用S-PLUS做金融数据统计分析 英文PDF|Epub|txt|kindle电子书版本网盘下载

用S-PLUS做金融数据统计分析 英文PDF格式电子书版下载

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Part Ⅰ DATA EXPLORATION,ESTIMATION AND SIMULATION3

1 UNIVARIATE EXPLORATORY DATA ANALYSIS3

1.1 Data,Random Variables and Their Distributions3

1.1.1 The PCS Data4

1.1.2 The S＆P 500 Index and Financial Returns5

1.1.3 Random Variables and Their Distributions7

1.1.4 Examples of Probability Distribution Families8

1.2 First Exploratory Data Analysis Tools13

1.2.1 Random Samples13

1.2.2 Histograms14

1.3 More Nonparametric Density Estimation16

1.3.1 Kernel Density Estimation17

1.3.2 Comparison with the Histogram19

1.3.3 S＆P Daily Returns19

1.3.4 Importance of the Choice of the Bandwidth22

1.4 Quantiles and Q-Q Plots23

1.4.1 Understanding the Meaning of Q-Q Plots24

1.4.2 Value at Risk and Expected Shortfall25

1.5 Estimation from Empirical Data28

1.5.1 The Empirical Distribution Function28

1.5.2 Order Statistics29

1.5.3 Empirical Q-Q Plots30

1.6 Random Generators and Monte Carlo Samples31

1.7 Extremes and Heavy Tail Distributions35

1.7.1 S＆P Daily Returns,Once More35

1.7.2 The Example of the PCS Index37

1.7.3 The Example of the Weekly S＆P Returns41

Problems43

Notes ＆ Complements46

2 MULTIVARIATE DATA EXPLORATION49

2.1 Multivariate Data and First Measure of Dependence49

2.1.1 Density Estimation51

2.1.2 The Correlation Coefficient53

2.2 The Multivariate Normal Distribution56

2.2.1 Simulation of Random Samples57

2.2.2 The Bivariate Case58

2.2.3 A Simulation Example59

2.2.4 Let's Have Some Coffee60

2.2.5 Is the Joint Distribution Normal?62

2.3 Marginals and More Measures of Dependence63

2.3.1 Estimation of the Coffee Log-Return Distributions64

2.3.2 More Measures of Dependence68

2.4 Copulas and Random Simulations70

2.4.1 Copulas71

2.4.2 First Examples of Copula Families72

2.4.3 Copulas and General Bivariate Distributions74

2.4.4 Fitting Copulas76

2.4.5 Monte Carlo Simulations with Copulas77

2.4.6 A Risk Management Example80

2.5 Principal Component Analysis84

2.5.1 Identification of the Principal Components of a Data Set84

2.5.2 PCA with S-Plus87

2.5.3 Effective Dimension of the Space of Yield Curves87

2.5.4 Swap Rate Curves90

Appendix 1:Calculus with Random Vectors and Matrices92

Appendix 2:Families ofCopulas95

Problems98

Notes ＆ Complements101

Part Ⅱ REGRESSION105

3 PARAMETRIC REGRESSION105

3.1 Simple Linear Regression105

3.1.1 Getting the Data106

3.1.2 First Plots107

3.1.3 Regression Set-up108

3.1.4 Simple Linear Regression111

3.1.5 Cost Minimizations114

3.1.6 Regression as a Minimization Problem114

3.2 Regression for Prediction ＆ Sensitivities116

3.2.1 Prediction116

3.2.2 Introductory Discussion of Sensitivity and Robustness118

3.2.3 Comparing L2 and L1 Regressions119

3.2.4 Taking Another Look at the Coffee Data121

3.3 Smoothing versus Distribution Theory123

3.3.1 Regression and Conditional Expectation123

3.3.2 Maximum Likelihood Approach124

3.4 Multiple Regression129

3.4.1 Notation129

3.4.2 The S-Plus Function lm130

3.4.3 R2 as a Regression Diagnostic131

3.5 Matrix Formulation and Linear Models133

3.5.1 Linear Models134

3.5.2 Least Squares(Linear)Regression Revisited134

3.5.3 First Extensions139

3.5.4 Testing the CAPM142

3.6 Polynomial Regression145

3.6.1 Polynomial Regression as a Linear Model146

3.6.2 Example of S-Plus Commands146

3.6.3 Important Remark148

3.6.4 Prediction with Polynomial Regression148

3.6.5 Choice of the Degree p150

3.7 Nonlinear Regression150

3.8 Term Structure of Interest Rates:A Crash Course154

3.9 Parametric Yield Curve Estimation160

3.9.1 Estimation Procedures160

3.9.2 Practical Implementation161

3.9.3 S-Plus Experiments163

3.9.4 Concluding Remarks165

Appendix:Cautionary Notes on Some S-Plus Idiosyncracies166

Problems169

Notes ＆ Complements172

4 LOCAL ＆ NONPARAMETRIC REGRESSION175

4.1 Review of the Regression Setup175

4.2 Natural Splines as Local Smoothers177

4.3 Nonparametric Scatterplot Smoothers178

4.3.1 Smoothing Splines179

4.3.2 Locally Weighted Regression181

4.3.3 A Robust Smoother182

4.3.4 The Super Smoother183

4.3.5 The Kernel Smoother183

4.4 More Yield Curve Estimation186

4.4.1 A First Estimation Method186

4.4.2 A Direct Application of Smoothing Splines188

4.4.3 US and Japanese Instantaneous Forward Rates188

4.5 Multivariate Kernel Regression189

4.5.1 Running the Kernel in S-Plus192

4.5.2 An Example Involving the June 1998 S＆P Futures Contract193

4.6 Projection Pursuit Regression197

4.6.1 The S-Plus Function ppreg198

4.6.2 ppreg Prediction of the S&P Indicators200

4.7 Nonparametric Option Pricing205

4.7.1 Generalities on Option Pricing205

4.7.2 Nonparametric Pricing Alternatives212

4.7.3 Description of the Data213

4.7.4 The Actual Experiment214

4.7.5 Numerical Results220

Appendix:Kernel Density Estimation ＆ Kernel Regression222

Problems225

Notes ＆ Complements233

Part Ⅲ TIME SERIES ＆ STATE SPACE MODELS239

5 TIME SERIES MODELS:AR,MA,ARMA,＆ ALL THAT239

5.1 Notation and First Definitions239

5.1.1 Notation239

5.1.2 Regular Time Series and Signals240

5.1.3 Calendar and Irregular Time Series241

5.1.4 Example of Daily S＆P 500 Futures Contracts243

5.2 High Frequency Data245

5.2.1 TimeDate Manipulations248

5.3 Time Dependent Statistics and Stationarity253

5.3.1 Statistical Moments253

5.3.2 The Notion of Stationarity254

5.3.3 The Search for Stationarity258

5.3.4 The Example of the CO2 Concentrations261

5.4 First Examples of Models263

5.4.1 White Noise264

5.4.2 Random Walk267

5.4.3 Auto Regressive Time Series268

5.4.4 Moving Average Time Series272

5.4.5 Using the Backward Shift Operator B275

5.4.6 Linear Processes276

5.4.7 Causality,Stationarity and Invertibility277

5.4.8 ARMA Time Series281

5.4.9 ARIMA Models282

5.5 Fitting Models to Data282

5.5.1 Practical Steps282

5.5.2 S-Plus Implementation284

5.6 Putting a Price on Temperature289

5.6.1 Generalities on Degree Days290

5.6.2 Temperature Options291

5.6.3 Statistical Analysis of Temperature Historical Data294

Appendix:More S-Plus Idiosyncracies301

Problems304

Notes ＆ Complements308

6 MULTIVARIATE TIME SERIES,LINEAR SYSTEMS & KALMAN FILTERING311

6.1 Multivariate Time Series311

6.1.1 Stationarity and Auto-Covariance Functions312

6.1.2 Multivariate White Noise312

6.1.3 Multivariate AR Models313

6.1.4 Backto Temperature Options316

6.1.5 Multivariate MA ＆ ARIMA Models318

6.1.6 Cointegration319

6.2 State Space Models321

6.3 Factor Models as Hidden Markov Processes323

6.4 Kalman Filtering of Linear Systems326

6.4.1 One-Step-Ahead Prediction326

6.4.2 Derivation of the Recursive Filtering Equations327

6.4.3 Writing an S Function for Kalman Prediction329

6.4.4 Filtering331

6.4.5 More Predictions332

6.4.6 Estimation of the Parameters333

6.5 Applications to Linear Models335

6.5.1 State Space Representation of Linear Models335

6.5.2 Linear Models with Time Varying Coefficients336

6.5.3 CAPM with Time Varying β's337

6.6 State Space Representation of Time Series338

6.6.1 The Case of AR Series339

6.6.2 The General Case of ARMA Series341

6.6.3 Fitting ARMA Models by Maximum Likelihood342

6.7 Example:Prediction of Quarterly Earnings343

Problems346

Notes ＆ Complements351

7 NONLINEAR TIME SERIES:MODELS AND SIMULATION353

7.1 First Nonlinear Time Series Models353

7.1.1 Fractional Time Series354

7.1.2 Nonlinear Auto-Regressive Series355

7.1.3 Statistical Estimation356

7.2 More Nonlinear Models:ARCH,GARCH ＆ All That358

7.2.1 Motivation358

7.2.2 ARCH Models359

7.2.3 GARCH Models361

7.2.4 S-Plus Commands362

7.2.5 Fitting a GARCH Model to Real Data363

7.2.6 Generalizations371

7.3 Stochastic Volatility Models373

7.4 Discretization of Stochastic Differential Equations378

7.4.1 Discretization Schemes379

7.4.2 Monte Carlo Simulations:A First Example381

7.5 Random Simulation and Scenario Generation383

7.5.1 A Simple Model for the S＆P 500 Index383

7.5.2 Modeling the Short Interest Rate386

7.5.3 Modeling the Spread388

7.5.4 Putting Everything Together389

7.6 Filtering of Nonlinear Systems391

7.6.1 Hidden Markov Models391

7.6.2 General Filtering Approach392

7.6.3 Particle Filter Approximations393

7.6.4 Filtering in Finance?Statistical Issues396

7.6.5 Application:Tracking Volatility397

Appendix:Preparing Index Data403

Problems404

Notes ＆ Complements408

APPENDIX:AN INTRODUCTION TO S AND S-Plus411

References429

Notation Index433

Data Set Index435

S-Plus Index437

Author Index441

Subject Index445