- 1. INTRODUCTION
1.1 Four Important Practical Problems
1.2 Stochastic and Deterministic Dynamic Mathematical Models
1.3 Basic Ideas in Model Building
- 2. AUTOCORRELATION FUNCTION AND SPECTRUM OF STATIONARY PROCESSES
2.1 Autocorrelation Properties of Stationary Models
2.2 Spectral Properties of Stationary Models
A2.1 Appendix: Link Between the Sample Spectrum and Autocovariance Function Estimate
- 3. LINEAR STATIONARY MODELS
3.1 General Linear Process
3.2 Autoregressive Processes
3.3 Moving Average Processes
3.4 Mixed Autoregressive-Moving Average Processes
A3.1 Appendix: Autocovariances, Autocovariance Generating Function, and Stationarity Conditions for a General Linear Process
A3.2 Appendix: Recursive Method for Calculating Estimates of Autoregressive Parameters
- 4. LINEAR NONSTATIONARY MODELS
4.1 Autoregressive Integrated Moving Average Processes
4.2 Three Explicit Forms for the Autoregressive Integrated Moving Average Model
4.3 Integrated Moving Average Processes
A4.1 Appendix: Linear Difference Equations
A4.2 Appendix: IMA(0, 1, 1) Process With Deterministic Drift
A4.3 Appendix: ARIMA Processes With Added Noise
- 5. FORECASTING
5.1 Minimum Mean Square Error Forecasts and Their Properties
5.2 Calculating and Updating Forecasts
5.3 Forecast Function and Forecast Weights
5.4 Examples of Forecast Functions and Their Updating
5.5 Use of State Space Model Formulation for Exact Forecasting
5.6 Summary
A5.1 Appendix: Correlations Between Forecast Errors
A5.2 Appendix: Forecast Weights for Any Lead Time
A5.3 Appendix: Forecasting in Terms of the General Integrated Form
- 6. MODEL IDENTIFICATION
6.1 Objectives of Identification
6.2 Identification Techniques
6.3 Initial Estimates for the Parameters
6.4 Model Multiplicity
A6.1 Appendix: Expected Behavior of the Estimated Autocorrelation Function for a Nonstationary Process
A6.2 Appendix: General Method for Obtaining Initial Estimates of the Parameters of a Mixed Autoregressive-Moving Average Process
- 7. MODEL ESTIMATION
7.1 Study of the Likelihood and Sum of Squares Functions
7.2 Nonlinear Estimation
7.3 Some Estimation Results for Specific Models
7.4 Estimation Using Bayes' Theorem
7.5 Likelihood Function Based on the State Space Model
A7.1 Appendix: Review of Normal Distribution Theory
A7.2 Appendix: Review of Linear Least Squares Theory
A7.3 Appendix: Exact Likelihood Function for Moving Average and Mixed Processes
A7.4 Appendix: Exact Likelihood Function for an Autoregressive Process
A7.5 Appendix: Examples of the Effect of Parameter Estimation Errors on Probability Limits for Forecasts
A7.6 Appendix: Special Note on Estimation of Moving Average Parameters
- 8. MODEL DIAGNOSTIC CHECKING
8.1 Checking the Stochastic Model
8.2 Diagnostic Checks Applied to Residuals
8.3 Use of Residuals to Modify the Model
- 9. SEASONAL MODELS
9.1 Parsimonious Models for Seasonal Time Series
9.2 Representation of the Airline Data by a Multiplicative (0, 1, 1) X (0, 1, 1)_12 Seasonal Model
9.3 Some Aspects of More General Seasonal Models
9.4 Structural Component Models and Deterministic Seasonal Components
A9.1 Appendix: Autocovariances for Some Seasonal Models
- 10. TRANSFER FUNCTION MODELS
10.1 Linear Transfer Function Models
10.2 Discrete Dynamic Models Represented by Difference Equations
10.3 Relation Between Discrete and Continuous Models
A10.1 Appendix: Continuous Models With Pulsed Inputs
A10.2 Appendix: Nonlinear Transfer Functions and Linearization
- 11. IDENTIFICATION, FITTING, AND CHECKING OF TRANSFER FUNCTION MODELS
11.1 Cross Correlation Function
11.2 Identification of Transfer Function Models
11.3 Fitting and Checking Transfer Function Models
11.4 Some Examples of Fitting and Checking Transfer Function Models
11.5 Forecasting Using Leading Indicators
11.6 Some Aspects of the Design of Experiments to Estimate Transfer Functions
A11.1 Appendix: Use of Cross Spectral Analysis for Transfer Function Model Identification
A11.2 Appendix: Choice of Input to Provide Optimal Parameter Estimates
- 12. INTERVENTION ANALYSIS MODELS AND OUTLIER DETECTION
12.1 Intervention Analysis Methods
12.2 Outlier Analysis for Time Series
12.3 Estimation for ARMA Models With Missing Values
- 13. ASPECTS OF PROCESS CONTROL
13.1 Process Monitoring and Process Adjustment
13.2 Process Adjustment Using Feedback Control
13.3 Excessive Adjustment Sometimes Required by MMSE Control
13.4 Minimum Cost Control With Fixed Costs of Adjustment and Monitoring
13.5 Monitoring Values of Parameters of Forecasting and Feedback Adjustment Schemes
A13.1 Appendix: Feedback Control Schemes Where the Adjustment Variance Is Restricted
A13.2 Appendix: Choice of the Sampling Interval
- COLLECTION OF TABLES AND CHARTS
- COLLECTION OF TIME SERIES USED FOR EXAMPLES IN THE TEXT AND IN EXERCISES
- REFERENCES
- EXERCISES AND PROBLEMS
- AUTHOR INDEX
- SUBJECT INDEX