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

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

24.2 The Classical Time-Series Component Model Table 24.1 Earnings per share of Philip Morris YearEPS 1977$

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

24.2 The Classical Time-Series Component Model Table 24.2 Quarterly Earnings per share of IBM Corporation Quarter Year $2.12$2.97$-0.96$

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

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

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

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

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

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

24.3Moving Average and Seasonally Adjusted Time-Series Table 24.3

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

24.3Moving Average and Seasonally Adjusted Time-Series

（ 24.7 ） （ 24.7a ） （ 24.8 ）

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

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

24.3Moving Average and Seasonally Adjusted Time-Series

Figure 24.7 Trend of Ratio for Johnson & Johnson

24.3Moving Average and Seasonally Adjusted Time-Series （ ）

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

24.4 Linear and Log-Linear Time Trend Regressions （ ） （ ） （ ）

24.4 Linear and Log-Linear Time Trend Regressions

Figure 24.9 Ford’s Annual Sales ( )

24.4 Linear and Log-Linear Time Trend Regressions Figure 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 Model Error C Total Root MSE R-square Dep Mean Adj. R-sq C. V

24.4 Linear and Log-Linear Time Trend Regressions Figure 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 ¦ INTERCEP PERIOD Durbin-Watson D0.405 (For Number of Obs.)23 1st Order Autocorrelation0.751

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

24.4 Linear and Log-Linear Time Trend Regressions

24.5 Exponential Smoothing and Forecasting （ ）

24.5 Exponential Smoothing and Forecasting （ ） （ ）

24.5 Exponential Smoothing and Forecasting

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

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

24.5 Exponential Smoothing and Forecasting （ ） （ 24.19a ） （ 24.19b ）

24.5 Exponential Smoothing and Forecasting

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

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

24.5 Exponential Smoothing and Forecasting （ ）

24.6 Autoregressive Forecasting Model （ ） （ ） （ ）

24.6 Autoregressive Forecasting Model

Figure Quarterly Sales Data for Johnson & Johnson

24.6 Autoregressive Forecasting Model （ ） （ ） （ ）

24.6 Autoregressive Forecasting Model (24.27)

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.

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

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, 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

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

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

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

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

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

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

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

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

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

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

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