"金融统计与数据分析：R语言实例指南（第二版）-736页PDF电子书"

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The electronic book "Statistics and Data Analysis for Financial Engineering with R examples" by David Ruppert and David S. Matteson is a comprehensive guide to statistical analysis in the field of finance. With a total of 736 pages, this second edition covers a wide range of topics including time series analysis, regression modeling, risk management, and portfolio optimization. The book is designed for both students and professionals in the field of financial engineering. It provides practical examples and exercises using the R statistical software, making it an invaluable resource for those looking to apply statistical techniques to real-world financial problems. David Ruppert, a professor at Cornell University, and David S. Matteson have extensive experience in the field of statistics and financial engineering. Their expertise is evident throughout the book, as they provide clear explanations of complex concepts and demonstrate how to apply statistical methods to financial data. Overall, "Statistics and Data Analysis for Financial Engineering with R examples" is a thorough and informative resource for anyone looking to enhance their statistical analysis skills in the context of finance. Whether you are a student studying financial engineering or a professional working in the field, this book is sure to provide valuable insights and practical tools for success.

Contents xv

8.9 R Lab ..................................................208

8.9.1 Simulating from Copula Models ....................208

8.9.2 Fitting Copula Models to Bivariate Return Data .....210

8.10 Exercises ...............................................213

References ...................................................214

9 Regression: Basics ..........................................217

9.1 Introduction ............................................217

9.2 Straight-Line Regression .................................218

9.2.1 Least-Squares Estimation ..........................218

9.2.2 Variance of



....................................222

9.3 Multiple Linear Regression ...............................223

9.3.1 Standard Errors, t-Values, and p-Values .............225

9.4 Analysis of Variance, Sums of Squares, and R

..............227

9.4.1 ANOVA Table ...................................227

9.4.2 Degrees of Freedom (DF) ..........................229

9.4.3 Mean Sums of Squares (MS) and F -Tests ............229

9.4.4 Adjusted R

.....................................231

9.5 Model Selection .........................................231

9.6 Collinearity and Variance Inﬂation ........................233

9.7 Partial Residual Plots ....................................240

9.8 Centering the Predictors .................................242

9.9 Orthogonal Polynomials ..................................243

9.10 Bibliographic Notes ......................................243

9.11 R Lab ..................................................243

9.11.1 U.S. Macroeconomic Variables .....................243

9.12 Exercises ...............................................245

References ...................................................248

10 Regression: Troubleshooting ................................249

10.1 Regression Diagnostics ...................................249

10.1.1 Leverages ........................................251

10.1.2 Residuals ........................................252

10.1.3 Cook’s Distance ..................................253

10.2 Checking Model Assumptions .............................255

10.2.1 Nonnormality ....................................256

10.2.2 Nonconstant Variance .............................258

10.2.3 Nonlinearity .....................................259

10.3 Bibliographic Notes ......................................262

10.4 R Lab ..................................................263

10.4.1 Current Population Survey Data ...................263

10.5 Exercises ...............................................265

References ...................................................268

xvi Contents

11 Regression: Advanced Topics ...............................269

11.1 The Theory Behind Linear Regression .....................269

11.1.1 Maximum Likelihood Estimation for Regression ......270

11.2 Nonlinear Regression ....................................271

11.3 Estimating Forward Rates from Zero-Coupon Bond Prices ....276

11.4 Transform-Both-Sides Regression ..........................281

11.4.1 How TBS Works .................................283

11.5 Transforming Only the Response ..........................284

11.6 Binary Regression .......................................286

11.7 Linearizing a Nonlinear Model ............................291

11.8 Robust Regression .......................................293

11.9 Regression and Best Linear Prediction .....................295

11.9.1 Best Linear Prediction ............................295

11.9.2 Prediction Error in Best Linear Prediction ...........297

11.9.3 Regression Is Empirical Best Linear Prediction .......298

11.9.4 Multivariate Linear Prediction .....................298

11.10 Regression Hedging ......................................298

11.11 Bibliographic Notes ......................................300

11.12 R Lab ..................................................300

11.12.1 Nonlinear Regression ..............................300

11.12.2 Response Transformations .........................302

11.12.3 Binary Regression: Who Owns an Air Conditioner? . . . 303

11.13 Exercises ...............................................304

References ...................................................305

12 Time Series Models: Basics .................................307

12.1 Time Series Data ........................................307

12.2 Stationary Processes .....................................307

12.2.1 White Noise .....................................310

12.2.2 Predicting White Noise ............................311

12.3 Estimating Parameters of a Stationary Process ..............312

12.3.1 ACF Plots and the Ljung–Box Test .................312

12.4 AR(1) Processes ........................................314

12.4.1 Properties of a Stationary AR(1) Process ............315

12.4.2 Convergence to the Stationary Distribution ..........316

12.4.3 Nonstationary AR(1) Processes .....................317

12.5 Estimation of AR(1) Processes ............................318

12.5.1 Residuals and Model Checking .....................318

12.5.2 Maximum Likelihood and Conditional Least-Squares . . 323

12.6 AR(p)Models ..........................................325

12.7 Moving Average (MA) Processes ..........................328

12.7.1 MA(1) Processes .................................328

12.7.2 General MA Processes ............................330

12.8 ARMA Processes ........................................331

12.8.1 The Backwards Operator ..........................331

Contents xvii

12.8.2 The ARMA Model ................................332

12.8.3 ARMA(1,1) Processes .............................332

12.8.4 Estimation of ARMA Parameters ...................333

12.8.5 The Diﬀerencing Operator .........................333

12.9 ARIMA Processes .......................................334

12.9.1 Drifts in ARIMA Processes ........................337

12.10 Unit Root Tests .........................................338

12.10.1 How Do Unit Root Tests Work? ....................341

12.11 Automatic Selection of an ARIMA Model ..................342

12.12 Forecasting .............................................342

12.12.1 Forecast Errors and Prediction Intervals .............344

12.12.2 Computing Forecast Limits by Simulation ...........346

12.13 Partial Autocorrelation Coeﬃcients ........................349

12.14 Bibliographic Notes ......................................352

12.15 R Lab ..................................................352

12.15.1 T-bill Rates ......................................352

12.15.2 Forecasting ......................................355

12.16 Exercises ...............................................356

References ...................................................360

13 Time Series Models: Further Topics ........................361

13.1 Seasonal ARIMA Models .................................361

13.1.1 Seasonal and Nonseasonal Diﬀerencing ..............362

13.1.2 Multiplicative ARIMA Models .....................362

13.2 Box–Cox Transformation for Time Series ...................365

13.3 Time Series and Regression ...............................367

13.3.1 Residual Correlation and Spurious Regressions .......368

13.3.2 Heteroscedasticity and Autocorrelation Consistent

(HAC) Standard Errors ...........................373

13.3.3 Linear Regression with ARMA Errors ...............377

13.4 Multivariate Time Series .................................380

13.4.1 The Cross-Correlation Function ....................380

13.4.2 Multivariate White Noise ..........................382

13.4.3 Multivariate ACF Plots and the Multivariate

Ljung-Box Test...................................383

13.4.4 Multivariate ARMA Processes .....................384

13.4.5 Prediction Using Multivariate AR Models ...........387

13.5 Long-Memory Processes ..................................389

13.5.1 The Need for Long-Memory Stationary Models .......389

13.5.2 Fractional Diﬀerencing ............................390

13.5.3 FARIMA Processes ...............................391

13.6 Bootstrapping Time Series................................394

13.7 Bibliographic Notes ......................................395

13.8 R Lab ..................................................395

13.8.1 Seasonal ARIMA Models ..........................395

13.8.2 Regression with HAC Standard Errors ..............396

xviii Contents

13.8.3 Regression with ARMA Noise ......................397

13.8.4 VAR Models .....................................397

13.8.5 Long-Memory Processes ...........................399

13.8.6 Model-Based Bootstrapping of an ARIMA Process . . . . 400

13.9 Exercises ...............................................401

References ...................................................403

14 GARCH Models ............................................405

14.1 Introduction ............................................405

14.2 Estimating Conditional Means and Variances ...............406

14.3 ARCH(1) Processes ......................................407

14.4 The AR(1)+ARCH(1) Model .............................409

14.5 ARCH(p)Models........................................411

14.6 ARIMA(p

,d,q

)+GARCH(p

)Models...............411

14.6.1 Residuals for ARIMA(p

,d,q

)+GARCH(p

)

Models ..........................................412

14.7 GARCH Processes Have Heavy Tails .......................413

14.8 Fitting ARMA+GARCH Models ..........................413

14.9 GARCH Models as ARMA Models ........................418

14.10 GARCH(1,1) Processes ..................................419

14.11 APARCH Models .......................................421

14.12 Linear Regression with ARMA+GARCH Errors .............424

14.13 Forecasting ARMA+GARCH Processes ....................426

14.14 Multivariate GARCH Processes ...........................428

14.14.1 Multivariate Conditional Heteroscedasticity ..........428

14.14.2 Basic Setting.....................................431

14.14.3 Exponentially Weighted Moving Average (EWMA)

Model ...........................................432

14.14.4 Orthogonal GARCH Models .......................433

14.14.5 Dynamic Orthogonal Component (DOC) Models .....436

14.14.6 Dynamic Conditional Correlation (DCC) Models .....439

14.14.7 Model Checking ..................................441

14.15 Bibliographic Notes ......................................443

14.16 R Lab ..................................................443

14.16.1 Fitting GARCH Models ...........................443

14.16.2 The GARCH-in-Mean (GARCH-M) Model ..........445

14.16.3 Fitting Multivariate GARCH Models ................445

14.17 Exercises ...............................................447

References ...................................................451

15 Cointegration...............................................453

15.1 Introduction ............................................453

15.2 Vector Error Correction Models ...........................455

15.3 Trading Strategies .......................................459

15.4 Bibliographic Notes ......................................460

Contents xix

15.5 R Lab ..................................................460

15.5.1 Cointegration Analysis of Midcap Prices .............460

15.5.2 Cointegration Analysis of Yields ....................460

15.5.3 Cointegration Analysis of Daily Stock Prices .........461

15.5.4 Simulation .......................................462

15.6 Exercises ...............................................462

References ...................................................463

16 Portfolio Selection ..........................................465

16.1 Trading Oﬀ Expected Return and Risk .....................465

16.2 One Risky Asset and One Risk-Free Asset ..................465

16.2.1 Estimating E(R)andσ

..........................467

16.3 Two Risky Assets .......................................468

16.3.1 Risk Versus Expected Return ......................468

16.4 Combining Two Risky Assets with a Risk-Free Asset .........469

16.4.1 Tangency Portfolio with Two Risky Assets ...........469

16.4.2 Combining the Tangency Portfolio with the Risk-Free

Asset ...........................................471

16.4.3 Eﬀect of ρ

.....................................472

16.5 Selling Short ............................................473

16.6 Risk-Eﬃcient Portfolios with N Risky Assets ...............474

16.7 Resampling and Eﬃcient Portfolios ........................479

16.8 Utility .................................................484

16.9 Bibliographic Notes ......................................488

16.10 R Lab ..................................................488

16.10.1 Eﬃcient Equity Portfolios .........................488

16.10.2 Eﬃcient Portfolios with Apple, Exxon-Mobil, Target,

and McDonald’s Stock ............................489

16.10.3 Finding the Set of Possible Expected Returns ........490

16.11 Exercises ...............................................491

References ...................................................493

17 The Capital Asset Pricing Model ...........................495

17.1 Introduction to the CAPM ...............................495

17.2 The Capital Market Line (CML) ..........................496

17.3 Betas and the Security Market Line .......................499

17.3.1 Examples of Betas ................................500

17.3.2 Comparison of the CML with the SML ..............500

17.4 The Security Characteristic Line ..........................501

17.4.1 Reducing Unique Risk by Diversiﬁcation .............503

17.4.2 Are the Assumptions Sensible? .....................504

17.5 Some More Portfolio Theory ..............................504

17.5.1 Contributions to the Market Portfolio’s Risk .........505

17.5.2 Derivation of the SML ............................505

17.6 Estimation of Beta and Testing the CAPM .................507

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