图书简介

About the author xiii Preface xv About the Companion website xvii 1 Fundamental Concepts and Issues in Multivariate Time Series Analysis 1 1.1 Introduction 1 1.2 Fundamental concepts 3 1.2.1 Correlation and partial correlation matrix functions 3 1.2.2 Vector white noise process 7 1.2.3 Moving average and autoregressive representations of vector processes 7 Projects 9 References 9 2 Vector Time Series Models 11 2.1 Vector moving average processes 11 2.2 Vector autoregressive processes 14 2.2.1 Granger causality 18 2.3 Vector autoregressive moving average processes 18 2.4 Nonstationary vector autoregressive moving average processes 21 2.5 Vector time series model building 21 2.5.1 Identification of vector time series models 21 2.5.2 Sample moments of a vector time series 22 2.5.2.1 Sample mean and sample covariance matrices 22 2.5.2.2 Sample correlation matrix function 23 2.5.2.3 Sample partial correlation matrix function and extended cross-correlation matrices 24 2.5.3 Parameter estimation, diagnostic checking, and forecasting 24 2.5.4 Cointegration in vector time series 25 2.6 Seasonal vector time series model 26 2.7 Multivariate time series outliers 27 2.7.1 Types of multivariate time series outliers and detections 27 2.7.2 Outlier detection through projection pursuit 29 2.8 Empirical examples 32 2.8.1 First model of US monthly retail sales revenue 32 2.8.2 Second model of US monthly retail sales revenue 43 2.8.3 US macroeconomic indicators 47 2.8.4 Unemployment rates with outliers 58 Software code 65 Projects 100 References 101 3 Multivariate Time Series Regression Models 105 3.1 Introduction 105 3.2 Multivariate multiple time series regression models 105 3.2.1 The classical multiple regression model 105 3.2.2 Multivariate multiple regression model 106 3.3 Estimation of the multivariate multiple time series regression model 108 3.3.1 The Generalized Least Squares (GLS) estimation 108 3.3.2 Empirical Example I - U.S. retail sales and some national indicators 109 3.4 Vector time series regression models 114 3.4.1 Extension of a VAR model to VARX models 114 3.4.2 Empirical Example II - VARX models for U.S. retail sales and some national indicators 115 3.5 Empirical Example III - Total mortality and air pollution in California 120 Software code 129 Projects 137 References 137 4 Principle Component Analysis of Multivariate Time Series 139 4.1 Introduction 139 4.2 Population PCA 140 4.3 Implications of PCA 141 4.4 Sample principle components 142 4.5 Empirical examples 145 4.5.1 Daily stock returns from the first set of 10 stocks 145 4.5.1.1 The PCA based on the sample covariance matrix 147 4.5.1.2 The PCA based on the sample correlation matrix 150 4.5.2 Monthly Consumer Price Index (CPI) from five sectors 152 4.5.2.1 The PCA based on the sample covariance matrix 153 4.5.2.2 The PCA based on the sample correlation matrix 154 Software code 157 Projects 160 References 161 5 Factor Analysis of Multivariate Time Series 163 5.1 Introduction 163 5.2 The orthogonal factor model 163 5.3 Estimation of the factor model 165 5.3.1 The principal component method 165 5.3.2 Empirical Example I - Model 1 on daily stock returns from the second set of 10 stocks 166 5.3.3 The maximum likelihood method 169 5.3.4 Empirical Example II - Model 2 on daily stock returns from the second set of 10 stocks 173 5.4 Factor rotation 175 5.4.1 Orthogonal rotation 176 5.4.2 Oblique rotation 176 5.4.3 Empirical Example III - Model 3 on daily stock returns from the second set of 10 stocks 177 5.5 Factor scores 178 5.5.1 Introduction 178 5.5.2 Empirical Example IV - Model 4 on daily stock returns from the second set of 10 stocks 179 5.6 Factor models with observable factors 181 5.7 Another empirical example - Yearly U.S. sexually transmitted diseases (STD) 183 5.7.1 Principal components analysis (PCA) 183 5.7.1.1 PCA for standardized Zt 183 5.7.1.2 PCA for unstandardized Zt 186 5.7.2 Factor analysis 186 5.8 Concluding remarks 193 Software code 194 Projects 200 References 201 6 Multivariate GARCH Models 203 6.1 Introduction 203 6.2 Representations of multivariate GARCH models 204 6.2.1 VEC and DVEC models 204 6.2.2 Constant Conditional Correlation (CCC) models 206 6.2.3 BEKK models 207 6.2.4 Factor models 208 6.3 O-GARCH and GO-GARCH models 209 6.4 Estimation of GO-GARCH models 210 6.4.1 The two-step estimation method 210 6.4.2 The weighted scatter estimation method 211 6.5 Properties of the weighted scatter estimator 213 6.5.1 Asymptotic distribution and statistical inference 213 6.5.2 Combining information from different weighting functions 214 6.6 Empirical examples 215 6.6.1 U.S. weekly interest over time on six exercise items 215 6.6.1.1 Choose a best VAR/VARMA model 216 6.6.1.2 Finding a VARMA-ARCH/GARCH model 218 6.6.1.3 The fitted values from VAR(1)-ARCH(1) model 221 6.6.2 Daily log-returns of the SP 500 index and three financial stocks 222 6.6.3 The analysis of the Dow Jones Industrial Average of 30 stocks 225 Software code 229 Projects 234 References 234 7 Repeated Measurements 237 7.1 Introduction 237 7.2 Multivariate analysis of variance 239 7.2.1 Test treatment effects 239 7.2.2 Empirical Example I - First analysis on body weight of rats under three different treatments 241 7.3 Models utilizing time series structure 243 7.3.1 Fixed effects model 243 7.3.2 Some common variance-covariance structures 247 7.3.3 Empirical Example II - Further analysis on body weight of rats under three different treatments 250 7.3.4 Random effects and mixed effects models 252 7.4 Nested random effects model 253 7.5 Further generalization and remarks 254 7.6 Another empirical example - the oral condition of neck cancer patients 255 Software code 257 Projects 258 References 258 8 Space-Time Series Models 261 8.1 Introduction 261 8.2 Space-time autoregressive integrated moving average (STARIMA) models 262 8.2.1 Spatial weighting matrix 262 8.2.2 STARIMA models 265 8.2.3 STARMA models 266 8.2.4 ST-ACF and ST-PACF 267 8.3 Generalized space-time autoregressive integrated moving average (GSTARIMA) models 272 8.4 Iterative model building of STARMA and GSTARMA models 273 8.5 Empirical examples 273 8.5.1 Vehicular theft data 273 8.5.2 The annual U.S. labor force count 279 8.5.3 U.S. yearly sexually transmitted disease data 281 Software code 289 Projects 298 References 298 9 Multivariate Spectral Analysis of Time Series 301 9.1 Introduction 301 9.2 Spectral representations of multivariate time series processes 304 9.3 The estimation of the spectral density matrix 309 9.3.1 The smoothed spectrum matrix 309 9.3.2 Multitaper smoothing 313 9.3.3 Smoothing spline 315 9.3.4 Bayesian method 316 9.3.5 Penalized Whittle likelihood 317 9.3.6 VARMA spectral estimation 318 9.4 Empirical examples of stationary vector time series 320 9.4.1 Sample spectrum 320 9.4.2 Bayesian method 325 9.4.3 Penalized Whittle likelihood method 327 9.4.4 Example of VAR spectrum estimation 327 9.5 Spectrum analysis of a nonstationary vector time series 329 9.5.1 Introduction 329 9.5.2 Spectrum representations of a nonstationary multivariate process 331 9.5.2.1 Time-varying autoregressive model 332 9.5.2.2 Smoothing spline ANOVA model 333 9.5.2.3 Piecewise vector autoregressive model 334 9.5.2.4 Bayesian methods 336 9.6 Empirical spectrum example of nonstationary vector time series 337 Software code 341 Projects 434 References 435 10 Dimension Reduction in High-Dimensional Multivariate Time Series Analysis 437 10.1 Introduction 437 10.2 Existing methods 438 10.2.1 Regularization methods 439 10.2.1.1 The lasso method 439 10.2.1.2 The lag-weighted lasso method 440 10.2.1.3 The hierarchical vector autoregression (HVAR) method 440 10.2.2 The space-time AR (STAR) model 442 10.2.3 The model-based cluster method 443 10.2.4 The factor analysis 443 10.3 The proposed method for high-dimension reduction 444 10.4 Simulation studies 446 10.4.1 Scenario 1 446 10.4.2 Scenario 2 449 10.4.3 Scenario 3 449 10.5 Empirical examples 452 10.5.1 The macroeconomic time series 452 10.5.2 The yearly U.S. STD data 457 10.6 Further discussions and remarks 459 10.6.1 More on clustering 459 10.6.2 Forming aggregate data through both time domain and frequency domain clustering 461 10.6.2.1 Example of time domain clustering 461 10.6.2.2 Example of frequency domain clustering 461 10.6.2.2.1 Clustering using similarity measures 463 10.6.2.2.2 Clustering by subjective observation 463 10.6.2.2.3 Hierarchical clustering 463 10.6.2.2.4 Nonhierarchical clustering using the K-means method 463 10.6.3 The specification of aggregate matrix and its associated aggregate dimension 466 10.6.4 Be aware of other forms of aggregation 466 10.A Appendix: Parameter Estimation Results of Various Procedures 467 10.A.1 Further details of the macroeconomic time series 467 10.A.1.1 VAR(1) 467 10.A.1.2 Lasso 468 10.A.1.3 Componentwise 470 10.A.1.4 Own-other 471 10.A.1.5 Elementwise 473 10.A.1.6 The factor model 475 10.A.1.7 The model-based cluster 475 10.A.1.8 The proposed method 477 10.A.2 Further details of the STD time series 478 10.A.2.1 VAR 478 10.A.2.2 Lasso 478 10.A.2.3 Componentwise 479 10.A.2.4 Own-other 481 10.A.2.5 Elementwise 482 10.A.2.6 The STAR model 484 10.A.2.7 The factor model 486 10.A.2.8 The model-based cluster 487 10.A.2.9 The proposed method 488 Software code 490 Projects 505 References 506 Author index 509 Subject index 515

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