Intro -- Wiley Series in Probability and Statistics -- Title Page -- Copyright -- Dedication -- Preface to the Fifth Edition -- Preface to the Fourth Edition -- Preface to the Third Edition -- Chapter 1: Introduction -- 1.1 Five Important Practical Problems -- 1.2 Stochastic and Deterministic Dynamic Mathematical Models -- 1.3 Basic Ideas in Model Building -- Appendix A1.1 Use Of The R Software -- Exercises -- Part One: Stochastic Models and Their Forecasting -- Chapter 2: Autocorrelation Function and Spectrum of Stationary Processes -- 2.1 Autocorrelation Properties of Stationary Models -- 2.2 Spectral Properties of Stationary Models -- Appendix A2.1 Link Between the Sample Spectrum and Autocovariance Function Estimate -- Exercises -- Chapter 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 -- Appendix A3.1 Autocovariances, Autocovariance Generating Function, and Stationarity Conditions for a General Linear Process -- Appendix A3.2 Recursive Method for Calculating Estimates of Autoregressive Parameters -- Exercises -- Chapter 4: Linear Nonstationary Models -- 4.1 Autoregressive Integrated Moving Average Processes -- 4.2 Three Explicit Forms for the Arima Model -- 4.3 Integrated Moving Average Processes -- Appendix A4.1 Linear Difference Equations -- Appendix A4.2 IMA(0, 1, 1) Process with Deterministic Drift -- Appendix A4.3 Arima Processes with Added Noise -- Exercises -- Chapter 5: Forecasting -- 5.1 Minimum Mean Square Error Forecasts and Their Properties -- 5.2 Calculating Forecasts and Probability Limits -- 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.

Appendix A5.1 Correlation Between Forecast Errors -- Appendix A5.2 Forecast Weights for Any Lead Time -- Appendix A5.3 Forecasting in Terms of the General Integrated Form -- Exercises -- Part Two: Stochastic Model Building -- Chapter 6: Model Identification -- 6.1 Objectives of Identification -- 6.2 Identification Techniques -- 6.3 Initial Estimates for the Parameters -- 6.4 Model Multiplicity -- Appendix A6.1 Expected Behavior of the Estimated Autocorrelation Function for a Nonstationary Process -- Exercises -- Chapter 7: Parameter 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 Likelihood Function Based on the State-Space Model -- 7.5 Estimation Using Bayes' Theorem -- Appendix A7.1 Review of Normal Distribution Theory -- Appendix A7.2 Review of Linear Least-Squares Theory -- Appendix A7.3 Exact Likelihood Function for Moving Average and Mixed Processes -- Appendix A7.4 Exact Likelihood Function for an Autoregressive Process -- Appendix A7.5 Asymptotic Distribution of Estimators for Autoregressive Models -- Appendix A7.6 Examples of the Effect of Parameter Estimation Errors on Variances of Forecast Errors and Probability Limits for Forecasts -- Appendix A7.7 Special Note on Estimation of Moving Average Parameters -- Exercises -- Chapter 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 -- Exercises -- Chapter 9: Analysis of Seasonal Time Series -- 9.1 Parsimonious Models for Seasonal Time Series -- 9.2 Representation of the Airline Data by a Multiplicative (0, 1, 1) × (0, 1, 1)12 Model -- 9.3 Some Aspects of More General Seasonal Arima Models -- 9.4 Structural Component Models and Deterministic Seasonal Components.

9.5 Regression Models with Time Series Error Terms -- Appendix A9.1 Autocovariances for some Seasonal Models -- Exercises -- Chapter 10: Additional Topics and Extensions -- 10.1 Tests for Unit Roots in Arima Models -- 10.2 Conditional Heteroscedastic Models -- 10.3 Nonlinear Time Series Models -- 10.4 Long Memory Time Series Processes -- Exercises -- Part Three: Transfer Function and Multivariate Model Building -- Chapter 11: Transfer Function Models -- 11.1 Linear Transfer Function Models -- 11.2 Discrete Dynamic Models Represented by Difference Equations -- 11.3 Relation Between Discrete and Continuous Models -- Appendix A11.1 Continuous Models with Pulsed Inputs -- Appendix A11.2 Nonlinear Transfer Functions and Linearization -- Exercises -- Chapter 12: Identification, Fitting, and Checking of Transfer Function Models -- 12.1 Cross-Correlation Function -- 12.2 Identification of Transfer Function Models -- 12.3 Fitting and Checking Transfer Function Models -- 12.4 Some Examples of Fitting and Checking Transfer Function Models -- 12.5 Forecasting with Transfer Function Models Using Leading Indicators -- 12.6 Some Aspects of the Design of Experiments to Estimate Transfer Functions -- Appendix A12.1 Use of Cross-Spectral Analysis for Transfer Function Model Identification -- Appendix A12.2 Choice of Input to Provide Optimal Parameter Estimates -- Exercises -- Chapter 13: Intervention Analysis, Outlier Detection, and Missing Values -- 13.1 Intervention Analysis Methods -- 13.2 Outlier Analysis for Time Series -- 13.3 Estimation for ARMA Models with Missing Values -- Exercises -- Chapter 14: Multivariate Time Series Analysis -- 14.1 Stationary Multivariate Time Series -- 14.2 Vector Autoregressive Models -- 14.3 Vector Moving Average Models -- 14.4 Vector Autoregressive--Moving Average Models.

14.5 Forecasting for Vector Autoregressive--Moving Average Processes -- 14.6 State-Space form of the Varma Model -- 14.7 Further Discussion of Varma Model Specification -- 14.8 Nonstationarity and Cointegration -- Appendix A14.1 Spectral Characteristics and Linear Filtering Relations for Stationary Multivariate Processes -- Exercises -- Part Four: Design of Discrete Control Schemes -- Chapter 15: Aspects of Process Control -- 15.1 Process Monitoring and Process Adjustment -- 15.2 Process Adjustment Using Feedback Control -- 15.3 Excessive Adjustment Sometimes Required by MMSE Control -- 15.4 Minimum Cost Control with Fixed Costs of Adjustment and Monitoring -- 15.5 Feedforward Control -- 15.6 Monitoring Values of Parameters of Forecasting and Feedback Adjustment Schemes -- Appendix A15.1 Feedback Control Schemes Where the Adjustment Variance is Restricted -- Appendix A15.2 Choice of the Sampling Interval -- Exercises -- Part Five: Charts and Tables -- Collection of Tables and Charts -- Collection of Time Series Used for Examples in the Text and in Exercises -- References -- Index -- End User License Agreement.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2022. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.