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An essential guide on high dimensional multivariate time series including all the latest topics from one of the leading experts in the field

Following the highly successful and much lauded book, Time Series Analysis-Univariate and Multivariate Methods, this new work by William W.S. Wei focuses on high dimensional multivariate time series, and is illustrated with numerous high dimensional empirical time series. Beginning with the fundamentalconcepts and issues of multivariate time series analysis,this book covers many topics that are not found in general multivariate time series books. Some of these are repeated measurements, space-time series modelling, and dimension reduction. The book also looks at vector time series models, multivariate time series regression models, and principle component analysis of multivariate time series. Additionally, it provides readers with information on factor analysis of multivariate time series, multivariate GARCH models, and multivariate spectral analysis of time series.

With the development of computers and the internet, we have increased potential for data exploration. In the next few years, dimension will become a more serious problem. Multivariate Time Series Analysis and its Applications provides some initial solutions, which may encourage the development of related software needed for the high dimensional multivariate time series analysis.

Written by bestselling author and leading expert in the field
Covers topics not yet explored in current multivariate books
Features classroom tested material
Written specifically for time series courses

Multivariate Time Series Analysis and its Applications is designed for an advanced time series analysis course. It is a must-have for anyone studying time series analysis and is also relevant for students in economics, biostatistics, and engineering.




Table of contents

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/