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E-raamat: Time Series Analysis: Forecasting and Control

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(Formerly of University of Wisconsin-Madison), (University of Wisconsin-Madison), (Lancaster University, UK), (University of Wisconsin-Madison)
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Time Series Analysis: Forecasting and ControlSuurem pilt
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Praise for the Fourth Edition

“The book follows faithfully the style of the original edition. The approach is heavily motivated by real-world time series, and by developing a complete approach to model building, estimation, forecasting and control."

- Mathematical Reviews

Bridging classical models and modern topics, the Fifth Edition of Time Series Analysis: Forecasting and Control maintains a balanced presentation of the tools for modeling and analyzing time series. Also describing the latest developments that have occurred in the field over the past decade through applications from areas such as business, finance, and engineering, theFifth Edition continues to serve as one of the most influential and prominent works on the subject.

Time Series Analysis: Forecasting and Control, Fifth Edition provides a clearly written exploration of the key methods for building, classifying, testing, and analyzing stochastic models for time series and describes their use in five important areas of application: forecasting; determining the transfer function of a system; modeling the effects of intervention events; developing multivariate dynamic models; and designing simple control schemes. Along with these classical uses, the new edition covers modern topics with new features that include:

  • A redesigned chapter on multivariate time series analysis with an expanded treatment of Vector Autoregressive, or VAR models, along with a discussion of the analytical tools needed for modeling vector time series
  • An expanded chapter on special topics covering unit root testing, time-varying volatility models such as ARCH and GARCH, nonlinear time series models, and long memory models
  • Numerous examples drawn from finance, economics, engineering, and other related fields
  • The use of the publicly available R software for graphical illustrations and numerical calculations along with scripts that demonstrate the use of R for model building and forecasting
  • Updates to literature references throughout and new end-of-chapter exercises
  • Streamlined chapter introductions and revisions that update and enhance the exposition
Time Series Analysis: Forecasting and Control, Fifth Edition is a valuable real-world reference for researchers and practitioners in time series analysis, econometrics, finance, and related fields. The book is also an excellent textbook for beginning graduate-level courses in advanced statistics, mathematics, economics, finance, engineering, and physics.
Preface To The Fifth Edition xix
Preface To The Fourth Edition xxiii
Preface To The Third Edition xxv
1 Introduction
1(18)
1.1 Five Important Practical Problems,
2(4)
1.1.1 Forecasting Time Series,
2(1)
1.1.2 Estimation of Transfer Functions,
3(1)
1.1.3 Analysis of Effects of Unusual Intervention Events to a System,
4(1)
1.1.4 Analysis of Multivariate Time Series,
4(1)
1.1.5 Discrete Control Systems,
5(1)
1.2 Stochastic and Deterministic Dynamic Mathematical Models,
6(8)
1.2.1 Stationary and Nonstationary Stochastic Models for Forecasting and Control,
7(4)
1.2.2 Transfer Function Models,
11(2)
1.2.3 Models for Discrete Control Systems,
13(1)
1.3 Basic Ideas in Model Building,
14(3)
1.3.1 Parsimony,
14(1)
1.3.2 Iterative Stages in the Selection of a Model,
15(2)
Appendix A1.1 Use of the R Software,
17(1)
Exercises,
18(1)
Part One Stochastic Models And Their Forecasting 19(158)
2 Autocorrelation Function and Spectrum of Stationary Processes
21(26)
2.1 Autocorrelation Properties of Stationary Models,
21(13)
2.1.1 Time Series and Stochastic Processes,
21(3)
2.1.2 Stationary Stochastic Processes,
24(2)
2.1.3 Positive Definiteness and the Autocovariance Matrix,
26(3)
2.1.4 Autocovariance and Autocorrelation Functions,
29(1)
2.1.5 Estimation of Autocovariance and Autocorrelation Functions,
30(1)
2.1.6 Standard Errors of Autocorrelation Estimates,
31(3)
2.2 Spectral Properties of Stationary Models,
34(9)
2.2.1 Periodogram of a Time Series,
34(1)
2.2.2 Analysis of Variance,
35(1)
2.2.3 Spectrum and Spectral Density Function,
36(4)
2.2.4 Simple Examples of Autocorrelation and Spectral Density Functions,
40(3)
2.2.5 Advantages and Disadvantages of the Autocorrelation and Spectral Density Functions,
43(1)
Appendix A2.1 Link Between the Sample Spectrum and Autocovariance Function Estimate,
43(1)
Exercises,
44(3)
3 Linear Stationary Models
47(41)
3.1 General Linear Process,
47(7)
3.1.1 Two Equivalent Forms for the Linear Process,
47(3)
3.1.2 Autocovariance Generating Function of a Linear Process,
50(1)
3.1.3 Stationarity and Invertibility Conditions for a Linear Process,
51(1)
3.1.4 Autoregressive and Moving Average Processes,
52(2)
3.2 Autoregressive Processes,
54(14)
3.2.1 Stationarity Conditions for Autoregressive Processes,
54(2)
3.2.2 Autocorrelation Function and Spectrum of Autoregressive Processes,
56(2)
3.2.3 The First-Order Autoregressive Process,
58(1)
3.2.4 Second-Order Autoregressive Process,
59(5)
3.2.5 Partial Autocorrelation Function,
64(2)
3.2.6 Estimation of the Partial Autocorrelation Function,
66(1)
3.2.7 Standard Errors of Partial Autocorrelation Estimates,
66(1)
3.2.8 Calculations in R,
67(1)
3.3 Moving Average Processes,
68(7)
3.3.1 Invertibility Conditions for Moving Average Processes,
68(1)
3.3.2 Autocorrelation Function and Spectrum of Moving Average Processes,
69(1)
3.3.3 First-Order Moving Average Process,
70(1)
3.3.4 Second-Order Moving Average Process,
71(4)
3.3.5 Duality Between Autoregressive and Moving Average Processes,
75(1)
3.4 Mixed Autoregressive—Moving Average Processes,
75(7)
3.4.1 Stationarity and Invertibility Properties,
75(2)
3.4.2 Autocorrelation Function and Spectrum of Mixed Processes,
77(1)
3.4.3 First Order Autoregressive First-Order Moving Average Process,
78(3)
3.4.4 Summary,
81(1)
Appendix A3.1 Autocovariances, Autocovariance Generating Function, and Stationarity Conditions for a General Linear Process,
82(2)
Appendix A3.2 Recursive Method for Calculating Estimates of Autoregressive Parameters,
84(2)
Exercises,
86(2)
4 Linear Nonstationary Models ,
88(41)
4.1 Autoregressive Integrated Moving Average Processes,
88(9)
4.1.1 Nonstationary First-Order Autoregressive Process,
88(2)
4.1.2 General Model for a Nonstationary Process Exhibiting Homogeneity,
90(4)
4.1.3 General Form of the ARIMA Model,
94(3)
4.2 Three Explicit Forms for the ARIMA Model,
97(9)
4.2.1 Difference Equation Form of the Model,
97(1)
4.2.2 Random Shock Form of the Model,
98(5)
4.2.3 Inverted Form of the Model,
103(3)
4.3 Integrated Moving Average Processes,
106(10)
4.3.1 Integrated Moving Average Process of Order (0, 1, 1),
107(3)
4.3.2 Integrated Moving Average Process of Order (0, 2, 2),
110(4)
4.3.3 General Integrated Moving Average Process of Order (0, d, q),
114(2)
Appendix A4.1 Linear Difference Equations,
116(5)
Appendix A4.2 IMA(0, 1, 1) Process with Deterministic Drift,
121(1)
Appendix A4.3 ARIMA Processes with Added Noise,
122(4)
A4.3.1 Sum of Two Independent Moving Average Processes,
122(1)
A4.3.2 Effect of Added Noise on the General Model,
123(1)
A4.3.3 Example for an IMA(0, 1, 1) Process with Added White Noise,
124(1)
A4.3.4 Relation between the IMA(0, 1, 1) Process and a Random Walk,
125(1)
A4.3.5 Autocovariance Function of the General Model with Added Correlated Noise,
125(1)
Exercises,
126(3)
5 Forecasting
129(48)
5.1 Minimum Mean Square Error Forecasts and Their Properties,
129(6)
5.1.1 Derivation of the Minimum Mean Square Error Forecasts,
131(1)
5.1.2 Three Basic Forms for the Forecast,
132(3)
5.2 Calculating Forecasts and Probability Limits,
135(4)
5.2.1 Calculation of ψ Weights,
135(1)
5.2.2 Use of the ψ Weights in Updating the Forecasts,
136(1)
5.2.3 Calculation of the Probability Limits at Different Lead Times,
137(1)
5.2.4 Calculation of Forecasts Using R,
138(1)
5.3 Forecast Function and Forecast Weights,
139(5)
5.3.1 Eventual Forecast Function Determined by the Autoregressive Operator,
140(1)
5.3.2 Role of the Moving Average Operator in Fixing the Initial Values,
140(2)
5.3.3 Lead 1 Forecast Weights,
142(2)
5.4 Examples of Forecast Functions and Their Updating,
144(11)
5.4.1 Forecasting an IMA(0, 1, 1) Process,
144(3)
5.4.2 Forecasting an IMA(0, 2, 2) Process,
147(2)
5.4.3 Forecasting a General IMA(0, d, q) Process,
149(1)
5.4.4 Forecasting Autoregressive Processes,
150(3)
5.4.5 Forecasting a (1, 0, 1) Process,
153(1)
5.4.6 Forecasting a (1, 1, 1) Process,
154(1)
5.5 Use of State-Space Model Formulation for Exact Forecasting,
155(7)
5.5.1 State-Space Model Representation for the ARIMA Process,
155(2)
5.5.2 Kalman Filtering Relations for Use in Prediction,
157(3)
5.5.3 Smoothing Relations in the State Variable Model,
160(2)
5.6 Summary,
162(2)
Appendix A5.1 Correlation Between Forecast Errors,
164(2)
A5.1.1 Autocorrelation Function of Forecast Errors at Different Origins,
164(1)
A5.1.2 Correlation Between Forecast Errors at the Same Origin with Different Lead Times,
165(1)
Appendix A5.2 Forecast Weights for any Lead Time,
166(2)
Appendix A5.3 Forecasting in Terms of the General Integrated Form,
168(6)
A5.3.1 General Method of Obtaining the Integrated Form,
168(2)
A5.3.2 Updating the General Integrated Form,
170(1)
A5.3.3 Comparison with the Discounted Least-Squares Method,
171(3)
Exercises,
174(3)
Part Two Stochastic Model Building 177(218)
6 Model Identification
179(30)
6.1 Objectives of Identification,
179(1)
6.1.1 Stages in the Identification Procedure,
180(1)
6.2 Identification-Techniques,
180(14)
6.2.1 Use of the Autocorrelation and Partial Autocorrelation Functions in Identification,
180(3)
6.2.2 Standard Errors for Estimated Autocorrelations and Partial Autocorrelations,
183(2)
6.2.3 Identification of Models for Some Actual Time Series,
185(5)
6.2.4 Some Additional Model Identification Tools,
190(4)
6.3 Initial Estimates for the Parameters,
194(8)
6.3.1 Uniqueness of Estimates Obtained from the Autocovariance Function,
194(1)
6.3.2 Initial Estimates for Moving Average Processes,
194(2)
6.3.3 Initial Estimates for Autoregressive Processes,
196(1)
6.3.4 Initial Estimates for Mixed Autoregressive—Moving Average Processes,
197(1)
6.3.5 Initial Estimate of Error Variance,
198(1)
6.3.6 Approximate Standard Error for /7),
199(1)
6.3.7 Choice Between Stationary and Nonstationary Models in Doubtful Cases,
200(2)
6.4 Model Multiplicity,
202(4)
6.4.1 Multiplicity of Autoregressive—Moving Average Models,
202(2)
6.4.2 Multiple Moment Solutions for Moving Average Parameters,
204(1)
6.4.3 Use of the Backward Process to Determine Starting Values,
205(1)
Appendix A6.1 Expected Behavior of the Estimated Autocorrelation Function for a Nonstationary Process,
206(1)
Exercises,
207(2)
7 Parameter Estimation
209(75)
7.1 Study of the Likelihood and Sum-of-Squares Functions,
209(17)
7.1.1 Likelihood Function,
209(1)
7.1.2 Conditional Likelihood for an ARIMA Process,
210(1)
7.1.3 Choice of Starting Values for Conditional Calculation,
211(2)
7.1.4 Unconditional Likelihood, Sum-of-Squares Function, and Least-Squares Estimates,
213(3)
7.1.5 General Procedure for Calculating the Unconditional Sum of Squares,
216(2)
7.1.6 Graphical Study of the Sum-of-Squares Function,
218(2)
7.1.7 Examination of the Likelihood Function and Confidence Regions,
220(6)
7.2 Nonlinear Estimation,
226(10)
7.2.1 General Method of Approach,
226(1)
7.2.2 Numerical Estimates of the Derivatives,
227(1)
7.2.3 Direct Evaluation of the Derivatives,
228(1)
7.2.4 General Least-Squares Algorithm for the Conditional Model,
229(2)
7.2.5 ARIMA Models Fitted to Series A—F,
231(2)
7.2.6 Large-Sample Information Matrices and Covariance Estimates,
233(3)
7.3 Some Estimation Results for Specific Models,
236(6)
7.3.1 Autoregressive Processes,
236(2)
7.3.2 Moving Average Processes,
238(1)
7.3.3 Mixed Processes,
238(1)
7.3.4 Separation of Linear and Nonlinear Components in Estimation,
239(1)
7.3.5 Parameter Redundancy,
240(2)
7.4 Likelihood Function Based on the State-Space Model,
242(3)
7.5 Estimation Using Bayes' Theorem,
245(6)
7.5.1 Bayes' Theorem,
245(1)
7.5.2 Bayesian Estimation of Parameters,
246(1)
7.5.3 Autoregressive Processes,
247(2)
7.5.4 Moving Average Processes,
249(1)
7.5.5 Mixed Processes,
250(1)
Appendix A7.1 Review of Normal Distribution Theory,
251(5)
A7.1.1 Partitioning of a Positive-Definite Quadratic Form,
251(1)
A7.1.2 Two Useful Integrals,
252(1)
A7.1.3 Normal Distribution,
253(2)
A7.1.4 Student's t Distribution,
255(1)
Appendix A7.2 Review of Linear Least-Squares Theory,
256(3)
A7.2.1 Normal Equations and Least Squares,
256(1)
A7.2.2 Estimation of Error Variance,
257(1)
A7.2.3 Covariance Matrix of Least-Squares Estimates,
257(1)
A7.2.4 Confidence Regions,
257(1)
A7.2.5 Correlated Errors,
258(1)
Appendix A7.3 Exact Likelihood Function for Moving Average and Mixed Processes,
259(7)
Appendix A7.4 Exact Likelihood Function for an Autoregressive Process,
266(8)
Appendix A7.5 Asymptotic Distribution of Estimators for Autoregressive Models,
274(3)
Appendix A7.6 Examples of the Effect of Parameter Estimation Errors on Variances of Forecast Errors and Probability Limits for Forecasts,
277(3)
Appendix A7.7 Special Note on Estimation of Moving Average Parameters,
280(1)
Exercises,
280(4)
8 Model Diagnostic Checking
284(21)
8.1 Checking the Stochastic Model,
284(3)
8.1.1 General Philosophy,
284(1)
8.1.2 Overfitting,
285(2)
8.2 Diagnostic Checks Applied to Residuals,
287(14)
8.2.1 Autocorrelation Check,
287(2)
8.2.2 Portmanteau Lack-of-Fit Test,
289(5)
8.2.3 Model Inadequacy Arising from Changes in Parameter Values,
294(1)
8.2.4 Score Tests for Model Checking,
295(2)
8.2.5 Cumulative Periodogram Check,
297(4)
8.3 Use of Residuals to Modify the Model,
301(2)
8.3.1 Nature of the Correlations in the Residuals When an Incorrect Model Is Used,
301(1)
8.3.2 Use of Residuals to Modify the Model,
302(1)
Exercises,
303(2)
9 Analysis of Seasonal Time Series
305(47)
9.1 Parsimonious Models for Seasonal Time Series,
305(5)
9.1.1 Fitting Versus Forecasting,
306(1)
9.1.2 Seasonal Models Involving Adaptive Sines and Cosines,
307(1)
9.1.3 General Multiplicative Seasonal Model,
308(2)
9.2 Representation of the Airline Data by a Multiplicative (0, 1, 1) x (0, 1, 1)12 Model,
310(15)
9.2.1 Multiplicative (0, 1, 1) X (0, 1 , 1)12 Model,
310(1)
9.2.2 Forecasting,
311(7)
9.2.3 Model Identification,
318(2)
9.2.4 Parameter Estimation,
320(4)
9.2.5 Diagnostic Checking,
324(1)
9.3 Some Aspects of More General Seasonal ARIMA Models,
325(6)
9.3.1 Multiplicative and Nonmultiplicative Models,
325(2)
9.3.2 Model Identification,
327(1)
9.3.3 Parameter Estimation,
328(1)
9.3.4 Eventual Forecast Functions for Various Seasonal Models,
329(2)
9.3.5 Choice of Transformation,
331(1)
9.4 Structural Component Models and Deterministic Seasonal Components,
331(8)
9.4.1 Structural Component Time Series Models,
332(3)
9.4.2 Deterministic Seasonal and Trend Components and Common Factors,
335(1)
9.4.3 Estimation of Unobserved Components in Structural Models,
336(3)
9.5 Regression Models with Time Series Error Terms,
339(6)
9.5.1 Model Building, Estimation, and Forecasting Procedures for Regression Models,
340(4)
9.5.2 Restricted Maximum Likelihood Estimation for Regression Models,
344(1)
Appendix A9.1 Autocovariances for Some Seasonal Models,
345(4)
Exercises,
349(3)
10 Additional Topics and Extensions
352(43)
10.1 Tests for Unit Roots in ARIMA Models,
353(8)
10.1.1 Tests for Unit Roots in AR Models,
353(5)
10.1.2 Extensions of Unit Root Testing to Mixed ARIMA Models,
358(3)
10.2 Conditional Heteroscedastic Models,
361(16)
10.2.1 The ARCH Model,
362(4)
10.2.2 The GARCH Model,
366(1)
10.2.3 Model Building and Parameter Estimation,
367(3)
10.2.4 An Illustrative Example: Weekly S&P 500 Log Returns,
370(2)
10.2.5 Extensions of the ARCH and GARCH Models,
372(5)
10.2.6 Stochastic Volatility Models,
377(1)
10.3 Nonlinear Time Series Models,
377(8)
10.3.1 Classes of Nonlinear Models,
378(3)
10.3.2 Detection of Nonlinearity,
381(1)
10.3.3 An Empirical Example,
382(3)
10.4 Long Memory Time Series Processes,
385(7)
10.4.1 Fractionally Integrated Processes,
385(4)
10.4.2 Estimation of Parameters,
389(3)
Exercises,
392(3)
Part Three Transfer Function And Multivariate Model Building 395(164)
11 Transfer Function Models
397(31)
11.1 Linear Transfer Function Models,
397(7)
11.1.1 Discrete Transfer Function,
398(2)
11.1.2 Continuous Dynamic Models Represented by Differential Equations,
400(4)
11.2 Discrete Dynamic Models Represented by Difference Equations,
404(10)
11.2.1 General Form of the Difference Equation,
404(2)
11.2.2 Nature of the Transfer Function,
406(1)
11.2.3 First- and Second-Order Discrete Transfer Function Models,
407(5)
11.2.4 Recursive Computation of Output for Any Input,
412(1)
11.2.5 Transfer Function Models with Added Noise,
413(1)
11.3 Relation Between Discrete and Continuous Models,
414(6)
11.3.1 Response to a Pulsed Input,
415(2)
11.3.2 Relationships for First- and Second-Order Coincident Systems,
417(2)
11.3.3 Approximating General Continuous Models by Discrete Models,
419(1)
Appendix A11.1 Continuous Models with Pulsed Inputs,
420(4)
Appendix A11.2 Nonlinear Transfer Functions and Linearization,
424(2)
Exercises,
426(2)
12 Identification, Fitting, and Checking of Transfer Function Models
428(53)
12.1 Cross-Correlation Function,
429(6)
12.1.1 Properties of the Cross-Covariance and Cross-Correlation Functions,
429(2)
12.1.2 Estimation of the Cross-Covariance and Cross-Correlation Functions,
431(2)
12.1.3 Approximate Standard Errors of Cross-Correlation Estimates,
433(2)
12.2 Identification of Transfer Function Models,
435(11)
12.2.1 Identification of Transfer Function Models by Prewhitening the Input,
437(1)
12.2.2 Example of the Identification of a Transfer Function Model,
438(4)
12.2.3 Identification of the Noise Model,
442(2)
12.2.4 Some General Considerations in Identifying Transfer Function Models,
444(2)
12.3 Fitting and Checking Transfer Function Models,
446(7)
12.3.1 Conditional Sum-of-Squares Function,
446(1)
12.3.2 Nonlinear Estimation,
447(2)
12.3.3 Use of Residuals for Diagnostic Checking,
449(1)
12.3.4 Specific Checks Applied to the Residuals,
450(3)
12.4 Some Examples of Fitting and Checking Transfer Function Models,
453(8)
12.4.1 Fitting and Checking of the (las Furnace Model,
453(5)
12.4.2 Simulated Example with Two Inputs,
458(3)
12.5 Forecasting with Transfer Function Models Using Leading Indicators,
461(8)
12.5.1 Minimum Mean Square Error Forecast,
461(4)
12.5.2 Forecast of CO2 Output from Gas Furnace,
465(3)
12.5.3 Forecast of Nonstationary Sales Data Using a Leading Indicator,
468(1)
12.6 Some Aspects of the Design of Experiments to Estimate Transfer Functions,
469(2)
Appendix A12.1 Use of Cross-Spectral Analysis for Transfer Function Model Identification,
471(2)
A12.1.1 Identification of Single-Input Transfer Function Models,
471(1)
A12.1.2 Identification of Multiple-Input Transfer Function Models,
472(1)
Appendix A12.2 Choice of Input to Provide Optimal Parameter Estimates,
473(4)
A12.2.1 Design of Optimal Inputs for a Simple System,
473
A12.2.2 Numerical Example,
416(61)
Exercises,
477(4)
13 Intervention Analysis, Outlier Detection, and Missing Values
481(24)
13.1 Intervention Analysis Methods,
481(7)
13.1.1 Models for Intervention Analysis,
481(3)
13.1.2 Example of Intervention Analysis,
484(1)
13.1.3 Nature of the MLE for a Simple Level Change Parameter Model,
485(3)
13.2 Outlier Analysis for Time Series,
488(7)
13.2.1 Models for Additive and Innovational Outliers,
488(1)
13.2.2 Estimation of Outlier Effect for Known Timing of the Outlier,
489(2)
13.2.3 Iterative Procedure for Outlier Detection,
491(1)
13.2.4 Examples of Analysis of Outliers,
492(3)
13.3 Estimation for ARMA Models with Missing Values,
495(7)
13.3.1 State-Space Model and Kalman Filter with Missing Values,
496(2)
13.3.2 Estimation of Missing Values of an ARMA Process,
498(4)
Exercises,
502(3)
14 Multivariate Time Series Analysis
505(54)
14.1 Stationary Multivariate Time Series,
506(3)
14.1.1 Cross-Covariance and Cross-Correlation Matrices,
506(1)
14.1.2 Covariance Stationarity,
507(1)
14.1.3 Vector White Noise Process,
507(1)
14.1.4 Moving Average Representation of a Stationary Vector Process,
508(1)
14.2 Vector Autoregressive Models,
509(15)
14.2.1 VAR(p) Model,
509(1)
14.2.2 Moment Equations and Yule—Walker Estimates,
510(1)
14.2.3 Special Case: VAR(1) Model,
511(2)
14.2.4 Numerical Example,
513(2)
14.2.5 Initial Model Building and Least-Squares Estimation for VAR Models,
515(3)
14.2.6 Parameter Estimation and Model Checking,
518(1)
14.2.7 An Empirical Example,
519(5)
14.3 Vector Moving Average Models,
524(3)
14.3.1 Vector MA(q) Model,
524(1)
14.3.2 Special Case: Vector MA(1) Model,
525(1)
14.3.3 Numerical Example,
525(1)
14.3.4 Model Building for Vector MA Models,
526(1)
14.4 Vector Autoregressive—Moving Average Models,
527(7)
14.4.1 Stationarity and Invertibility Conditions,
527(1)
14.4.2 Covariance Matrix Properties of VARMA Processes,
528(1)
14.4.3 Nonuniqueness and Parameter Identifiability for VARMA Models,
528(1)
14.4.4 Model Specification for VARMA Processes,
529(3)
14.4.5 Estimation and Model Checking for VARMA Models,
532(1)
14.4.6 Relation of VARMA Models to Transfer Function and ARMAX Models,
533(1)
14.5 Forecasting for Vector Autoregressive—Moving Average Processes,
534(2)
14.5.1 Calculation of Forecasts from ARMA Difference Equation,
534(2)
14.5.2 Forecasts from Infinite VMA Form and Properties of Forecast Errors,
536(1)
14.6 State-Space Form of the VARMA Model,
536(3)
14.7 Further Discussion of VARMA Model Specification,
539(7)
14.7.1 Kronecker Structure for VARMA Models,
539(4)
14.7.2 An Empirical Example,
543(2)
14.7.3 Partial Canonical Correlation Analysis for Reduced-Rank Structure,
545(1)
14.8 Nonstationarity and Cointegration,
546(6)
14.8.1 Vector ARIMA Models,
546(1)
14.8.2 Cointegration in Nonstationary Vector Processes,
547(2)
14.8.3 Estimation and Inferences for Cointegrated VAR Models,
549(3)
Appendix A14.1 Spectral Characteristics and Linear Filtering Relations for Stationary Multivariate Processes,
552(2)
A14.1.1 Spectral Characteristics for Stationary Multivariate Processes,
552(1)
A14.1.2 Linear Filtering Relations for Stationary Multivariate Processes,
553(1)
Exercises,
554(5)
Part Four Design Of Discrete Control Schemes 559(58)
15 Aspects of Process
561(56)
15.1 Process Monitoring and Process Adjustment,
562(4)
15.1.1 Process Monitoring,
562(2)
15.1.2 Process Adjustment,
564(2)
15.2 Process Adjustment Using Feedback Control,
566(14)
15.2.1 Feedback Adjustment Chart,
567(2)
15.2.2 Modeling the Feedback Loop,
569(1)
15.2.3 Simple Models for Disturbances and Dynamics,
570(3)
15.2.4 General Minimum Mean Square Error Feedback Control Schemes,
573(2)
15.2.5 Manual Adjustment for Discrete Proportional—Integral Schemes,
575(3)
15.2.6 Complementary Roles of Monitoring and Adjustment,
578(2)
15.3 Excessive Adjustment Sometimes Required by MMSE Control,
580(2)
15.3.1 Constrained Control,
581(1)
15.4 Minimum Cost Control with Fixed Costs of Adjustment and Monitoring,
582(6)
15.4.1 Bounded Adjustment Scheme for Fixed Adjustment Cost,
583(1)
15.4.2 Indirect Approach for Obtaining a Bounded Adjustment Scheme,
584(1)
15.4.3 Inclusion of the Cost of Monitoring,
585(3)
15.5 Feedforward Control,
588(11)
15.5.1 Feedforward Control to Minimize Mean Square Error at the Output,
588(3)
15.5.2 An Example: Control of the Specific Gravity of an Intermediate Product,
591(2)
15.5.3 Feedforward Control with Multiple Inputs,
593(1)
15.5.4 Feedforward—Feedback Control,
594(2)
15.5.5 Advantages and Disadvantages of Feedforward and Feedback Control,
596(1)
15.5.6 Remarks on Fitting Transfer Function—Noise Models Using Operating Data,
597(2)
15.6 Monitoring Values of Parameters of Forecasting and Feedback Adjustment Schemes,
599(1)
Appendix A15.1 Feedback Control Schemes Where the Adjustment Variance Is Restricted,
600(9)
A15.1.1 Derivation of Optimal Adjustment,
601(2)
A15.1.2 Case Where S Is Negligible,
603(6)
Appendix A15.2 Choice of the Sampling Interval,
609(4)
A15.2.1 Illustration of the Effect of Reducing Sampling Frequency,
610(1)
A15.2.2 Sampling an IMA(0, 1, 1) Process,
610(3)
Exercises,
613(4)
Part Five Charts And Tables 617(25)
Collection Of Tables And Charts
619(6)
Collection Of Time Series Used For Examples In The Text And In Exercises
625(17)
References 642(17)
Index 659
The late George E. P. Box, PhD, was professor emeritus of statistics at the University of Wisconsin-Madison. He was a Fellow of the American Academy of Arts and Sciences and a recipient of the Samuel S. Wilks Memorial Medal of the American Statistical Association, the Shewhart Medal of the American Society for Quality, and the Guy Medal in Gold of the Royal Statistical Society. Dr. Box was also author of seven Wiley books.

The late Gwilym M. Jenkins, PhD, was professor of systems engineering at Lancaster University in the United Kingdom, where he was also founder and managing director of the International Systems Corporation of Lancaster. A Fellow of the Institute of Mathematical Statistics and the Institute of Statisticians, Dr. Jenkins had a prestigious career in both academia and consulting work that included positions at Imperial College London, Stanford University, Princeton University, and the University of Wisconsin-Madison. He was widely known for his work on time series analysis, most notably his groundbreaking work with Dr. Box on the Box-Jenkins models.

The late Gregory C. Reinsel, PhD, was professor and former chair of the department of Statistics at the University of Wisconsin-Madison. Dr. Reinsel's expertise was focused on time series analysis and its applications in areas as diverse as economics, ecology, engineering, and meteorology. He authored over seventy refereed articles and three books, and was a Fellow of both the American Statistical Association and the Institute of Mathematical Statistics.

Greta M. Ljung, PhD, is a statistical consultant residing in Lexington, MA. She received her doctorate from the University of Wisconsin-Madison where she did her research in time series analysis under the direction of Professor George Box. Dr. Ljung's career includes teaching positions at Boston University and Massachusetts Institute of Technology, and a position as Principal Scientist at AIR Worldwide in Boston. Her many accomplishments include joint work with George Box on a time series goodness of fit test, which is widely applied in econometrics and other fields.
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