A Course in Time Series Analysis / Edition 1

A Course in Time Series Analysis / Edition 1

by Daniel Pena, George C. Tiao, Ruey S. Tsay
     
 

ISBN-10: 047136164X

ISBN-13: 9780471361640

Pub. Date: 12/04/2000

Publisher: Wiley

New statistical methods and future directions of research in time series

A Course in Time Series Analysis demonstrates how to build time series models for univariate and multivariate time series data. It brings together material previously available only in the professional literature and presents a unified view of the most advanced procedures available for time

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Overview

New statistical methods and future directions of research in time series

A Course in Time Series Analysis demonstrates how to build time series models for univariate and multivariate time series data. It brings together material previously available only in the professional literature and presents a unified view of the most advanced procedures available for time series model building. The authors begin with basic concepts in univariate time series, providing an up-to-date presentation of ARIMA models, including the Kalman filter, outlier analysis, automatic methods for building ARIMA models, and signal extraction. They then move on to advanced topics, focusing on heteroscedastic models, nonlinear time series models, Bayesian time series analysis, nonparametric time series analysis, and neural networks. Multivariate time series coverage includes presentations on vector ARMA models, cointegration, and multivariate linear systems. Special features include:

  • Contributions from eleven of the world's leading figures in time series
  • Shared balance between theory and application
  • Exercise series sets
  • Many real data examples
  • Consistent style and clear, common notation in all contributions
  • 60 helpful graphs and tables

    Requiring no previous knowledge of the subject, A Course in Time Series Analysis is an important reference and a highly useful resource for researchers and practitioners in statistics, economics, business, engineering, and environmental analysis.

    An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.

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  • Product Details

    ISBN-13:
    9780471361640
    Publisher:
    Wiley
    Publication date:
    12/04/2000
    Series:
    Wiley Series in Probability and Statistics Series, #322
    Pages:
    496
    Product dimensions:
    6.34(w) x 9.57(h) x 1.11(d)

    Related Subjects

    Table of Contents

    1. Introduction 1
    D. Pena and G. C. Tiao

    1.1. Examples of time series problems, 1

    1.1.1. Stationary series, 2

    1.1.2. Nonstationary series, 3

    1.1.3. Seasonal series, 5

    1.1.4. Level shifts and outliers in time series, 7

    1.1.5. Variance changes, 7

    1.1.6. Asymmetric time series, 7

    1.1.7. Unidirectional-feedback relation between series, 9

    1.1.8. Comovement and cointegration, 10

    1.2. Overview of the book, 10

    1.3. Further reading, 19

    PART I BASIC CONCEPTS IN UNIVARIATE TIME SERIES

    2. Univariate Time Series: Autocorrelation, Linear Prediction, Spectrum, and State-Space Model 25
    G. T. Wilson

    2.1. Linear time series models, 25

    2.2. The autocorrelation function, 28

    2.3. Lagged prediction and the partial autocorrelation function, 33

    2.4. Transformations to stationarity, 35

    2.5. Cycles and the periodogram, 37

    2.6. The spectrum, 42

    2.7. Further interpretation of time series acf, pacf, and spectrum, 46

    2.8. State-space models and the Kalman Filter, 48

    3. Univariate Autoregressive Moving-Average Models 53
    G. C. Tiao

    3.1. Introduction, 53

    3.1.1. Univariate ARMA models, 54

    3.1.2. Outline of the chapter, 55

    3.2. Some basic properties of univariate ARMA models, 55

    3.2.1. The ø and TT weights, 56

    3.2.2. Stationarity condition and autocovariance structure o f z „ 58

    3.2.3. The autocorrelation function, 59

    3.2.4. The partial autocorrelation function, 60

    3.2.5. The extended autocorrelaton function, 61

    3.3. Model specification strategy, 63

    3.3.1. Tentative specification, 63

    3.3.2. Tentative model specification via SEACF, 67

    3.4. Examples, 68

    4. Model Fitting and Checking, and the Kalman Filter 86
    G. T. Wilson

    4.1. Prediction error and the estimation criterion, 86

    4.2. The likelihood of ARMA models, 90

    4.3. Likelihoods calculated using orthogonal errors, 94

    4.4. Properties of estimates and problems in estimation, 98

    4.5. Checking the fitted model, 101

    4.6. Estimation by fitting to the sample spectrum, 104

    4.7. Estimation of structural models by the Kalman filter, 105

    5. Prediction and Model Selection 111
    D. Pefia

    5.1. Introduction, 111

    5.2. Properties of minimum mean-square error prediction, 112

    5.2.1. Prediction by the conditional expectation, 112

    5.2.2. Linear predictions, 113

    5.3. The computation of ARIMA forecasts, 114

    5.4. Interpreting the forecasts from ARIMA models, 116

    5.4.1. Nonseasonal models, 116

    5.4.2. Seasonal models, 120

    5.5. Prediction confidence intervals, 123

    5.5.1. Known parameter values, 123

    5.5.2. Unknown parameter values, 124

    5.6. Forecast updating, 125

    5.6.1. Computing updated forecasts, 125

    5.6.2. Testing model stability, 125

    5.7. The combination of forecasts, 129

    5.8. Model selection criteria, 131

    5.8.1. The FPE and AIC criteria, 131

    5.8.2. The Schwarz criterion, 133

    5.9. Conclusions, 133

    6. Outliers, Influential Observations, and Missing Data 136
    D. Pena

    6.1. Introduction, 136

    6.2. Types of outliers in time series, 138

    6.2.1. Additive outliers, 138

    6.2.2. Innovative outliers, 141

    6.2.3. Level shifts, 143

    6.2.4. Outliers and intervention analysis, 146

    6.3. Procedures for outlier identification and estimation, 147

    6.3.1. Estimation of outlier effects, 148

    6.3.2. Testing for outliers, 149

    6.4. Influential observations, 152

    6.4.1. Influence on time series, 152

    6.4.2. Influential observations and outliers, 153

    6.5. Multiple outliers, 154

    6.5.1. Masking effects, 154

    6.5.2. Procedures for multiple outlier identification, 156

    6.6. Missing-value estimation, 160

    6.6.1. Optimal interpolation and inverse autocorrelation function, 160

    6.6.2. Estimation of missing values, 162

    6.7. Forecasting with outliers, 164

    6.8. Other approaches, 166

    6.9. Appendix, 166

    7. Automatic Modeling Methods for Univariate Series 171
    V. Gomez and A. Maravall

    7.1. Classical model identification methods, 171

    7.1.1. Subjectivity of the classical methods, 172

    7.1.2. The difficulties with mixed ARMA models, 173

    7.2. Automatic model identification methods, 173

    7.2.1. Unit root testing, 174

    7.2.2. Penalty function methods, 174

    7.2.3. Pattern identification methods, 175

    7.2.4. Uniqueness of the solution and the purpose of modeling, 176

    7.3. Tools for automatic model identification, 177

    7.3.1. Test for the log-level specification, 177

    7.3.2. Regression techniques for estimating unit roots, 178

    7.3.3. The Hannan-Rissanen method, 181

    7.3.4. Liu's filtering method, 185

    7.4. Automatic modeling methods in the presence of outliers, 186

    7.4.1. Algorithms for automatic outlier detection and correction, 186

    7.4.2. Estimation and filtering techniques to speed up the algorithms, 190

    7.4.3. The need to robustify automatic modeling methods, 191

    7.4.4. An algorithm for automatic model identification in the presence of outliers, 191

    7.5. An automatic procedure for the general regression-ARIMA model in the presence of outlierw, special effects, and, possibly, missing observations, 192

    7.5.1. Missing observations, 192

    7.5.2. Trading day and Easter effects, 193

    7.5.3. Intervention and regression effects, 194

    7.6. Examples, 194

    7.7. Tabular summary, 196

    8. Seasonal Adjustment and Signal Extraction Time Series 202
    V. Gomez and A. Maravall

    8.1. Introduction, 202

    8.2. Some remarks on the evolution of seasonal adjustment methods, 204

    8.2.1. Evolution of the methodologic approach, 204

    8.2.2. The situation at present, 207

    8.3. The need for preadjustment, 209

    8.4. Model specification, 210

    8.5. Estimation of the components, 213

    8.5.1. Stationary case, 215

    8.5.2. Nonstationary series, 217

    8.6 Historical or final estimator, 218

    8.6.1. Properties of final estimator, 218

    8.6.2. Component versus estimator, 219

    8.6.3. Covariance between estimators, 221

    8.7. Estimators for recent periods, 221

    8.8. Revisions in the estimator, 223

    8.8.1. Structure of the revision, 223

    8.8.2. Optimality of the revisions, 224

    8.9. Inference, 225

    8.9.1. Optical Forecasts of the Components, 225

    8.9.2. Estimation error, 225

    8.9.3. Growth rate precision, 226

    8.9.4. The gain from concurrent adjustment, 227

    8.9.5. Innovations in the components (pseudoinnovations), 228

    8.10. An example, 228

    8.11. Relation with fixed filters, 235

    8.12. Short-versus long-term trends; measuring economic cycles, 236

    PART II ADVANCED TOPICS IN UNIVARIATE TIME SERIES

    9. Heteroscedastic Models
    R. S. Tsay

    9.1. The ARCH model, 250

    9.1.1. Some simple properties of ARCH models, 252

    9.1.2. Weaknesses of ARCH models, 254

    9.1.3. Building ARCH models, 254

    9.1.4. An illustrative example, 255

    9.2. The GARCH Model, 256

    9.2.1. An illustrative example, 257

    9.2.2. Remarks, 259

    9.3. The exponential GARCH model, 260

    9.3.1. An illustrative example, 261

    9.4. The CHARMA model, 262

    9.5. Random coefficient autoregressive (RCA) model, 263

    9.6. Stochastic volatility model, 264

    9.7. Long-memory stochastic volatility model, 265

    10. Nonlinear Time Series Models: Testing and Applications 267
    R. S. Tsay

    10.1. Introduction, 267

    10.2. Nonlinearity tests, 268

    10.2.1. The test, 268

    10.2.2. Comparison and application, 270

    10.3. The Tar model, 274

    10.3.1. U.S. real GNP, 275

    10.3.2. Postsample forecasts and discussion, 279

    10.4. Concluding remarks, 282

    11. Bayesian Time Series Analysis 286
    R. S. Tsay

    11.1. Introduction, 286

    11.2. A general univariate time series model, 288

    11.3. Estimation, 289

    11.3.1. Gibbs sampling, 291

    11.3.2. Griddy Gibbs, 292

    11.3.3. An illustrative example, 292

    11.4. Model discrimination, 294

    11.4.1. A mixed model with switching, 295

    11.4.2. Implementation, 296

    11.5. Examples, 297

    12 Nonparametric Time Series Analysis: Nonparametric Regression, Locally Weighted Regression, Autoregression, and Quantile Regression 308
    S. Heiler

    12.1 Introduction, 308

    12.2 Nonparametric regression, 309

    12.3 Kernel estimation in time series, 314

    12.4 Problems of simple kernel estimation and restricted approaches, 319

    12.5 Locally weighted regression, 321

    12.6 Applications of locally weighted regression to time series, 329

    12.7 Parameter selection, 330

    12.8 Time series decomposition with locally weighted regression, 336

    13. Neural Network Models 348
    K. Hornik and F. Leisch

    13.1. Introduction, 348

    13.2. The multilayer perceptron, 349

    13.3. Autoregressive neural network models, 354

    13.3.1. Example: Sunspot series, 355

    13.4. The recurrent perceptron, 356

    13.4.1. Examples of recurrent neural network models, 357

    13.4.2. A unifying view, 359

    PART III MULTIVARIATE TIME SERIES

    14. Vector ARMA Models 365
    G. C. Tiao

    14.1. Introduction, 365

    14.2. Transfer function or unidirectional models, 366

    14.3. The vector ARMA model, 368

    14.3.1. Some simple examples, 368

    14.3.2. Relationship to transfer function model, 371

    14.3.3. Cross-covariance and correlation matrices, 371

    14.3.4. The partial autoregression matrices, 372

    14.4. Model building strategy for multiple time series, 373

    14.4.1. Tentative specification, 373

    14.4.2. Estimation, 378

    14.4.3. Diagnostic checking, 379

    14.5. Analyses of three examples, 380

    14.5.1. The SCC data, 380

    14.5.2. The gas furnace data, 383

    14.5.3. The census housing data, 387

    14.6. Structural analysis of multivariate time series, 392

    14.6.1. A canonical analysis of multiple time series, 395

    14.7. Scalar component models in multiple time series, 396

    14.7.1. Scalar component models, 398

    14.7.2. Exchangeable models and overparameterization, 400

    14.7.3. Model specification via canonical correlation analysis, 402

    14.7.4. An illustrative example, 403

    14.7.5. Some further remarks, 404

    15. Cointegration in the VAR Model 408
    5. Johansen

    15.1. Introduction, 408

    15.1.1. Basic definitions, 409

    15.2. Solving autoregressive equations, 412

    15.2.1. Some examples, 412

    15.2.2. An inversion theorem for matrix polynomials, 414

    15.2.3. Granger's representation, 417

    15.2.4. Prediction, 419

    15.3. The statistical model for / ( l ) variables, 420

    15.3.1. Hypotheses on cointegrating relations, 421

    15.3.2. Estimation of cointegrating vectors and calculation of test statistics, 422

    15.3.3. Estimation of â under restrictions, 426

    15.4. Asymptotic theory, 426

    15.4.1. Asymptotic results, 427

    15.4.2. Test for cointegrating rank, 427

    15.4.3. Asymptotic distribution of â and test for restrictions on â, 429

    15.5. Various applications of the cointegration model, 432

    15.5.1. Rational expectations, 432

    15.5.2. Arbitrage pricing theory, 433

    15.5.3. Seasonal cointegration, 433

    16. Identification of Linear Dynamic Multiinput/Multioutput Systems 436
    M. Deistler

    16.1. Introduction and problem statement, 436

    16.2. Representations of linear systems, 438

    16.2.1. Input/output representations, 438

    16.2.2. Solutions of linear vector difference equations (VDEs), 440

    16.2.3. ARMA and state-space representations, 441

    16.3. The structure of state-space systems, 443

    16.4. The structure of ARMA systems, 444

    16.5. The realization of state-space systems, 445

    16.5.1. General structure, 445

    16.5.2. Echelon forms, 447

    16.6. The realization of ARMA systems, 448

    16.7. Parametrization, 449

    16.8. Estimation of real-valued parameters, 452

    16.9. Dynamic specification, 454

    INDEX 457

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