holt-Winters Forecasting Model for Seasonal Series

58. Appendix 25B. The Holt-Winters Forecasting Model for Seasonal Series

59. Appendix 25B. The Holt-Winters Forecasting Model for Seasonal Series

60. Appendix 25B. The Holt-Winters Forecasting Model for Seasonal Series