Yaffee, Robert

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Introduction toTime SeriesAnalysis andForecastingwith Applications of SAS and SPSSRobert A. YaffeeStatistics and Social Science GroupAcademie Computing Service of the Information Technology ServicesNew York UniversityNew York, New YorkandDivision of Geriatrie PsychiatryState University of New York Health Science Center at BrooklynBrooklyn, NYwithMonnie McGeeHunter CollegeCity University of New YorkNew York, New YorkACADEMIC PRESS, INC.An Imprint of ElsevierAmsterdam Boston Heidelberg London New York Oxford Paris San DiegoSan Francisco Singapore Sydney TokyoContentsPreface	 xvChapter 1Introduction and Overview1.1. Purpose	 11.2. Time Series	 21.3. Missing Data	 31.4. Sample Size	 31.5. Representativeness	 41.6. Scope of Application	 41.7. Stochastic and Deterministic Processes	 51.8. Stationarity	 51.9. Methodological Approaches 	 71.10. Importance	 91.11. Notation	 91.11.1. Gender	 91.11.2. Summation	 101.11.3. Expectation	 111.11.4. Lag Operator 	 121.11.5. The Difference Operator	 121.11.6. Mean-Centering the Series	 12References	 13Chapter 2Extrapolative and Decomposition Models2.1. Introduction	 15viiviii	 Contents2.2. Goodness-of-Fit Indicators 	 152.3. Averaging Techniques 	 182.3.1. The Simple Average	 182.3.2. The Single Moving Average 	 182.3.3. Centered Moving Averages	 202.3.4. Double Moving Averages 	 202.3.5. Weighted Moving Averages	 222.4. Exponential Smoothing 	 232.4.1. Simple Exponential Smoothing 	 232.4.2. Holt's Linear Exponential Smoothing 	 322.4.3. The Dampened Trend Linear ExponentialSmoothing Model	 382.4.4. Exponential Smoothing for Series with Trend andSeasonality: Winter's Methods 	 392.4.5. Basic Evaluation of Exponential Smoothing 	 432.5. Decomposition Methods	 452.5.1. Components of a Series 	 452.5.2. Trends	 462.5.3. Seasonality	 502.5.4. Cycles	 502.5.5. Background	 502.5.6. Overview of X-11	 522.6. New Features of Census X-12	 66References	 66Chapter 3Introduction to Box-Jenkins Time Series Analysis3.1. Introduction	 693.2. The Importance of Time Series Analysis Modeling	693.3. Limitations	 703.4. Assumptions	 703.5. Time Series	 743.5.1. Moving Average Processes	743.5.2. Autoregressive Processes	763.5.3. ARMA Processes	 773.5.4. Nonstationary Series and Transformationsto Stationarity	 773.6. Tests for Nonstationarity	 813.6.1. The Dickey-Fuller Test	81Contents	 ix3.6.2. Augmented Dickey-Fuller Test	 843.6.3. Assumptions of the Dickey-Fuller andAugmented Dickey-Fuller Tests	 853.6.4. Programming the Dickey-Fuller Test	 863.7. Stabilizing the Variance	 903.8. Structural or Regime Stability	 923.9. Strict Stationarity	 933.10. Implications of Stationarity	 943.10.1. For Autoregression	 943.10.2. Implications of Stationarity for MovingAverage Processes	 97References	 99Chapter 4The Basic ARIMA Model4.1. Introduction to ARIMA	 1014.2. Graphical Analysis of Time Series Data	 1024.2.1. Time Sequence Graphs	 1024.2.2. Correlograms and Stationarity 	 1064.3. Basic Formulation of the AutoregressiveIntegrated Moving Average Model 	 1084.4. The Sample Autocorrelation Function	 1104.5. The Standard Error of the ACF	 1184.6. The Bounds of Stationarity and Invertibility	 1194.7. The Sample Partial Autocorrelation Function	 1224.7.1. Standard Error of the PACF	 1254.8. Bounds of Stationarity and Invertibility Reviewed	 1254.9. Other Sample Autocorrelation Functions 	 1264.10. Tentative Identification of Characteristic Patterns ofIntegrated, Autoregressive, Moving Average, andARMA Processes	 1284.10.1. Preliminary Programming Syntax forIdentification of the Model	 1284.10.2. Stationarity Assessment	 1324.10.3. Identifying Autoregressive Models	 1344.10.4. Identifying Moving Average Models	 1374.10.5. Identifying Mixed Autoregressive-MovingAverage Models	 142References	 149x	 ContentsChapter 5Seasonal ARIMA Models5.1. Cyclicity	 1515.2. Seasonal Nonstationarity	 1545.3. Seasonal Differencing	 1615.4. Multiplicative Seasonal Models	 1625.4.1. Seasonal Autoregressive Models	 1645.4.2. Seasonal Moving Average Models	 1665.4.3. Seasonal Autoregressive MovingAverage Models	 1685.5. The Autocorrelation Structure of SeasonalARIMA Models	 1695.6. Stationarity and Invertibility of SeasonalARIMA Models	 1705.7. A Modeling Strategy for the SeasonalARIMA Model	 1715.7.1. Identification of Seasonal Nonstationarity	1715.7.2. Purely Seasonal Models	1715.7.3. A Modeling Strategy for General MultiplicativeSeasonal Models	 1735.8. Programming Seasonal MultiplicativeBox—Jenkins Models	1835.8.1. SAS Programming Syntax	1835.8.2. SPSS Programming Syntax	 1855.9. Alternative Methods of Modeling Seasonality	1865.10. The Question of Deterministic or StochasticSeasonality	 188References	 189Chapter 6Estimation and Diagnosis6.1. Introduction6.2. Estimation6.2.1. Conditional Least Squares6.2.2. Unconditional Least Squares6.2.3. Maximum Likelihood Estimation6.2.4. Computer Applications6.3. Diagnosis of the ModelReferences191191192195198204208213Contents	 xiChapter 7Metadiagnosis and Forecasting7.1. Introduction	 2157.2. Metadiagnosis 	 2177.2.1. Statistical Program Output ofMetadiagnostic Criteria	 2217.3. Forecasting with Box–Jenkins Models	 2227.3.1. Forecasting Objectives	 2227.3.2. Basic Methodology of Forecasting 	 2247.3.3. The Forecast Function	 2257.3.4. The Forecast Error	 2327.3.5. Forecast Error Variance	 2327.3.6. Forecast Confidence Intervals	 2337.3.7. Forecast Profiles for Basic Processes	 2347.4. Characteristics of the Optimal Forecast 	 2447.5. Basic Combination of Forecasts	 2457.6. Forecast Evaluation	 2487.7. Statistical Package Forecast Syntax	 2517.7.1. Introduction	 2517.7.2. SAS Syntax	 2527.7.3. SPSS Syntax	 2547.8. Regression Combination of Forecasts	 256References	 263Chapter 8Intervention Analysis8.1. Introduction: Event Interventions andTheir Impacts	 2658.2. Assumptions of the Event Intervention(Impact) Model	 2678.3. Impact Analysis Theory	 2688.3.1. Intervention Indicators 	 2688.3.2. The Intervention (Impulse Response) Function	 2708.3.3. The Simple Step Function: Abrupt Onset,Permanent Duration	 2708.3.4. First-Order Step Function: Gradual Onset,Permanent Duration	 2728.3.5. Abrupt Onset, Temporary Duration	 276xii	 Contents8.3.6. Abrupt Onset and Oscillatory Decay	 2788.3.7. Graduated Onset and Gradual Decay	 2798.4. Significance Tests for Impulse Response Functions	 2808.5. Modeling Strategies for Impact Analysis	 2828.5.1. The Box-Jenkins-Tiao Strategy	 2838.5.2. Full Series Modeling Strategy	 2858.6. Programming Impact Analysis 	 2888.6.1. Art Example of SPSS Impact Analysis Syntax 	 2908.6.2. An Example of SAS Impact Analysis Syntax 	 2978.6.3. Example: The Impact of Watergate an NixonPresidential Approval Ratings	 3148.7. Applications of Impact Analysis	 3428.8. Advantages of Intervention Analysis 	 3458.9. Limitations of Intervention Analysis 	 346References	 350Chapter 9Transfer Function Models9.1. Definition of a Transfer Function	 3539.2. Importance	 3549.3. Theory of the Transfer Function Model 	 3559.3.1. The Assumption of the Single-Input Case	 3559.3.2. The Basic Nature of the Single-InputTransfer Function	 3559.4. Modeling Strategies	 3689.4.1. The Conventional Box-JenkinsModeling Strategy	 3689.4.2. The Linear Transfer Function Modeling Strategy 	 3999.5. Cointegration	 4209.6. Long-Run and Short-Run Effects inDynamic Regression	 4219.7. Basic Characteristics of a Good Time Series Model	422References	 423Chapter 10Autoregressive Error Models10.1. The Nature of Serial Correlation of Error 	 42510.1.1. Regression Analysis and the Consequences ofAutocorrelated Error	 426Contents	 xiii10.2. Sources of Autoregressive Error	 43510.3. Autoregressive Models with SeriallyCorrelated Errors	 43710.4. Tests for Serial Correlation of Error	 43710.5. Corrective Algorithms for Regression Models withAutocorrelated Error	 43910.6. Forecasting with Autocorrelated Error Models 	 44110.7. Programming Regression withAutocorrelated Errors	 44310.7.1. SAS PROC AUTOREG	 44310.7.2. SPSS ARIMA Procedures for AutoregressiveError Models	 45210.8. Autoregression in Combining Forecasts	 45810.9. Models with Stochastic Variance 	 46210.9.1. ARCH and GARCH Models 	 46310.9.2. ARCH Models for Combining Forecasts 	 464References	 465Chapter 11A Review of Model and Forecast Evaluation11.1. Model and Forecast Evaluation 	 46711.2. Model Evaluation	 46811.3. Comparative Forecast Evaluation 	 46911.3.1. Capability of Forecast Methods 	 47111.4. Comparison of Individual Forecast Methods	 47611.5. Comparison of Combined Forecast Models	 477References	 478Chapter 12Power Analysis and Sample Size Determination forWell-Known Time Series ModelsMonnie McGee12.1. Census X-11	 48212.2. Box–Jenkins Models	 48312.3. Tests for Nonstationarity 	 48612.4. Intervention Analysis and Transfer Functions	 48712.5. Regression with Autoregressive Errors 	 490xiv	 Contents	12.6. Conclusion	 491	References	 492Appendix A	 495Glossary	 497Index	 513

Introduction to Time Series Analysis and Forecasting: With Applications of SAS and SPSS

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