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Multivariate Time Series Analysis and Applications
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Multivariate Time Series Analysis and Applications

  • Wei, William, W. S.
  • |
  • Wiley
  • |
  • 2019-03-18 출간
  • |
  • 680페이지
  • |
  • English
  • |
  • ISBN 9781119502852
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목차


About the author

Preface

Chapter 1 Fundamental Concepts and Issues of Multivariate Time Series Analysis

1.1 Introduction

1.2 Fundamental Concepts

1.2.1 Correlation and Partial Correlation Matrix Functions

1.2.2 Vector White Noise Process

1.2.3 Moving Average and Autoregressive Representations of Vector Processes

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References

Chapter 2 Vector Time Series Models

2.1 Vector Moving Average Processes

2.2 Vector Autoregressive Processes

2.3 Vector Autoregressive Moving Average Processes

2.4 Nonstationary Vector Autoregressive Moving Average Processes

2.5 Vector Time Series Model Building

2.5.1 Identification of Vector Time Series Models

2.5.2 Sample Moments of a Vector Time Series

2.5.3 Parameter Estimation, Diagnostic Checking, and Forecasting

2.5.4 Cointegration in Vector Time Series

2.6 Seasonal Vector Time Series Model

2.7 Multivariate Time Series Outliers

2.7.1 Types of Multivariate Time Series Outliers and Detections

2.7.2 Outlier Detection Through Projection Pursuit

2.8 Empirical Examples

2.8.1 First Model on U.S. Monthly Retail Sales Revenue

2.8.2 Second Model on U.S. Monthly Retail Sales Revenue

2.8.3 U.S. Macroeconomic Indicators

2.8.4 Unemployment Rates with Outliers

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Chapter 3 Multivariate Time Series Regression Models

3.1 Introduction

3.2 Multivariate Multiple Time Series Regression Models

3.2.1 Classical Multiple Regression Model

3.2.2 Multivariate Multiple Regression Model

3.3 Estimation of Multivariate Multiple Time Series Regression Model

3.3.1 The Generalized Least Squares (GLS) Estimation

3.3.2 Empirical Example I ? U.S. Retail Sales and Some National Indicators

3.4 Vector Time Series Regression Models

3.4.1 Extension of a VAR Model to VARX Models

3.4.2 Empirical Example II ? VARX Model for U.S. Retail Sales and Some National Indicators

3.5 Empirical Example III ? Total Mortality and Air Pollution in California Software Code

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Chapter 4 Principle Component Analysis of Multivariate Time Series

4.1 Introduction

4.2 Population Principal Component Analysis

4.3 Implications of Principal Component Analysis

4.4 Sample Principle Components

4.5 Empirical Examples

4.5.1 Daily Stock Returns from the First Set of Ten Stocks

4.5.2 Monthly Consumer Price Index (CPI) from Five Sectors

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Chapter 5 Factor Analysis of Multivariate Time Series

5.1 Introduction

5.2 The Orthogonal Factor Model

5.3 Estimation of the Factor Model

5.3.1 The Principal Component Method

5.3.2 Empirical Example I ? Model 1 on Daily Stock Returns from the Second Set of Ten Stocks

5.3.3 The Maximum Likelihood Method

5.3.4 Empirical Example II ? Model 2 on Daily Stock Returns from the Second Set of Ten Stocks

5.4 Factor Rotation

5.4.1 Orthogonal Rotation

5.4.2 Oblique Rotation

5.4.3 Empirical Example III ? Model 3 on Daily Stock Returns from the Second Set of Ten Stocks

5.5 Factor Scores

5.5.1 Introduction

5.5.2 Empirical Example IV ? Model 4 on Daily Stock Returns from the Second Set of Ten Stocks

5.6 Factor Models with Observable Factors

5.7 Another Empirical Example ? Yearly U.S. Sexually Transmitted Disease (STD)

5.7.1 Principal Component Analysis (PCA)

5.7.1.1 PCA for Standardized

5.7.1.2 PCAforUnstandardized

5.7.2 Factor Analysis

5.8 Concluding Remarks

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Chapter 6 Multivariate GARCH Models

6.1 Introduction

6.2 Representations of Multivariate GARCH Models

6.2.1 VEC and DVEC Models

6.2.2 Constant Conditional Correlation (CCC) Models

6.2.3 BEKK Models

6.2.4 Factor Models

6.3 O-GARCH and GO-GARCH Models

6.4 Estimation of GO-GARCH Models

6.4.1 The Two Step Estimation Method

6.4.2 The Weighted Scatter Estimation Method

6.5 Properties of the Weighted Scatter Estimator

6.5.1 Asymptotic Distribution and Statistical Inference

6.5.2 Combining Information from Different Weighting Functions

6.6 Empirical Examples

6.6.1 U.S. Weekly Interest Over Time on Six Exercise Items

6.6.2 Daily Log-returns of the SP 500 Index and Three Financial Stocks

6.6.3 The Analysis of Dow Jones Industrial Average of 30 Stocks

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Chapter 7 Repeated Measurements

7.1 Introduction

7.2 Multivariate Analysis of Variance

7.2.1 Test Treatment Effects

7.2.2 Empirical Example I - First Analysis on Body Weight of Rats Under Three Different Treatments

7.3 Models Utilizing Time Series Structure

7.3.1 Fixed Effects Model

7.3.2 Some Common Variance-Covariance Structures

7.3.3 Empirical Example II - Further Analysis on Body Weight of Rats Under Three Different Treatments

7.3.4 Random Effects and Mixed Effects Models

7.4 Nested Random Effects Model

7.5 Further Generalization and Remarks

7.6 Another Empirical Example - The Oral Condition of Neck Cancer Patients

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Chapter 8 Space-Time Series Models

8.1 Introduction

8.2 Space-Time Autoregressive Integrated Moving Average (STARIMA) Models

8.2.1 Spatial Weighting Matrix

8.2.2 STARIMA Models

8.2.3 STARMA Models

8.2.4 ST-ACF and ST-PACF

8.3 Generalized Space-Time Autoregressive Integrated Moving Average (GSTARIMA) Models

8.4 Iterative Model Building of STARMA and GSTARMA Models

8.5 Empirical Examples

8.5.1 Vehicular Theft Data

8.5.2 The Annual U.S. Labor Force Count

8.5.3 U.S. Yearly Sexually Transmitted Disease Data

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Chapter 9 Multivariate Spectral Analysis of Time Series

9.1 Introduction

9.2 Spectral Representations of Multivariate Time Series Processes

9.3 The Estimation of the Spectral Density Matrix

9.3.1 The Smoothed Spectrum Matrix

9.3.2 Multitaper Smoothing

9.3.3 Smoothing Spline

9.3.4 Bayesian Method

9.3.5 Penalized Whittle Likelihood

9.3.6 VARMA Spectral Estimation

9.4 Empirical Examples of Stationary Vector Time Series

9.4.1 Sample Spectrum

9.4.2 Bayesian Method

9.4.3 Penalized Whittle Likelihood Method

9.4.4 Example of VAR Spectrum Estimation

9.5 Spectrum Analysis of Nonstationary Vector Time Series

9.5.1 Introduction

9.5.2 Spectrum Representations of a Nonstationary Multivariate Process

9.5.2.1 Time-varying Autoregressive Model

9.5.2.2 Smoothing Spline ANOVA Model

9.5.2.3 Piecewise Vector Autoregressive Model

9.5.2.4 Bayesian Methods

9.6 Empirical Spectrum Example of Nostationary Vector Time Series

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Chapter 10 Dimension Reduction in High Dimensional Multivariate Time Series Analysis

10.1 Introduction

10.2 Existing Methods

10.2.1 Regularization Methods

10.2.1.1 The Lasso Method

10.2.1.2 The Lag-weighted Lasso Method

10.2.1.3 The Hierarchical Vector Autoregression (HVAR) Method

10.2.2 The Space-Time AR (STAR) Model

10.2.3 The Model-based Cluster Method

10.2.4 The Factor Analysis

10.3 The Proposed Method for High Dimension Reduction

10.4 Simulation Studies

10.4.1 Scenario 1

10.4.2 Scenario 2

10.4.3 Scenario 3

10.5 Empirical Examples

10.5.1 The Macroeconomic Time Series

10.5.2 The Yearly U.S. Sexually Transmitted Disease Data

10.6 Further Discussions and Remarks

10.6.1 More on Clustering

10.6.2 Forming Aggregate Data Through Both Time Domain and Frequency Domain Clustering

10.6.3 The Specification of Aggregate Matrix and Its Associated Aggregate Dimension

10.6.4 Be Aware of Other Forms of Aggregation

Appendix: Parameter Estimation Results of Various Procedures

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Data Appendix (Bookdata)

Author Index

Subject Index
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