Analysis of Financial Time Series

This book provides a broad, mature, and systematic introduction to current financial econometric models and their applications to modeling and prediction of financial time series data. It utilizes real-world examples and real financial data throughout the book to apply the models and methods described.

The author begins with basic characteristics of financial time series data before covering three main topics:
* Analysis and application of univariate financial time series
* The return series of multiple assets
* Bayesian inference in finance methods

Key features of the new edition include additional coverage of modern day topics such as arbitrage, pair trading, realized volatility, and credit risk modeling; a smooth transition from S-Plus to R; and expanded empirical financial data sets.

The overall objective of the book is to provide some knowledge of financial time series, introduce some statistical tools useful for analyzing these series and gain experience in financial applications of various econometric methods.

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