An accessible guide to the multivariate time series tools used in numerous real-world applications

Multivariate Time Series Analysis: With R and Financial Applications is the much anticipated sequel coming from one of the most influential and prominent experts on the topic of time series. Through a fundamental balance of theory and methodology, the book supplies readers with a comprehensible approach to financial econometric models and their applications to real-world empirical research.

Differing from the traditional approach to multivariate time series, the book focuses on reader comprehension by emphasizing structural specification, which results in simplified parsimonious VAR MA modeling. Multivariate Time Series Analysis: With R and Financial Applications utilizes the freely available R software package to explore complex data and illustrate related computation and analyses. Featuring the techniques and methodology of multivariate linear time series, stationary VAR models, VAR MA time series and models, unitroot process, factor models, and factor-augmented VAR models, the book includes:

• Over 300 examples and exercises to reinforce the presented content

• User-friendly R subroutines and research presented throughout to demonstrate modern applications

• Numerous datasets and subroutines to provide readers with a deeper understanding of the material

Multivariate Time Series Analysis is an ideal textbook for graduate-level courses on time series and quantitative finance and upper-undergraduate level statistics courses in time series. The book is also an indispensable reference for researchers and practitioners in business, finance, and econometrics.

RUEY S. TSAY, PhD, is H.G.B. Alexander Professor of Econometrics and Statistics at The University of Chicago Booth School of Business. He has written over 125 published articles in the areas of business and economic forecasting, data analysis, risk management, and process control. A Fellow of the American Statistical Association, the Institute of Mathematical Statistics, and Academia Sinica, Dr. Tsay is author of Analysis of Financial Time Series, Third Edition and An Introduction to Analysis of Financial Data with R, and coauthor of A Course in Time Series Analysis, all published by Wiley.

1 Multivariate Linear Time Series 1

1.1 Introduction 1

1.2 Some Basic Concepts 5

1.3 Cross Covariance and Correlation Matrices 8

1.4 Sample Cross-Correlation Matrices 9

1.5 Testing Zero Cross Correlations 12

1.6 Forecasting 15

1.7 Model Representations 17

1.8 Outline of the Book 21

1.9 Software 22

2 Stationary VAR Models 25

2.1 Introduction 25

2.2 VAR(1) Models 26

2.3 VAR(2) Models 34

2.4 VAR(p) Models 37

2.4.1 A VAR(1) Representation 38

2.5 Estimation 40

2.6 Order Selection 55

2.7 Model Checking 60

2.8 Linear Constraints 73

2.9 Forecasting 75

2.10 Impulse Response Functions 82

2.11 Forecast Error Variance Decomposition 87

2.12 Proofs 89

3 VARMA Time Series 97

3.1 Vector MA Models 98

3.2 Specifying VMA Order 103

3.3 Estimation of VMA Models 104

3.4 Forecasting of VMA Models 117

3.5 VARMA Models 118

3.6 Implications of VARMA Models 128

3.7 Linear Transforms of VARMA Processes 131

3.8 Temporal Aggregation of VARMA Processes 134

3.9 Likelihood Function of a VARMA Model 135

3.10 Innovations Approach to Exact Likelihood Function 143

3.11 Asymptotic Distribution of Maximum Likelihood Estimates 148

3.12 Model Checking of Fitted VARMA Models 150

3.13 Forecasting of VARMA Models 151

3.14 Tentative Order Identification 153

3.15 Empirical Analysis of VARMA Models 162

3.16 Appendix 178

4 Structural Specification of VARMA Models 185

4.1 The Kronecker Index Approach 186

4.2 The Scalar-Component Approach 198

4.3 Statistics For Order Specification 204

4.4 Finding Kronecker Indices 206

4.5 Finding Scalar Component Models 211

4.6 Estimation 221

4.7 An Example 229

4.8 Appendix: Canonical Correlation Analysis 243

5 Unit-Root Processes 249

5.1 Univariate Unit-Root Processes 250

5.2 Multivariate Unit-Root Processes 262

5.3 Spurious Regressions 273

5.4 Multivariate Exponential Smoothing 274

5.5 Co-integration 277

5.6 An Error-Correction Form 279

5.7 Implications of Co-Integrating Vectors 282

5.8 Parameterization of Co-Integrating Vectors 284

5.9 Co-Integration Tests 284

5.10 Estimation of Error-Correction Models 294

5.11 Applications 299

5.12 Discussion 307

5.13 Appendix 308

6 Factor Models and Selected Topics 313

6.1 Seasonal Models 313

6.2 Principal Component Analysis 321

6.3 Use of Exogenous Variables 325

6.4 Missing Values 337

6.5 Factor Models 343

6.6 Classification and Clustering Analysis 365

7 Multivariate Volatility Models 379

7.1 Testing Conditional Heteroscedasticity 381

7.2 Estimation of Multivariate Volatility Models 388

7.3 Diagnostic Checks of Volatility Models 389

7.4 Exponentially Weighted Moving Average 393

7.5 BEKK Models 396

7.6 Cholesky Decomposition and Volatility Modeling 400

7.7 Dynamic Conditional Correlation Models 407

7.8 Orthogonal Transformation 412

7.9 Copula-Based Models 421

7.10 Principal Volatility Components 432

A Review of Mathematics and Statistics 443

A.1 Review of Vectors and Matrices 443

A.2 Least Squares Estimation 453

A.3 Multivariate Normal Distributions 455

A.4 Multivariate Student-t Distribution 456

A.5 Wishart and Inverted Wishart Distributions 456

A.6 Vector and Matrix Differentials 458