Modeling financial time series with S-plus / Eric Zivot, Jiahui Wang.

Format:

Book

Author/Creator:

Zivot, Eric.

Contributor:

Wang, Jiahui.

Alumni and Friends Memorial Book Fund.

Language:

English

Subjects (All):

Finance--Mathematical models.

Finance.

Time-series analysis.

Finance--Econometric models.

S-Plus.

Physical Description:

xxii, 998 pages : illustrations cm

Edition:

Second edition.

Place of Publication:

New York, NY : Springer, [2006]

Summary:

The field of financial econometrics has exploded over the last decade. This book represents an integration of theory, methods, and examples using the S-PLUS statistical modeling language and the S+FinMetrics module to facilitate the practice of financial econometrics. This is the first book to show the power of S-PLUS for the analysis of time series data. It is written for researchers and practitioners in the finance industry, academic researchers in economics and finance, and advanced MBA and graduate students in economics and finance. Readers are assumed to have a basic knowledge of S-PLUS and a solid grounding in basic statistics and time series concepts.

This second edition is updated to cover S+FinMetrics 2.0 and includes new chapters on copulas, nonlinear regime switching models, continuous-time financial models, generalized method of moments, semi-nonparametric conditional density models, and the efficient method of moments.

Contents:

1 S and S-PLUS 1

1.2 S Objects 2

1.2.2 Class 3

1.3 Modeling Functions in S+FinMetrics 8

1.3.1 Formula Specification 8

1.4 S-PLUS Resources 12

1.4.2 Internet 13

2 Time Series Specification, Manipulation, and Visualization in S-PLUS 15

2.2 The Specification of "timeSeries" Objects in S-PLUS 15

2.2.1 Basic Manipulations 18

2.2.2 S-PLUS "timeDate" Objects 19

2.2.3 Creating Common "timeDate" Sequences 24

2.2.4 Miscellaneous Time and Date Functions 28

2.2.5 Creating "timeSeries" Objects 28

2.2.6 Aggregating and Disaggregating Time Series 31

2.2.7 Merging Time Series 38

2.2.8 Dealing with Missing Values Using the S+FinMetrics Function interpNA 39

2.3 Time Series Manipulation in S-PLUS 40

2.3.1 Creating Lags and Differences 40

2.3.2 Return Definitions 43

2.3.3 Computing Asset Returns Using the S+FinMetrics Function getReturns 46

2.4 Visualizing Time Series in S-PLUS 48

2.4.1 Plotting "timeSeries" Using the S-PLUS Generic plot Function 48

2.4.2 Plotting "timeSeries" Using the S+FinMetrics Trellis Plotting Functions 52

3 Time Series Concepts 57

3.2 Univariate Time Series 58

3.2.1 Stationary and Ergodic Time Series 58

3.2.2 Linear Processes and ARMA Models 64

3.2.3 Autoregressive Models 66

3.2.4 Moving Average Models 71

3.2.5 ARMA(p,q) Models 74

3.2.6 Estimation of ARMA Models and Forecasting 76

3.2.7 Martingales and Martingale Difference Sequences 83

3.2.8 Long-run Variance 85

3.2.9 Variance Ratios 88

3.3 Univariate Nonstationary Time Series 93

3.4 Long Memory Time Series 97

3.5 Multivariate Time Series 101

3.5.1 Stationary and Ergodic Multivariate Time Series 101

3.5.2 Multivariate Wold Representation 106

3.5.3 Long Run Variance 107

4 Unit Root Tests 111

4.2 Testing for Nonstationarity and Stationarity 112

4.3 Autoregressive Unit Root Tests 114

4.3.1 Simulating the DF and Normalized Bias Distributions 116

4.3.2 Trend Cases 118

4.3.3 Dickey-Fuller Unit Root Tests 120

4.3.4 Phillips-Perron Unit Root Tests 127

4.4 Stationarity Tests 129

4.4.1 Simulating the KPSS Distributions 130

4.4.2 Testing for Stationarity Using the S+FinMetrics Function stationaryTest 131

4.5 Some Problems with Unit Root Tests 132

4.6 Efficient Unit Root Tests 132

4.6.1 Point Optimal Tests 133

4.6.2 DF-GLS Tests 134

4.6.3 Modified Efficient PP Tests 134

4.6.4 Estimating [lambda superscript 2] 135

4.6.5 Choosing Lag Lengths to Achieve Good Size and Power 135

5 Modeling Extreme Values 141

5.2 Modeling Maxima and Worst Cases 142

5.2.1 The Fisher-Tippet Theorem and the Generalized Extreme Value Distribution 143

5.2.2 Estimation of the GEV Distribution 147

5.2.3 Return Level 153

5.3 Modeling Extremes Over High Thresholds 157

5.3.1 The Limiting Distribution of Extremes Over High Thresholds and the Generalized Pareto Distribution 159

5.3.2 Estimating the GPD by Maximum Likelihood 164

5.3.3 Estimating the Tails of the Loss Distribution 165

5.3.4 Risk Measures 171

5.4 Hill's Non-parametric Estimator of Tail Index 174

5.4.1 Hill Tail and Quantile Estimation 175

6 Time Series Regression Modeling 181

6.2 Time Series Regression Model 182

6.2.1 Least Squares Estimation 183

6.2.2 Goodness of Fit 183

6.2.3 Hypothesis Testing 184

6.2.4 Residual Diagnostics 185

6.3 Time Series Regression Using the S+FinMetrics Function OLS 185

6.4 Dynamic Regression 201

6.4.1 Distributed Lags and Polynomial Distributed Lags 205

6.4.2 Polynomial Distributed Lag Models 207

6.5 Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation 208

6.5.1 The Eicker-White Heteroskedasticity Consistent (HC) Covariance Matrix Estimate 209

6.5.2 Testing for Heteroskedasticity 211

6.5.3 The Newey-West Heteroskedasticity and Autocorrelation Consistent (HAC) Covariance Matrix Estimate 214

6.6 Recursive Least Squares Estimation 217

6.6.1 CUSUM and CUSUMSQ Tests for Parameter Stability 218

6.6.2 Computing Recursive Least Squares Estimates Using the S+FinMetrics Function RLS 219

7 Univariate GARCH Modeling 223

7.2 The Basic ARCH Model 224

7.2.1 Testing for ARCH Effects 228

7.3 The GARCH Model and Its Properties 229

7.3.1 ARMA Representation of GARCH Model 230

7.3.2 GARCH Model and Stylized Facts 230

7.4 GARCH Modeling Using S+FinMetrics 232

7.4.1 GARCH Model Estimation 232

7.4.2 GARCH Model Diagnostics 235

7.5 GARCH Model Extensions 240

7.5.1 Asymmetric Leverage Effects and News Impact 241

7.5.2 Two Components Model 247

7.5.3 GARCH-in-the-Mean Model 250

7.5.4 ARMA Terms and Exogenous Variables in Conditional Mean Equation 252

7.5.5 Exogenous Explanatory Variables in the Conditional Variance Equation 254

7.5.6 Non-Gaussian Error Distributions 257

7.6 GARCH Model Selection and Comparison 260

7.6.1 Constrained GARCH Estimation 261

7.7 GARCH Model Prediction 262

7.8 GARCH Model Simulation 265

8 Long Memory Time Series Modeling 271

8.2 Long Memory Time Series 272

8.3 Statistical Tests for Long Memory 276

8.3.1 R/S Statistic 276

8.3.2 GPH Test 278

8.4 Estimation of Long Memory Parameter 280

8.4.1 R/S Analysis 280

8.4.2 Periodogram Method 282

8.4.3 Whittle's Method 283

8.5 Estimation of FARIMA and SEMIFAR Models 284

8.5.1 Fractional ARIMA Models 285

8.5.2 SEMIFAR Model 292

8.6 Long Memory GARCH Models 296

8.6.1 FIGARCH and FIEGARCH Models 296

8.6.2 Estimation of Long Memory GARCH Models 297

8.6.3 Custom Estimation of Long Memory GARCH Models 301

8.7 Prediction from Long Memory Models 304

8.7.1 Prediction from FARIMA/SEMIFAR Models 304

8.7.2 Prediction from FIGARCH/FIEGARCH Models 308

9 Rolling Analysis of Time Series 313

9.2 Rolling Descriptive Statistics 314

9.2.1 Univariate Statistics 314

9.2.2 Bivariate Statistics 321

9.2.3 Exponentially Weighted Moving Averages 323

9.2.4 Moving Average Methods for Irregularly Spaced High Frequency Data 327

9.2.5 Rolling Analysis of Miscellaneous Functions 334

9.3 Technical Analysis Indicators 337

9.3.1 Price Indicators 338

9.3.2 Momentum Indicators and Oscillators 338

9.3.3 Volatility Indicators 340

9.3.4 Volume Indicators 341

9.4 Rolling Regression 342

9.4.1 Estimating Rolling Regressions Using the S+FinMetrics Function rollOLS 343

9.4.2 Rolling Predictions and Backtesting 349

9.5 Rolling Analysis of General Models Using the S+FinMetrics Function roll 358

10 Systems of Regression Equations 361

10.2 Systems of Regression Equations 362

10.3 Linear Seemingly Unrelated Regressions 364

10.3.1 Estimation 364

10.3.2 Analysis of SUR Models with the S+FinMetrics Function SUR 367

10.4 Nonlinear Seemingly Unrelated Regression Models 374

10.4.1 Analysis of Nonlinear SUR Models with the S+FinMetrics Function NLSUR 375

11 Vector Autoregressive Models for Multivariate Time Series 385

11.2 The Stationary Vector Autoregression Model 386

11.2.1 Estimation 388

11.2.2 Inference on Coefficients 390

11.2.3 Lag Length Selection 390

11.2.4 Estimating VAR Models Using the S+FinMetrics Function VAR 390

11.3 Forecasting 398

11.3.1 Traditional Forecasting Algorithm 398

11.3.2 Simulation-Based Forecasting 402

11.4 Structural Analysis 406

11.4.1 Granger Causality 407

11.4.2 Impulse Response Functions 409

11.4.3 Forecast Error Variance Decompositions 414

11.5 An Extended Example 416

11.6 Bayesian Vector Autoregression 424

11.6.1 An Example of a Bayesian VAR Model 424

11.6.2 Conditional Forecasts 427

12 Cointegration 431

12.2 Spurious Regression and Cointegration 432

12.2.1 Spurious Regression 432

12.2.2 Cointegration 435

12.2.3 Cointegration and Common Trends 437

12.2.4 Simulating Cointegrated Systems 437

12.2.5 Cointegration and Error Correction Models 441

12.3 Residual-Based Tests

for Cointegration 444

12.3.1 Testing for Cointegration When the Cointegrating Vector Is Pre-specified 444

12.3.2 Testing for Cointegration When the Cointegrating Vector Is Estimated 447

12.4 Regression-Based Estimates of Cointegrating Vectors and Error Correction Models 450

12.4.1 Least Square Estimator 450

12.4.2 Stock and Watson's Efficient Lead/Lag Estimator 451

12.4.3 Estimating Error Correction Models by Least Squares 454

12.5 VAR Models and Cointegration 455

12.5.1 The Cointegrated VAR 456

12.5.2 Johansen's Methodology for Modeling Cointegration 458

12.5.3 Specification of Deterministic Terms 459

12.5.4 Likelihood Ratio Tests for the Number of Cointegrating Vectors 461

12.5.5 Testing Hypothesis on Cointegrating Vectors Using the S+FinMetrics Function coint 463

12.5.6 Maximum Likelihood Estimation of the Cointegrated VECM 467

12.5.7 Maximum Likelihood Estimation of the Cointegrated VECM Using the S+FinMetrics Function VECM 468

12.5.8 Forecasting from the VECM 474

12.6 Appendix: Maximum Likelihood Estimation of a Cointegrated VECM 476

13 Multivariate GARCH Modeling 481

13.2 Exponentially Weighted Covariance Estimate 482

13.3 Diagonal VEC Model 486

13.4 Multivariate GARCH Modeling in S+FinMetrics 487

13.4.1 Multivariate GARCH Model Estimation 487

13.4.2 Multivariate GARCH Model Diagnostics 490

13.5 Multivariate GARCH Model Extensions 496

13.5.1 Matrix-Diagonal Models 496

13.5.2 BEKK Models 498

13.5.3 Univariate GARCH-based Models 499

13.5.4 ARMA Terms and Exogenous Variables 504

13.5.5 Multivariate Conditional t-Distribution 508

13.6 Multivariate GARCH Prediction 509

13.7 Custom Estimation of GARCH Models 512

13.7.1 GARCH Model Objects 512

13.7.2 Revision of GARCH Model Estimation 514

13.8 Multivariate GARCH Model Simulation 515

14 State Space Models 519

14.2 State Space Representation 520

14.2.1 Initial Conditions 521

14.2.2 State Space Representation in S+FinMetrics/SsfPack 521

14.2.3 Missing Values 527

14.2.4 S+FinMetrics/SsfPack Functions for Specifying the State Space Form for Some Common Time Series Models 528

14.2.5 Simulating Observations from the State Space Model 540

14.3 Algorithms 543

14.3.1 Kalman Filter 543

14.3.2 Kalman Smoother 543

14.3.3 Smoothed State and Response Estimates 544

14.3.4 Smoothed Disturbance Estimates 544

14.3.5 Forecasting 544

14.3.6 S+FinMetrics/SsfPack Implementation of State Space Modeling Algorithms 545

14.4 Estimation of State Space Models 552

14.4.1 Prediction Error Decomposition of Log-Likelihood 552

14.4.2 Fitting State Space Models Using the S+FinMetrics/SsfPack Function SsfFit 554

14.4.3 Quasi-Maximum Likelihood Estimation 561

14.5 Simulation Smoothing 565

15 Factor Models for Asset Returns 569

15.2 Factor Model Specification 570

15.3 Macroeconomic Factor Models for Returns 571

15.3.1 Sharpe's Single Index Model 572

15.3.2 The General Multifactor Model 577

15.4 Fundamental Factor Model 580

15.4.1 BARRA-type Single Factor Model 581

15.4.2 BARRA-type Industry Factor Model 582

15.5 Statistical Factor Models for Returns 590

15.5.1 Factor Analysis 590

15.5.2 Principal Components 597

15.5.3 Asymptotic Principal Components 606

15.5.4 Determining the Number of Factors 610

16 Term Structure of Interest Rates 617

16.2 Discount, Spot and Forward Rates 618

16.2.1 Definitions and Rate Conversion 618

16.2.2 Rate Conversion in S+FinMetrics 619

16.3 Quadratic and Cubic Spline Interpolation 620

16.4 Smoothing Spline Interpolation 624

16.5 Nelson-Siegel Function 628

17 Robust Change Detection 635

17.2 REGARIMA Models 636

17.3 Robust Fitting of REGARIMA Models 637

17.4 Prediction Using REGARIMA Models 642

17.5 Controlling Robust Fitting of REGARIMA Models 643

17.5.1 Adding Seasonal Effects 643

17.5.2 Controlling Outlier Detection 645

17.5.3 Iterating the Procedure 647

17.6 Algorithms of Filtered [tau]-Estimation 649

17.6.1 Classical Maximum Likelihood Estimates 650

17.6.2 Filtered [tau]-Estimates 651

18 Nonlinear Time Series Models 653

18.2 BDS Test for Nonlinearity 654

18.2.1 BDS Test Statistic 655

18.2.2 Size of BDS Test 655

18.2.3 BDS Test as a Nonlinearity Test and a Misspecification Test 657

18.3 Threshold Autoregressive Models 662

18.3.1 TAR and SETAR Models 663

18.3.2 Tsay's Approach 664

18.3.3 Hansen's Approach 671

18.4 Smooth Transition Autoregressive Models 678

18.4.1 Logistic and Exponential STAR Models 678

18.4.2 Test for STAR Nonlinearity 680

18.4.3 Estimation of STAR Models 683

18.5 Markov Switching State Space Models 687

18.5.1 Discrete State Markov Process 688

18.5.2 Markov Switching AR Process 690

18.5.3 Markov Switching State Space Models 691

18.6 An Extended Example: Markov Switching Coincident Index 701

18.6.1 State Space Representation of Markov Switching Coincident Index Model 702

18.6.2 Approximate MLE of Markov Switching Coincident Index 705

19 Copulas 713

19.2 Motivating Example 714

19.3 Definitions and Basic Properties of Copulas 722

19.3.1 Properties of Distributions 722

19.3.2 Copulas and Sklar's Theorem 724

19.3.3 Dependence Measures and Copulas 726

19.4 Parametric Copula Classes and Families 729

19.4.1 Normal Copula 729

19.4.2 Normal Mixture Copula 730

19.4.3 Extreme Value Copula Class 730

19.4.4 Archimedean Copulas 732

19.4.5 Archimax Copulas 735

19.4.6 Representation of Copulas in S+FinMetrics 735

19.4.7 Creating Arbitrary Bivariate Distributions 743

19.4.8 Simulating from Arbitrary Bivariate Distributions 745

19.5 Fitting Copulas to Data 747

19.5.1 Empirical Copula 747

19.5.2 Maximum Likelihood Estimation 750

19.5.3 Fitting Copulas Using the S+FinMetrics/EVANESCE Function fit.copula 751

19.6 Risk Management Using Copulas 754

19.6.1 Computing Portfolio Risk Measures Using Copulas 754

19.6.2 Computing VaR and ES by Simulation 755

20 Continuous-Time Models for Financial Time Series 759

20.2 SDEs: Background 760

20.3 Approximating Solutions to SDEs 761

20.4 S+FinMetrics Functions for Solving SDEs 765

20.4.1 Problem-Specific Simulators 765

20.4.2 General Simulators 771

21 Generalized Method of Moments 785

21.2 Single Equation Linear GMM 786

21.2.1 Definition of the GMM Estimator 787

21.2.2 Specification Tests in Overidentified Models 791

21.2.3 Two-Stage Least Squares as an Efficient GMM Estimator 792

21.3 Estimation of S 793

21.3.1 Serially Uncorrelated Moments 794

21.3.2 Serially Correlated Moments 794

21.3.3 Estimating S Using the S+FinMetrics Function var.hac 797

21.4 GMM Estimation Using the S+FinMetrics Function GMM 797

21.5 Hypothesis Testing for Linear Models 808

21.5.1 Testing Restrictions on Coefficients 808

21.5.2 Testing Subsets of Orthogonality Conditions 812

21.5.3 Testing Instrument Relevance 813

21.6 Nonlinear GMM 816

21.6.1 Asymptotic Properties 818

21.6.2 Hypothesis Tests for Nonlinear Models 819

21.7 Examples of Nonlinear Models 819

21.7.1 Student's t Distribution 819

21.7.2 MA(1) Model 821

21.7.3 Euler Equation Asset Pricing Model 827

21.7.4 Stochastic Volatility Model 833

21.7.5 Interest Rate Diffusion Model 838

22 Seminonparametric Conditional Density Models 847

22.2 Overview of SNP Methodology 848

22.3 Estimating SNP Models in S+FinMetrics 851

22.3.1 Example Data 853

22.3.2 Markovian Time Series and the Gaussian Vector Autoregression Model 855

22.3.3 Hermite Expansion and the Semiparametric VAR 860

22.3.4 Conditional Heterogeneity 868

22.3.5 ARCH/GARCH Leading Term 874

22.4 SNP Model Selection 880

22.4.1 Random Restarts 881

22.4.2 The expand Function 886

22.4.3 The SNP.auto Function 889

22.5 SNP Model Diagnostics 891

22.5.1 Residual Analysis 892

22.5.2 Simulation 896

22.6 Prediction from an SNP Model 897

22.7 Data Transformations 899

22.7.1 Centering and Scaling Transformation 899

22.7.2 Transformations to Deal with Heavy Tailed Data 901

22.7.3 Transformation to Deal with Small SNP Density Values 903

22.8.1 SNP Models for Daily Returns on Microsoft Stock 904

22.8.2 SNP Models for Daily Returns on the S&P 500 Index 909

22.8.3 SNP Models for Weekly 3-Month U.S.

T-Bill Rates 914

23 Efficient Method of Moments 923

23.2 An Overview of the EMM Methodology 925

23.2.1 Continuous-Time Stochastic Volatility Model for Interest Rates 925

23.2.2 Minimum Chi-Squared Estimators 928

23.2.3 Efficiency Considerations 930

23.2.4 A General Purpose Auxiliary Model 935

23.2.5 The Projection Step 935

23.2.6 The Estimation Step 936

23.3 EMM Estimation in S+FinMetrics 938

23.3.1 Simulator Functions 940

23.3.2 SNP Auxiliary Model Estimation 943

23.4.1 MA(1) Model 944

23.4.2 Discrete-Time Stochastic Volatility Models 954

23.4.3 Interest Rate Diffusion Models 966.

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Alumni and Friends Memorial Book Fund.

ISBN:

0387279652

0387217630

OCLC:

63518964

Publisher Number:

9780387279657

Online:

Publisher description