Analysis of Financial Time Series, Third Edition (Wiley Series in Probability and Statistics)

Analysis of Financial Time Series......Page 4
Contents......Page 10
Preface......Page 20
Preface to the Second Edition......Page 22
Preface to the First Edition......Page 24
1 Financial Time Series and Their Characteristics......Page 28
1.1 Asset Returns......Page 29
1.2.1 Review of Statistical Distributions and Their Moments......Page 34
1.2.2 Distributions of Returns......Page 41
1.2.3 Multivariate Returns......Page 45
1.2.5 Empirical Properties of Returns......Page 46
1.3 Processes Considered......Page 49
Appendix: R Packages......Page 51
Exercises......Page 53
References......Page 54
2 Linear Time Series Analysis and Its Applications......Page 56
2.2 Correlation and Autocorrelation Function......Page 57
2.3 White Noise and Linear Time Series......Page 63
2.4 Simple AR Models......Page 64
2.4.1 Properties of AR Models......Page 65
2.4.2 Identifying AR Models in Practice......Page 73
2.4.3 Goodness of Fit......Page 80
2.4.4 Forecasting......Page 81
2.5 Simple MA Models......Page 84
2.5.1 Properties of MA Models......Page 86
2.5.2 Identifying MA Order......Page 87
2.5.3 Estimation......Page 88
2.5.4 Forecasting Using MA Models......Page 89
2.6.1 Properties of ARMA(1,1) Models......Page 91
2.6.3 Identifying ARMA Models......Page 93
2.6.4 Forecasting Using an ARMA Model......Page 95
2.6.5 Three Model Representations for an ARMA Model......Page 96
2.7 Unit-Root Nonstationarity......Page 98
2.7.1 Random Walk......Page 99
2.7.2 Random Walk with Drift......Page 100
2.7.4 General Unit-Root Nonstationary Models......Page 102
2.7.5 Unit-Root Test......Page 103
2.8 Seasonal Models......Page 108
2.8.1 Seasonal Differencing......Page 109
2.8.2 Multiplicative Seasonal Models......Page 111
2.9 Regression Models with Time Series Errors......Page 117
2.10 Consistent Covariance Matrix Estimation......Page 125
2.11 Long-Memory Models......Page 128
Appendix: Some SCA Commands......Page 130
Exercises......Page 131
References......Page 134
3 Conditional Heteroscedastic Models......Page 136
3.1 Characteristics of Volatility......Page 137
3.2 Structure of a Model......Page 138
3.3 Model Building......Page 140
3.3.1 Testing for ARCH Effect......Page 141
3.4 The ARCH Model......Page 143
3.4.1 Properties of ARCH Models......Page 144
3.4.3 Building an ARCH Model......Page 146
3.4.4 Some Examples......Page 150
3.5 The GARCH Model......Page 158
3.5.1 An Illustrative Example......Page 161
3.5.2 Forecasting Evaluation......Page 166
3.6 The Integrated GARCH Model......Page 167
3.7 The GARCH-M Model......Page 169
3.8 The Exponential GARCH Model......Page 170
3.8.1 Alternative Model Form......Page 171
3.8.3 Second Example......Page 172
3.8.4 Forecasting Using an EGARCH Model......Page 174
3.9 The Threshold GARCH Model......Page 176
3.10 The CHARMA Model......Page 177
3.11 Random Coefficient Autoregressive Models......Page 179
3.12 Stochastic Volatility Model......Page 180
3.13 Long-Memory Stochastic Volatility Model......Page 181
3.14 Application......Page 182
3.15.1 Use of High-Frequency Data......Page 186
3.15.2 Use of Daily Open, High, Low, and Close Prices......Page 189
3.16 Kurtosis of GARCH Models......Page 192
Appendix: Some RATS Programs for Estimating Volatility Models......Page 194
Exercises......Page 195
References......Page 198
4 Nonlinear Models and Their Applications......Page 202
4.1.1 Bilinear Model......Page 204
4.1.2 Threshold Autoregressive (TAR) Model......Page 206
4.1.3 Smooth Transition AR (STAR) Model......Page 211
4.1.4 Markov Switching Model......Page 213
4.1.5 Nonparametric Methods......Page 216
4.1.7 Nonlinear Additive AR Model......Page 225
4.1.9 Neural Networks......Page 226
4.2 Nonlinearity Tests......Page 232
4.2.1 Nonparametric Tests......Page 233
4.2.2 Parametric Tests......Page 236
4.2.3 Applications......Page 240
4.3 Modeling......Page 241
4.4.2 Forecasting Evaluation......Page 242
4.5 Application......Page 245
Appendix A: Some RATS Programs for Nonlinear Volatility Models......Page 249
Appendix B: R and S-Plus Commands for Neural Network......Page 250
Exercises......Page 251
References......Page 253
5 High-Frequency Data Analysis and Market Microstructure......Page 258
5.1 Nonsynchronous Trading......Page 259
5.2 Bid–Ask Spread......Page 262
5.3 Empirical Characteristics of Transactions Data......Page 264
5.4 Models for Price Changes......Page 271
5.4.1 Ordered Probit Model......Page 272
5.4.2 Decomposition Model......Page 275
5.5 Duration Models......Page 280
5.5.1 The ACD Model......Page 282
5.5.2 Simulation......Page 284
5.5.3 Estimation......Page 287
5.6 Nonlinear Duration Models......Page 291
5.7 Bivariate Models for Price Change and Duration......Page 292
5.8 Application......Page 298
Appendix A: Review of Some Probability Distributions......Page 303
Appendix B: Hazard Function......Page 306
Appendix C: Some RATS Programs for Duration Models......Page 307
Exercises......Page 309
References......Page 311
6 Continuous-Time Models and Their Applications......Page 314
6.2 Some Continuous-Time Stochastic Processes......Page 315
6.2.1 Wiener Process......Page 316
6.2.2 Generalized Wiener Process......Page 318
6.3.1 Review of Differentiation......Page 319
6.3.2 Stochastic Differentiation......Page 320
6.3.3 An Application......Page 321
6.3.4 Estimation of µ and ó......Page 322
6.4 Distributions of Stock Prices and Log Returns......Page 324
6.5 Derivation of Black–Scholes Differential Equation......Page 325
6.6.2 Formulas......Page 327
6.6.3 Lower Bounds of European Options......Page 331
6.6.4 Discussion......Page 332
6.7 Extension of Ito’s Lemma......Page 336
6.8 Stochastic Integral......Page 337
6.9 Jump Diffusion Models......Page 338
6.9.1 Option Pricing under Jump Diffusion......Page 342
6.10 Estimation of Continuous-Time Models......Page 345
Appendix A: Integration of Black–Scholes Formula......Page 346
Appendix B: Approximation to Standard Normal Probability......Page 347
Exercises......Page 348
References......Page 349
7 Extreme Values, Quantiles, and Value at Risk......Page 352
7.1 Value at Risk......Page 353
7.2 RiskMetrics......Page 355
7.2.1 Discussion......Page 358
7.2.3 Expected Shortfall......Page 359
7.3 Econometric Approach to VaR Calculation......Page 360
7.3.1 Multiple Periods......Page 363
7.4.1 Quantile and Order Statistics......Page 365
7.4.2 Quantile Regression......Page 368
7.5.1 Review of Extreme Value Theory......Page 369
7.5.2 Empirical Estimation......Page 372
7.5.3 Application to Stock Returns......Page 375
7.6 Extreme Value Approach to VaR......Page 380
7.6.1 Discussion......Page 383
7.6.2 Multiperiod VaR......Page 384
7.6.3 Return Level......Page 385
7.7 New Approach Based on the Extreme Value Theory......Page 386
7.7.1 Statistical Theory......Page 387
7.7.2 Mean Excess Function......Page 388
7.7.3 New Approach to Modeling Extreme Values......Page 390
7.7.4 VaR Calculation Based on the New Approach......Page 392
7.7.5 Alternative Parameterization......Page 394
7.7.6 Use of Explanatory Variables......Page 398
7.7.7 Model Checking......Page 399
7.7.8 An Illustration......Page 400
7.8 The Extremal Index......Page 404
7.8.1 The D(un) Condition......Page 405
7.8.2 Estimation of the Extremal Index......Page 408
Exercises......Page 411
References......Page 414
8 Multivariate Time Series Analysis and Its Applications......Page 416
8.1.1 Cross-Correlation Matrices......Page 417
8.1.3 Sample Cross-Correlation Matrices......Page 419
8.1.4 Multivariate Portmanteau Tests......Page 424
8.2.1 Reduced and Structural Forms......Page 426
8.2.2 Stationarity Condition and Moments of a VAR(1) Model......Page 428
8.2.3 Vector AR(p) Models......Page 430
8.2.4 Building a VAR(p) Model......Page 432
8.2.5 Impulse Response Function......Page 440
8.3 Vector Moving-Average Models......Page 444
8.4 Vector ARMA Models......Page 449
8.4.1 Marginal Models of Components......Page 454
8.5 Unit-Root Nonstationarity and Cointegration......Page 455
8.5.1 An Error Correction Form......Page 458
8.6 Cointegrated VAR Models......Page 459
8.6.1 Specification of the Deterministic Function......Page 461
8.6.2 Maximum-Likelihood Estimation......Page 462
8.6.3 Cointegration Test......Page 463
8.6.4 Forecasting of Cointegrated VAR Models......Page 464
8.6.5 An Example......Page 465
8.7 Threshold Cointegration and Arbitrage......Page 469
8.7.1 Multivariate Threshold Model......Page 471
8.7.2 The Data......Page 472
8.8 Pairs Trading......Page 473
8.8.1 Theoretical Framework......Page 474
8.8.2 Trading Strategy......Page 475
8.8.3 Simple Illustration......Page 476
Appendix A: Review of Vectors and Matrices......Page 483
Appendix B: Multivariate Normal Distributions......Page 487
Appendix C: Some SCA Commands......Page 488
Exercises......Page 489
References......Page 491
9 Principal Component Analysis and Factor Models......Page 494
9.1 A Factor Model......Page 495
9.2.1 Single-Factor Model......Page 497
9.2.2 Multifactor Models......Page 501
9.3 Fundamental Factor Models......Page 503
9.3.1 BARRA Factor Model......Page 504
9.3.2 Fama–French Approach......Page 509
9.4.1 Theory of PCA......Page 510
9.4.2 Empirical PCA......Page 512
9.5 Statistical Factor Analysis......Page 516
9.5.1 Estimation......Page 517
9.5.3 Applications......Page 519
9.6 Asymptotic Principal Component Analysis......Page 525
9.6.1 Selecting the Number of Factors......Page 526
9.6.2 An Example......Page 527
Exercises......Page 528
References......Page 530
10 Multivariate Volatility Models and Their Applications......Page 532
10.1 Exponentially Weighted Estimate......Page 533
10.2.1 Diagonal Vectorization (VEC) Model......Page 537
10.2.2 BEKK Model......Page 540
10.3.1 Use of Correlations......Page 543
10.3.2 Cholesky Decomposition......Page 544
10.4.1 Constant-Correlation Models......Page 548
10.4.2 Time-Varying Correlation Models......Page 552
10.4.3 Dynamic Correlation Models......Page 558
10.5 Higher Dimensional Volatility Models......Page 564
10.6 Factor–Volatility Models......Page 570
10.7 Application......Page 573
10.8 Multivariate t Distribution......Page 575
Appendix: Some Remarks on Estimation......Page 576
Exercises......Page 581
References......Page 582
11 State-Space Models and Kalman Filter......Page 584
11.1 Local Trend Model......Page 585
11.1.1 Statistical Inference......Page 588
11.1.2 Kalman Filter......Page 589
11.1.3 Properties of Forecast Error......Page 591
11.1.4 State Smoothing......Page 593
11.1.5 Missing Values......Page 597
11.1.6 Effect of Initialization......Page 598
11.1.8 S-Plus Commands Used......Page 599
11.2 Linear State-Space Models......Page 603
11.3.1 CAPM with Time-Varying Coefficients......Page 604
11.3.2 ARMA Models......Page 607
11.3.3 Linear Regression Model......Page 614
11.3.4 Linear Regression Models with ARMA Errors......Page 615
11.3.5 Scalar Unobserved Component Model......Page 617
11.4.1 Kalman Filter......Page 618
11.4.2 State Estimation Error and Forecast Error......Page 621
11.4.3 State Smoothing......Page 622
11.4.4 Disturbance Smoothing......Page 624
11.5 Missing Values......Page 627
11.6 Forecasting......Page 628
11.7 Application......Page 629
Exercises......Page 636
References......Page 638
12 Markov Chain Monte Carlo Methods with Applications......Page 640
12.1 Markov Chain Simulation......Page 641
12.2 Gibbs Sampling......Page 642
12.3.1 Posterior Distributions......Page 644
12.3.2 Conjugate Prior Distributions......Page 645
12.4.1 Metropolis Algorithm......Page 649
12.4.3 Griddy Gibbs......Page 650
12.5 Linear Regression with Time Series Errors......Page 651
12.6 Missing Values and Outliers......Page 655
12.6.1 Missing Values......Page 656
12.6.2 Outlier Detection......Page 659
12.7 Stochastic Volatility Models......Page 663
12.7.1 Estimation of Univariate Models......Page 664
12.7.2 Multivariate Stochastic Volatility Models......Page 670
12.8 New Approach to SV Estimation......Page 676
12.9 Markov Switching Models......Page 687
12.10 Forecasting......Page 693
12.11 Other Applications......Page 696
Exercises......Page 697
References......Page 698
Index......Page 700