Financial Analysis, Planning and Forecasting Theory and Application

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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

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

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

25.2 The Classical Time-Series Component Model Figure 25.1 Earnings per share of Johnson & Johnson

25.2 The Classical Time-Series Component Model

25.2 The Classical Time-Series Component Model

25.2 The Classical Time-Series Component Model

25.2 The Classical Time-Series Component Model

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

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

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

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

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

25.3 Moving Average and Seasonally Adjusted Time-Series

25.3 Moving Average and Seasonally Adjusted Time-Series

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

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

25.3 Moving Average and Seasonally Adjusted Time-Series

25.3 Moving Average and Seasonally Adjusted Time-Series

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

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

25.3 Moving Average and Seasonally Adjusted Time-Series Figure 25.8 Adjusted Earnings per Share (EPS) of Johnson & Johnson

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

25.4 Linear and Log-Linear Time Trend Regressions

25.4 Linear and Log-Linear Time Trend Regressions

25.4 Linear and Log-Linear Time Trend Regressions

25.4 Linear and Log-Linear Time Trend Regressions

25.4 Linear and Log-Linear Time Trend Regressions

25.5 Exponential Smoothing and Forecasting （25.14）

25.5 Exponential Smoothing and Forecasting （25.15）（25.16）

25.5 Exponential Smoothing and Forecasting

25.5 Exponential Smoothing and Forecasting

25.5 Exponential Smoothing and Forecasting

25.5 Exponential Smoothing and Forecasting

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

25.5 Exponential Smoothing and Forecasting

25.5 Exponential Smoothing and Forecasting （25.20）

25.5 Exponential Smoothing and Forecasting

25.5 Exponential Smoothing and Forecasting

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

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

25.6 Autoregressive Forecasting Model

25.6 Autoregressive Forecasting Model

25.6 Autoregressive Forecasting Model

25.6 Autoregressive Forecasting Model (25.27)

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.

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

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, 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

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

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

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 4- 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

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

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

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

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

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

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

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

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

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