Analysis of Financial Time Series, 3rd Edition

Preface xvii

Preface to the Second Edition xix

Preface to the First Edition xxi

1 Financial Time Series and Their Characteristics 1

1.1 Asset Returns, 2

1.2 Distributional Properties of Returns, 7

1.3 Processes Considered, 22

2 Linear Time Series Analysis and Its Applications 29

2.1 Stationarity, 30

2.2 Correlation and Autocorrelation Function, 30

2.3 White Noise and Linear Time Series, 36

2.4 Simple AR Models, 37

2.5 Simple MA Models, 57

2.6 Simple ARMA Models, 64

2.7 Unit-Root Nonstationarity, 71

2.8 Seasonal Models, 81

2.9 Regression Models with Time Series Errors, 90

2.10 Consistent Covariance Matrix Estimation, 97

2.11 Long-Memory Models, 101

3 Conditional Heteroscedastic Models 109

3.1 Characteristics of Volatility, 110

3.2 Structure of a Model, 111

3.3 Model Building, 113

3.4 The ARCH Model, 115

3.5 The GARCH Model, 131

3.6 The Integrated GARCH Model, 140

3.7 The GARCH-M Model, 142

3.8 The Exponential GARCH Model, 143

3.9 The Threshold GARCH Model, 149

3.10 The CHARMA Model, 150

3.11 Random Coefficient Autoregressive Models, 152

3.12 Stochastic Volatility Model, 153

3.13 Long-Memory Stochastic Volatility Model, 154

3.14 Application, 155

3.15 Alternative Approaches, 159

3.16 Kurtosis of GARCH Models, 165

4 Nonlinear Models and Their Applications 175

4.1 Nonlinear Models, 177

4.2 Nonlinearity Tests, 205

4.3 Modeling, 214

4.4 Forecasting, 215

4.5 Application, 218

5 High-Frequency Data Analysis and Market Microstructure 231

5.1 Nonsynchronous Trading, 232

5.2 Bid–Ask Spread, 235

5.3 Empirical Characteristics of Transactions Data, 237

5.4 Models for Price Changes, 244

5.5 Duration Models, 253

5.6 Nonlinear Duration Models, 264

5.7 Bivariate Models for Price Change and Duration, 265

5.8 Application, 270

6 Continuous-Time Models and Their Applications 287

6.1 Options, 288

6.2 Some Continuous-Time Stochastic Processes, 288

6.3 Ito's Lemma, 292

6.4 Distributions of Stock Prices and Log Returns, 297

6.5 Derivation of Black–Scholes Differential Equation, 298

6.6 Black–Scholes Pricing Formulas, 300

6.7 Extension of Ito's Lemma, 309

6.8 Stochastic Integral, 310

6.9 Jump Diffusion Models, 311

6.10 Estimation of Continuous-Time Models, 318

7 Extreme Values, Quantiles, and Value at Risk 325

7.1 Value at Risk, 326

7.2 RiskMetrics, 328

7.3 Econometric Approach to VaR Calculation, 333

7.4 Quantile Estimation, 338

7.5 Extreme Value Theory, 342

7.6 Extreme Value Approach to VaR, 353

7.7 New Approach Based on the Extreme Value Theory, 359

7.8 The Extremal Index, 377

8 Multivariate Time Series Analysis and Its Applications 389

8.1 Weak Stationarity and Cross-Correlation Matrices, 390

8.2 Vector Autoregressive Models, 399

8.3 Vector Moving-Average Models, 417

8.4 Vector ARMA Models, 422

8.5 Unit-Root Nonstationarity and Cointegration, 428

8.6 Cointegrated VAR Models, 432

8.7 Threshold Cointegration and Arbitrage, 442

8.8 Pairs Trading, 446

9 Principal Component Analysis and Factor Models 467

9.1 A Factor Model, 468

9.2 Macroeconometric Factor Models, 470

9.3 Fundamental Factor Models, 476

9.4 Principal Component Analysis, 483

9.5 Statistical Factor Analysis, 489

9.6 Asymptotic Principal Component Analysis, 498

10 Multivariate Volatility Models and Their Applications 505

10.1 Exponentially Weighted Estimate, 506

10.2 Some Multivariate GARCH Models, 510

10.3 Reparameterization, 516

10.4 GARCH Models for Bivariate Returns, 521

10.5 Higher Dimensional Volatility Models, 537

10.6 Factor–Volatility Models, 543

10.7 Application, 546

10.8 Multivariate t Distribution, 548

11 State-Space Models and Kalman Filter 557

11.1 Local Trend Model, 558

11.2 Linear State-Space Models, 576

11.3 Model Transformation, 577

11.4 Kalman Filter and Smoothing, 591

11.5 Missing Values, 600

11.6 Forecasting, 601

11.7 Application, 602

12 Markov Chain Monte Carlo Methods with Applications 613

12.1 Markov Chain Simulation, 614

12.2 Gibbs Sampling, 615

12.3 Bayesian Inference, 617

12.4 Alternative Algorithms, 622

12.5 Linear Regression with Time Series Errors, 624

12.6 Missing Values and Outliers, 628

12.7 Stochastic Volatility Models, 636

12.8 New Approach to SV Estimation, 649

12.9 Markov Switching Models, 660

12.10 Forecasting, 666

12.11 Other Applications, 669

Exercises, 670

References, 671

Index 673