You are previewing Time Series Analysis: Forecasting and Control, Fourth Edition.
O'Reilly logo
Time Series Analysis: Forecasting and Control, Fourth Edition

Book Description

A modernized new edition of one of the most trusted books on time series analysis. Since publication of the first edition in 1970, Time Series Analysis has served as one of the most influential and prominent works on the subject. This new edition maintains its balanced presentation of the tools for modeling and analyzing time series and also introduces the latest developments that have occurred n the field over the past decade through applications from areas such as business, finance, and engineering.

The Fourth Edition provides a clearly written exploration of the key methods for building, classifying, testing, and analyzing stochastic models for time series as well as 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, modern topics are introduced through the book's new features, which include:

  • A new chapter on multivariate time series analysis, including a discussion of the challenge that arise with their modeling and an outline of the necessary analytical tools

  • New coverage of forecasting in the design of feedback and feedforward control schemes

  • A new chapter on nonlinear and long memory models, which explores additional models for application such as heteroscedastic time series, nonlinear time series models, and models for long memory processes

  • Coverage of structural component models for the modeling, forecasting, and seasonal adjustment of time series

  • A review of the maximum likelihood estimation for ARMA models with missing values

Numerous illustrations and detailed appendices supplement the book,while extensive references and discussion questions at the end of each chapter facilitate an in-depth understanding of both time-tested and modern concepts. With its focus on practical, rather than heavily mathematical, techniques, time Series Analysis, Fourth Edition is the upper-undergraduate and graduate levels. this book is also an invaluable reference for applied statisticians, engineers, and financial analysts.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright
  4. Dedication
  5. Contents
  6. Preface to the Fourth Edition
  7. Preface to the Third Edition
  8. CHAPTER ONE: Introduction
    1. 1.1 FIVE IMPORTANT PRACTICAL PROBLEMS
    2. 1.2 STOCHASTIC AND DETERMINISTIC DYNAMIC MATHEMATICAL MODELS
    3. 1.3 BASIC IDEAS IN MODEL BUILDING
  9. PART ONE: Stochastic Models and Their Forecasting
    1. CHAPTER TWO: Autocorrelation Function and Spectrum of Stationary Processes
      1. 2.1 AUTOCORRELATION PROPERTIES OF STATIONARY MODELS
      2. 2.2 SPECTRAL PROPERTIES OF STATIONARY MODELS
      3. APPENDIX A2.1 LINK BETWEEN THE SAMPLE SPECTRUM AND AUTOCOVARIANCE FUNCTION ESTIMATE
    2. CHAPTER THREE: Linear Stationary Models
      1. 3.1 GENERAL LINEAR PROCESS
      2. 3.2 AUTOREGRESSIVE PROCESSES
      3. 3.3 MOVING AVERAGE PROCESSES
      4. 3.4 MIXED AUTOREGRESSIVE–MOVING AVERAGE PROCESSES
      5. APPENDIX A3.1 AUTOCOVARIANCES, AUTOCOVARIANCE GENERATING FUNCTION, AND STATIONARITY CONDITIONS FOR A GENERAL LINEAR PROCESS
      6. APPENDIX A3.2 RECURSIVE METHOD FOR CALCULATING ESTIMATES OF AUTOREGRESSIVE PARAMETERS
    3. CHAPTER FOUR: Linear Nonstationary Models
      1. 4.1 AUTOREGRESSIVE INTEGRATED MOVING AVERAGE PROCESSES
      2. 4.2 THREE EXPLICIT FORMS FOR THE AUTOREGRESSIVE INTEGRATED MOVING AVERAGE MODEL
      3. 4.3 INTEGRATED MOVING AVERAGE PROCESSES
      4. APPENDIX A4.1 LINEAR DIFFERENCE EQUATIONS
      5. APPENDIX A4.2 IMA(0, 1, 1) PROCESS WITH DETERMINISTIC DRIFT
      6. APPENDIX A4.3 ARIMA PROCESSES WITH ADDED NOISE
    4. CHAPTER FIVE: Forecasting
      1. 5.1 MINIMUM MEAN SQUARE ERROR FORECASTS AND THEIR PROPERTIES
      2. 5.2 CALCULATING AND UPDATING FORECASTS
      3. 5.3 FORECAST FUNCTION AND FORECAST WEIGHTS
      4. 5.4 EXAMPLES OF FORECAST FUNCTIONS AND THEIR UPDATING
      5. 5.5 USE OF STATE-SPACE MODEL FORMULATION FOR EXACT FORECASTING
      6. 5.6 SUMMARY
      7. APPENDIX A5.1 CORRELATIONS BETWEEN FORECAST ERRORS
      8. APPENDIX A5.2 FORECAST WEIGHTS FOR ANY LEAD TIME
      9. APPENDIX A5.3 FORECASTING IN TERMS OF THE GENERAL INTEGRATED FORM
  10. PART TWO: Stochastic Model Building
    1. CHAPTER SIX: Model Identification
      1. 6.1 OBJECTIVES OF IDENTIFICATION
      2. 6.2 IDENTIFICATION TECHNIQUES
      3. 6.3 INITIAL ESTIMATES FOR THE PARAMETERS
      4. 6.4 MODEL MULTIPLICITY
      5. APPENDIX A6.1 EXPECTED BEHAVIOR OF THE ESTIMATED AUTOCORRELATION FUNCTION FOR A NONSTATIONARY PROCESS
      6. APPENDIX A6.2 GENERAL METHOD FOR OBTAINING INITIAL ESTIMATES OF THE PARAMETERS OF A MIXED AUTOREGRESSIVE–MOVING AVERAGE PROCESS
    2. CHAPTER SEVEN: Model Estimation
      1. 7.1 STUDY OF THE LIKELIHOOD AND SUM-OF-SQUARES FUNCTIONS
      2. 7.2 NONLINEAR ESTIMATION
      3. 7.3 SOME ESTIMATION RESULTS FOR SPECIFIC MODELS
      4. 7.4 LIKELIHOOD FUNCTION BASED ON THE STATE-SPACE MODEL
      5. 7.5 UNIT ROOTS IN ARIMA MODELS
      6. 7.6 ESTIMATION USING BAYES'S THEOREM
      7. APPENDIX A7.1 REVIEW OF NORMAL DISTRIBUTION THEORY
      8. APPENDIX A7.2 REVIEW OF LINEAR LEAST SQUARES THEORY
      9. APPENDIX A7.3 EXACT LIKELIHOOD FUNCTION FOR MOVING AVERAGE AND MIXED PROCESSES
      10. APPENDIX A7.4 EXACT LIKELIHOOD FUNCTION FOR AN AUTOREGRESSIVE PROCESS
      11. APPENDIX A7.5 ASYMPTOTIC DISTRIBUTION OF ESTIMATORS FOR AUTOREGRESSIVE MODELS
      12. APPENDIX A7.6 EXAMPLES OF THE EFFECT OF PARAMETER ESTIMATION ERRORS ON VARIANCES OF FORECAST ERRORS AND PROBABILITY LIMITS FOR FORECASTS
      13. APPENDIX A7.7 SPECIAL NOTE ON ESTIMATION OF MOVING AVERAGE PARAMETERS
    3. CHAPTER EIGHT: Model Diagnostic Checking
      1. 8.1 CHECKING THE STOCHASTIC MODEL
      2. 8.2 DIAGNOSTIC CHECKS APPLIED TO RESIDUALS
      3. 8.3 USE OF RESIDUALS TO MODIFY THE MODEL
    4. CHAPTER NINE: Seasonal Models
      1. 9.1 PARSIMONIOUS MODELS FOR SEASONAL TIME SERIES
      2. 9.2 REPRESENTATION OF THE AIRLINE DATA BY A MULTIPLICATIVE (0, 1, 1) × (0, 1, 1) 12 MODEL
      3. 9.3 SOME ASPECTS OF MORE GENERAL SEASONAL ARIMA MODELS
      4. 9.4 STRUCTURAL COMPONENT MODELS AND DETERMINISTIC SEASONAL COMPONENTS
      5. 9.5 REGRESSION MODELS WITH TIME SERIES ERROR TERMS
      6. APPENDIX A9.1 AUTOCOVARIANCES FOR SOME SEASONAL MODELS
    5. CHAPTER TEN: Nonlinear and Long Memory Models
      1. 10.1 AUTOREGRESSIVE CONDITIONAL HETEROSCEDASTIC (ARCH) MODELS
      2. 10.2 NONLINEAR TIME SERIES MODELS
      3. 10.3 LONG MEMORY TIME SERIES PROCESSES
  11. PART THREE: Transfer Function and Multivariate Model Building
    1. CHAPTER ELEVEN: Transfer Function Models
      1. 11.1 LINEAR TRANSFER FUNCTION MODELS
      2. 11.2 DISCRETE DYNAMIC MODELS REPRESENTED BY DIFFERENCE EQUATIONS
      3. 11.3 RELATION BETWEEN DISCRETE AND CONTINUOUS MODELS
      4. APPENDIX A11.1 CONTINUOUS MODELS WITH PULSED INPUTS
      5. APPENDIX A11.2 NONLINEAR TRANSFER FUNCTIONS AND LINEARIZATION
    2. CHAPTER TWELVE: Identification, Fitting, and Checking of Transfer Function Models
      1. 12.1 CROSS-CORRELATION FUNCTION
      2. 12.2 IDENTIFICATION OF TRANSFER FUNCTION MODELS
      3. 12.3 FITTING AND CHECKING TRANSFER FUNCTION MODELS
      4. 12.4 SOME EXAMPLES OF FITTING AND CHECKING TRANSFER FUNCTION MODELS
      5. 12.5 FORECASTING WITH TRANSFER FUNCTION MODELS USING LEADING INDICATORS
      6. 12.6 SOME ASPECTS OF THE DESIGN OF EXPERIMENTS TO ESTIMATE TRANSFER FUNCTIONS
      7. APPENDIX A12.1 USE OF CROSS SPECTRAL ANALYSIS FOR TRANSFER FUNCTION MODEL IDENTIFICATION
      8. APPENDIX A12.2 CHOICE OF INPUT TO PROVIDE OPTIMAL PARAMETER ESTIMATES
    3. CHAPTER THIRTEEN: Intervention Analysis Models and Outlier Detection
      1. 13.1 INTERVENTION ANALYSIS METHODS
      2. 13.2 OUTLIER ANALYSIS FOR TIME SERIES
      3. 13.3 ESTIMATION FOR ARMA MODELS WITH MISSING VALUES
    4. CHAPTER FOURTEEN: Multivariate Time Series Analysis
      1. 14.1 STATIONARY MULTIVARIATE TIME SERIES
      2. 14.2 LINEAR MODEL REPRESENTATIONS FOR STATIONARY MULTIVARIATE PROCESSES
      3. 14.3 NONSTATIONARY VECTOR AUTOREGRESSIVE-MOVING AVERAGE MODELS
      4. 14.4 FORECASTING FOR VECTOR AUTOREGRESSIVE-MOVING AVERAGE PROCESSES
      5. 14.5 STATE-SPACE FORM OF THE VECTOR ARMA MODEL
      6. 14.6 STATISTICAL ANALYSIS OF VECTOR ARMA MODELS
      7. 14.7 EXAMPLE OF VECTOR ARMA MODELING
  12. PART FOUR: Design of Discrete Control Schemes
    1. CHAPTER FIFTEEN: Aspects of Process Control
      1. 15.1 PROCESS MONITORING AND PROCESS ADJUSTMENT
      2. 15.2 PROCESS ADJUSTMENT USING FEEDBACK CONTROL
      3. 15.3 EXCESSIVE ADJUSTMENT SOMETIMES REQUIRED BY MMSE CONTROL
      4. 15.4 MINIMUM COST CONTROL WITH FIXED COSTS OF ADJUSTMENT AND MONITORING
      5. 15.5 FEEDFORWARD CONTROL
      6. 15.6 MONITORING VALUES OF PARAMETERS OF FORECASTING AND FEEDBACK ADJUSTMENT SCHEMES
      7. APPENDIX A15.1 FEEDBACK CONTROL SCHEMES WHERE THE ADJUSTMENT VARIANCE IS RESTRICTED
      8. APPENDIX A15.2 CHOICE OF THE SAMPLING INTERVAL
  13. PART FIVE: Charts and Tables
    1. Collection of Tables and Charts
    2. Collection of Time Series Used for Examples in the Text and in Exercises
    3. References
  14. PART SIX: Exercises and Problems
    1. CHAPTER 2
    2. CHAPTER 3
    3. CHAPTER 4
    4. CHAPTER 5
    5. CHAPTER 6
    6. CHAPTER 7
    7. CHAPTER 8
    8. CHAPTER 9
    9. CHAPTER 10
    10. CHAPTER 11
    11. CHAPTER 12
    12. CHAPTER 13
    13. CHAPTER 14
    14. CHAPTER 15
  15. Index