1. Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng F. Lee Rutgers University Chapter 24 Time-Series: Analysis, Model, and Forecasting

2. Outline  24.1 Introduction  24.2 The Classical Time-Series Component Model  24.3 Moving Average and Seasonally Adjusted Time-Series  24.4 Linear and Log-Linear Time Trend Regressions  24.5 Exponential Smoothing and Forecasting  24.6 Autoregressive Forecasting Model  Appendix 24A. The X-11 Model for Decomposing Time-Series Components  Appendix 24B. The Holt-Winters Forecasting Model for Seasonal Series

3. 24.2 The Classical Time-Series Component Model Table 24.1 Earnings per share of Philip Morris YearEPS 1977$1.399 19781.698 19792.043 19802.315 19812.635 19823.115 19833.59 19843.62 19855.235 19866.2 19877.84

4. 24.2 The Classical Time-Series Component Model Figure 24.1 Earnings per share of Philip Morris

5. 24.2 The Classical Time-Series Component Model Table 24.2 Quarterly Earnings per share of IBM Corporation Quarter Year1234 1995$2.12$2.97$-0.96$3.09 19961.412.512.453.93 19972.371.461.382.16 19981.081.541.62.55 19991.611.320.971.16 20000.851.11.111.52 200111.170.921.35 20020.690.030.780.6 20030.80.991.041.59 20040.811.030.931.7 20050.861.140.952.02 20061.091.311.472.35

6. 24.2 The Classical Time-Series Component Model Figure 24.2 Quarterly Earnings per share of IBM

7. 24.2 The Classical Time-Series Component Model Figure 24.3 S&P 500 Composite Index, 76/1-88/3

8. 24.2 The Classical Time-Series Component Model Figure 24.4 Three-Month Rate on Eurodollar Deposits, U.S. T-Bills, 1985-1988 (Quarterly Date)

9. 24.2 The Classical Time-Series Component Model Figure 24.5 Time-Series Decomposition

10. 24.2 The Classical Time-Series Component Model （ 24.1 ） （ 24.2 ） where T t = trend component C t = cyclical component S t = seasonal component I t = irregular component

11. 24.3Moving Average and Seasonally Adjusted Time-Series （ 24.3 ） （ 24.4 ） （ 24.5 ）

12. 24.3Moving Average and Seasonally Adjusted Time-Series Table 24.3

13. 24.3Moving Average and Seasonally Adjusted Time-Series （ 24.6 ）

14. 24.3Moving Average and Seasonally Adjusted Time-Series

15. （ 24.7 ） （ 24.7a ） （ 24.8 ）

16. 24.3Moving Average and Seasonally Adjusted Time-Series Figure 24.6 Earnings per Share Versus Moving-Average EPS for Johnson & Johnson

17. 24.3Moving Average and Seasonally Adjusted Time-Series （ 24.9 ）

18. 24.3Moving Average and Seasonally Adjusted Time-Series

20. Figure 24.7 Trend of Ratio for Johnson & Johnson

21. 24.3Moving Average and Seasonally Adjusted Time-Series （ 24.10 ）

22. 24.3Moving Average and Seasonally Adjusted Time-Series Figure 24.8 Adjusted Earnings per Share (EPS) of Johnson & Johnson

23. 24.4 Linear and Log-Linear Time Trend Regressions （ 24.11 ） （ 24.12 ） （ 24.13 ）

24. 24.4 Linear and Log-Linear Time Trend Regressions

25. Figure 24.9 Ford’s Annual Sales (1968-1990)

26. 24.4 Linear and Log-Linear Time Trend Regressions Figure 24.10 SAS Printout for Least-Squares Fit (Straight-Line Method) to Model: MODEL1 Department Variable: SALES Analysis of Variance SourceDF Sum of Squares Mean Square F Value Prob ＞ F Model110150900144 216.8290.0001 Error21 982834678.18 46801651.342 C Total22 11133734822 Root MSE6841.17324R-square0.9117 Dep Mean41245.17000Adj. R-sq0.9075 C. V.16.58660

27. 24.4 Linear and Log-Linear Time Trend Regressions Figure 24.10 SAS Printout for Least-Squares Fit (Straight-Line Method) to (Cont’d) Parameter Estimates VariableDF Parameter Estimate Standard Error T for H0: Parameter=0 Prob ＞ ¦ T ¦ INTERCEP13239.9485382948.62305441.0990.2843 PERIOD13167.101789215.0504383814.7270.0001 Durbin-Watson D0.405 (For Number of Obs.)23 1st Order Autocorrelation0.751

28. 24.4 Linear and Log-Linear Time Trend Regressions Figure 24.11 Observation (Year 1-23) and Forecast (Year 24-30) Sales Using the Straight-Line Model

29. 24.4 Linear and Log-Linear Time Trend Regressions

30. 24.5 Exponential Smoothing and Forecasting （ 24.14 ）

31. 24.5 Exponential Smoothing and Forecasting （ 24.15 ） （ 24.16 ）

32. 24.5 Exponential Smoothing and Forecasting

34. Figure 24.12 Annual Earnings per Share of J&J (Simple Exponential Smoothing)

35. 24.5 Exponential Smoothing and Forecasting Figure 24.13 Annual Earnings per Share of IBM (Simple Exponential Smoothing)

36. 24.5 Exponential Smoothing and Forecasting （ 24.18 ） （ 24.19a ） （ 24.19b ）

37. 24.5 Exponential Smoothing and Forecasting

38. Figure 24.14 Annual Earnings per Share of J&J with Forecasts Based on the Holt-Winters Model

39. 24.5 Exponential Smoothing and Forecasting Figure 24.15 Annual Earnings per Share of IBM with Forecasts Based on the Holt-Winters Model

40. 24.5 Exponential Smoothing and Forecasting （ 24.20 ）

41. 24.6 Autoregressive Forecasting Model （ 24.21 ） （ 24.22 ） （ 24.23 ）

42. 24.6 Autoregressive Forecasting Model

44. Figure 24.16 Quarterly Sales Data for Johnson & Johnson

45. 24.6 Autoregressive Forecasting Model （ 24.24 ） （ 24.25 ） （ 24.26 ）

46. 24.6 Autoregressive Forecasting Model (24.27)

47. 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.

48. Appendix 24A. The X-11 Model for Decomposing Time- Series Components （ 24A.1 ） Table 24A.1

49. Appendix 24A. The X-11 Model for Decomposing Time- Series Components Figure 24A.1 Original Sales and the X-11 Final Component Series of Caterpillar, 1969-1980 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

50. Appendix 24A. The X-11 Model for Decomposing Time- Series Components Table 24A.2

51. Appendix 24A. The X-11 Model for Decomposing Time- Series Components （ 24A.2 ）

52. Appendix 24A. The X-11 Model for Decomposing Time- Series Components Table 24A.3 Relative Contributions of Components to Changes in Caterpillar Sales for 1-, 2-, 3-, and 4- Quarter Time Spans Relative Contribution (in percent) Span in QuartersTrend-CycleSeasonalIrregularTotal 117.8629.2752.88100 246.9428.4424.62100 368.5013.0818.42100 482.58 0.1517.27100

53. Appendix 24B. The Holt-Winters Forecasting Model for Seasonal Series （ 24B.1 ） （ 24B.2 ） （ 24B.3 ） （ 24B.4 ）

54. Appendix 24B. The Holt-Winters Forecasting Model for Seasonal Series Table 24B.1

55. Appendix 24B. The Holt-Winters Forecasting Model for Seasonal Series 24B.2

56. Appendix 24B. The Holt-Winters Forecasting Model for Seasonal Series 24B.3

57. Appendix 24B. The Holt-Winters Forecasting Model for Seasonal Series

60. Figure 24B.1 Quarterly Earnings per Share of J&J (Actual and Smoothed EPS)

61. Appendix 24B. The Holt-Winters Forecasting Model for Seasonal Series Figure 24B.2 Quarterly Earnings per Share of J&J (Actual and Forecasted EPS)

62. Appendix 24B. The Holt-Winters Forecasting Model for Seasonal Series