Financial Analysis, Planning and Forecasting Theory and Application

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

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

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

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 Tt = trend component Ct = cyclical component St = seasonal component It = irregular component

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

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

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

14. 24.3 Moving Average and Seasonally Adjusted Time-Series

15. 24.3 Moving Average and Seasonally Adjusted Time-Series （24.7） （24.7a） （24.8）

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

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

18. 24.3 Moving Average and Seasonally Adjusted Time-Series

20. 24.3 Moving Average and Seasonally Adjusted Time-Series Figure 24.7 Trend of Ratio for Johnson & Johnson

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

22. 24.3 Moving 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. 24.4 Linear and Log-Linear Time Trend Regressions 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

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

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

33. 24.5 Exponential Smoothing and Forecasting

34. 24.5 Exponential Smoothing and Forecasting 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. 24.5 Exponential Smoothing and Forecasting 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. 24.6 Autoregressive Forecasting Model 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. Table 24A.1 Appendix 24A. The X-11 Model for Decomposing Time- Series Components （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. Table 24A.2 Appendix 24A. The X-11 Model for Decomposing Time- Series Components